THE 
 
 MECHANICS OF PUMPING MACHINERY 
 
THE MECHANICS 
 
 OF 
 
 PUMPING MACHINEEY 
 
 A TEXT-BOOK FOR TECHNICAL SCHOOLS AND A GUIDE 
 FOR PRACTICAL ENGINEERS 
 
 BY 
 DK. JULIUS WEISBACH 
 
 M 
 AND 
 
 PEOFESSOK GUSTAV HERRMANN 
 
 AUTHORISED TRANSLATION FROM THE SECOND GERMAN EDITION 
 
 BY 
 
 KARL P. DAHLSTROM, M.E., 
 
 LATE INSTRUCTOR OF MECHANICAL ENGINEERING AT THE LEHIGH UNIVERSITY 
 
 WITH 197 ILLUSTRATIONS 
 
 ILonlion 
 MACMILLAN AND CO., LIMITED 
 
 NEW YORK : THE MACMJLLAN COMPANY 
 1897 
 
 All rights reserved 
 
TEANSLATOB'S PEEFACE 
 
 THE volume herewith presented might be introduced in the 
 same words as its recent predecessor on The Mechanics of 
 Hoisting Machinery. It is a translation of a portion of 
 Professor Herrmann's revised edition of Weisbach's work on 
 Engineering Mechanics, which has not before appeared in 
 English. Moreover, it is destined mainly to serve as a text- 
 book for the advanced courses in the Mechanics of Machinery, 
 though it may also prove of value to the practical engineer. 
 
 Eesponding to the suggestion made by some critics of 
 the volume on Hoisting Machinery, the translator has under- 
 taken to supplement the text by a few remarks and refer- 
 ences respecting some developments in pumping practice since 
 the German original was published, and a few new illustra- 
 tions of modern types of pumps have been inserted. 
 
 Eeferences in the text to previous volumes of Weisbach's 
 Mechanics allude to the English translations unless otherwise 
 specified. 
 
 In editing the work, the translator has been greatly aided 
 by having had recourse to notes previously prepared by 
 Professor J. F. Klein of the Lehigh University. 
 
 August 1896. 
 
PROPERTY I 
 
 CONTENTS 
 
 PAGE 
 
 INTRODUCTION 1 
 
 CHAPTER I 
 
 EARLY FORMS OF WATER ELEVATORS . 
 
 CHAPTEE II 
 
 ELEMENTARY ACTION OF RECIPROCATING PUMPS ..... 46 
 
 CHAPTER III 
 
 THEORY OF RECIPROCATING PUMPS ....... 80 
 
 CHAPTER IV 
 
 TYPES OF RECIPROCATING PUMPS ........ 134 
 
 CHAPTER V 
 
 ROTARY PUMPS ........... 234 
 
 * CHAPTER VI 
 
 ADDITIONAL WATER-RAISING MACHINES . . . . . . .255 
 
INTRODUCTION 
 
 1. THE simplest, or at least the oldest, method of raising 
 liquids consisted in hailing, the liquid being elevated, together 
 with the vessels containing it, either by hand or by special 
 machines driven by prime movers. Various machines have 
 been devised for raising water in this manner, most of them 
 being known to the ancients, and almost exclusively employed 
 by them. 
 
 For very small lifts another method has been long in use, 
 namely, to throw up the water either by shovels operated by 
 hand or by the use of so-called flash-wheels. Both of the 
 above methods of raising water have found their principal 
 application in draining excavations or low lands, as well as for 
 irrigation and procuring 'water for agricultural or building 
 purposes. 
 
 As they permit of moderate lifts only, another plan was 
 introduced at a later date, when it became necessary to over- 
 come greater elevations. This consisted in subjecting the 
 water in a vessel to a pressure sufficient to balance a 
 column of water of a height exceeding the required lift. As 
 a consequence the water is forced from, the vessel upward 
 through a delivery pipe and discharged at the orifice of the 
 pipe. This principle is embodied in all water-raising machines 
 known as pumps, their action differing only in the manner of 
 exerting the pressure on the water. In ordinary piston-pumps, 
 which are by far the most widely used machines for elevating 
 water, the pressure is produced by a piston fitting closely in a 
 cylindrical tube. This piston is acted upon in the direction of 
 its axis by a force sufficient to move it, thereby effecting the 
 lifting operation. 
 
 B 
 
2 MECHANICS OF PUMPING MACHINERY 
 
 With these machines should also be classed the rotary 
 pumps, in which the vessel has the form of one or more solids 
 of revolution, and the piston or pistons consist of vanes or 
 wheels attached to a revolving shaft, since in all constructions 
 of this nature the space occupied by the water may be alter- 
 nately increased and diminished by the motion of the pistons, 
 the vessel being thus alternately filled and emptied. 
 
 It is only in special cases that the direct pressure of com- 
 pressed air or steam on the surface of the liquid has been 
 employed for raising the latter. Compressed air, for instance, 
 was used in HoeWs water-raising machine, which is now of 
 only historical interest, and, as is well known, the direct 
 pressure of steam was tried by Papin, and has been largely 
 introduced in sugar refineries for forcing the sugar juice 
 upward. More recently this method has been applied in a 
 water-raising contrivance known as the pulsometer. On the 
 whole it may be said, however, that the employment of direct 
 pressure of steam or compressed air for raising water is very 
 limited. 
 
 On the other hand, extensive use has of late been made of 
 the living force of the water itself as a means of overcoming 
 the opposing resistance, the water being given the velocity 
 required for this purpose. The contrivances based on this 
 principle differ essentially in the manner in which the living 
 force is communicated to the water. This is accomplished 
 either by rapidly rotating vanes, as in centrifugal pumps ; or by 
 means of a steam jet, as in Gifford's injector ; or by a jet of 
 water, as in Thompson's pump and other related constructions. 
 
 The pressure which forces the water upward is, of course, 
 to be understood to be the excess of pressure acting on the 
 water in the pump chamber above that of the atmosphere, as 
 the latter acts at the orifice of the efflux, and its resisting 
 influence must be overcome before the water can be raised. It 
 is also possible to produce the difference of pressure necessary 
 to move the water by removing the atmospheric pressure 
 originally existing in the pump chamber by any of the above- 
 mentioned methods. The external atmospheric pressure will 
 then act on the free surface of the water to be lifted, and 
 cause the latter to rise to a height corresponding to the 
 vacuum created, the maximum height being equal to that of 
 
INTRODUCTION 3 
 
 the water barometer (10'336 m. [33'9 ft.]). This action is 
 known as suction, and is usually found to exist in pumps, but 
 never occurs in the scoop and flash apparatus, and therefore 
 the existence of suction, or the possibility of it, is occasionally 
 regarded as the characteristic feature of a pump, although 
 there are pumps, of course, in the operation of which no suction 
 is exerted. 
 
CHAPTEE I 
 
 EARLY FORMS OF WATER ELEVATORS 
 
 2. Bailing. The simplest means of bailing water consists in 
 the employment of pails or buckets having a cubic contents of 
 about 10 litres [0*35 cub. ft.] In this manner one man may 
 lift the water to a height of 1 to 1-2 m. [3'28 to 3'94 ft.], and 
 when it is necessary to lift it to a greater elevation, two or 
 more men must be located one above the other, and the buckets 
 be allowed to pass from man to man. It is estimated that 
 one man can bail out fifteen buckets full per minute, and each 
 time lift it to a height of 1 m. [3 '2 8 ft.] This is equivalent 
 to an effect of 150 metre kilograms per minute [1085 ft. 
 Ibs.], and for an actual working time of 6 hours per day, the 
 day's work per man will therefore be only 6x60x150 = 
 54,000 m. kg. [390,590 ft. Ibs.], that is, equal to the work done 
 by one horse-power in 12 minutes. 
 
 If it is desired to raise the water higher by one man alone, 
 the bucket may be provided with a handle about 2 m. 
 [6*56 ft.] in length, which can serve as a lever. In this case 
 the buckets must evidently be smaller or may be only partly 
 filled. The daily performance in bailing water with a bucket 
 provided with a handle does not materially differ from the 
 results obtained with an ordinary bucket. It may be employed 
 to advantage when the labourer is located above, and not below, 
 the surface of the water, as he would otherwise be obliged to 
 bend over a great deal and have to raise a portion of his body 
 as well. 
 
 When it is required to raise water to greater heights, say 
 4 or 6 m. [13 to 20 ft.], from wells, for instance, the bucket 
 is suspended from a sweep or lever ACG with a counter- weight, 
 
CHAP. I 
 
 EARLY FORMS OF WATER ELEVATORS 
 
 as in Fig. 1. If the bucket, when half full, is balanced by 
 the counter-weight G, it will require the same effort to hoist 
 the full bucket as to lower it empty. The chord AB of the 
 arc described by the point of suspension A of the bucket E 
 should be at least equal to the depth of the well, in order that 
 the bucket may be sufficiently immersed into the water W. It 
 
 Fig. 1. 
 
 is also necessary to make the width of the well at least equal 
 to that of the bucket plus the height FH of the arc, in order to 
 have the bucket clear the walls of the well. 
 
 Water may be drawn from still greater depth by the use of 
 buckets or tubs if a simple guide pulley or a drum be employed ; for 
 instance, an ordinary winch or a whin with a bucket or tub secured 
 to each end of the hoisting rope. The two receptacles will then 
 balance each other, and therefore the driving effort will equal the 
 weight of the water in the ascending bucket. 
 
 At mines water is sometimes raised in barrels by means of a 
 vertical drum or a whin. The barrels are then filled through a 
 valve in their bottom opening inward when the water is reached. 
 
6 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 At the top of the shaft the discharging is done either by overturning 
 the barrel or by pulling open the valve. 
 
 3. Raising Water by Throwing. Like other heavy 
 bodies water may be thrown or flung to a moderate height. 
 The simplest implement used for this purpose is a shovel or 
 scoop, which may be employed either as an ordinary hand- 
 shovel or may be swung around 
 a fixed point. In the former case 
 it consists of a large wooden ladle 
 with a handle about 1 or 1'5 m. 
 [3 to 5 ft.] in length, and is made 
 use of when it is desired to remove 
 the water entirely from a space, as 
 from a boat, for instance. The 
 swinging or Dutch scoop (AB, Fig. 2) 
 
 is made of boards or sheet-iron, and is provided with a handle 
 BC, 3 to 4 m. [10 to 13 ft.] in length; it is suspended by a 
 rope D from a horse or a tripod. The scoop proper has a 
 length of 0-5 to 0'6 m. [ll to 2 ft.], a width of 0'3 m. [1 ft.]., 
 and a depth of 0*2 m. [8 ins.] The operator, in pushing the 
 scoop away from him by the handle, dips out about 15 litres 
 [|- cub. ft.] of water, and sends it about 1 m. [3^- ft.] high 
 and 2 m. [6-J- ft.] horizontally. Usually two helpers are placed 
 opposite the first workman, and assist in swinging the scoop 
 by pulling in ropes. One man cannot accomplish materially 
 better results by the use of the scoop than by bailing with a 
 bucket. When three men are engaged in the work they can 
 give the scoop 28 oscillations per minute, each time throwing 
 25 litres [0*9 cub. ft.] of water 1-1 m. [3'6 ft.] high. The 
 work done per minute will then be 25 x 28 x I'l = 770 m. kg. 
 [5580 ft. Ibs.], and consequently the daily performance, with 
 an actual working day of 6 hours, 
 
 770 x 60 x 6 = 277,200 m. kg. [2,006,200 ft. Ibs.], 
 
 so that the work done by each workman can be placed at 
 92,400 m. kg. [661,120 ft. Ibs.] 
 
 The throwing operation may be performed by the aid of 
 machines, such as the water-balance, shown in Fig. 3, and the 
 flash-wheels. 
 
EARLY FORMS OF WATER ELEVATORS 
 
 The former consists of a swinging scoop CD attached to a 
 balance beam ACB and moving in a channel or chase EF of 
 circular profile. Four or six labourers give the beam an 
 oscillating motion by pulling in ropes L, as in an ordinary 
 ringing pile-driver, 10 or 12 oscillations being made per 
 
 Fig. 3. 
 
 minute and 2'2 to 2'6 cub. m. [78 to 92 cub. ft.] of water 
 being in this time raised to a height of 1'2 in. [4 ft.] In 
 order to facilitate the return of the scoop D through the water, 
 flap- valves K r K 2 , K 3 (Fig. 4) are introduced, having a length 
 of 0-5 m. [1-64 ft.] and a width 
 of 0-2 m. [-66 ft.], and being sur- 
 rounded by an iron frame secured 
 to the end of the arm CD ; in this 
 frame the bearings for the gudgeons 
 of the valves are located. 
 
 4. Flash- Wheels. These are 
 of the form of ordinary water- 
 wheels running in a chase, only turn- 
 ing in the opposite direction, so that 
 the floats or paddles ascend in the 
 curved waterway and carry the water along to the desired level. 
 In order that as little water as possible may flow back in the 
 clearance space between the paddles and the chase, it is 
 necessary to rotate the wheel at a great velocity so as to fling 
 the water rather than lift it. When the prime mover is a 
 water-wheel, the flash-wheel is therefore not attached directly 
 to the water-wheel shaft but driven by means of a large gear 
 
 Fig. 4. 
 
MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 on the latter engaging a smaller one on the flash -wheel 
 shaft. 
 
 In Holland flash- wheels are commonly used for draining 
 low lands, the rotary motion being obtained from ordinary 
 windmills. A side elevation of a wheel of this kind is shown 
 in Fig 5. This wheel is 5 m. [16*4 ft.] in diameter, and 
 has 28 floats or paddles 0'3 to 0'5 m. [1 to 1-6 ft.] in 
 length and 0'15 to 0'24 m. [6 to 9 ins.] in width. The 
 clearance between the paddles and the chase is 25 mm. [1 in.], 
 both at the sides and at the bottom, and the water is raised 
 from 1 to 1-2 m. [3j to 4 ft.] The four spokes A, B, C, D 
 
 Fig. 5. 
 
 embrace the square shaft E, and their outer ends form four of 
 the paddles ; the spokes are not only tenoned into each other 
 but also tied together by two sets of braces and two rims, 
 which also serve as means of securing the other paddles. On 
 the shaft of the flash-wheel is a large bevel-gear which meshes 
 with a smaller bevel on the upright shaft of the windmill, 
 the latter making twice the number of revolutions of the 
 flash-wheel. A gate G- is placed at the beginning of the 
 channel F, which serves as a conduit for the raised water, and 
 is kept open by the action of the water flung against it ; when 
 the wind fails to turn the wheel or only revolves it slowly, the 
 gate closes automatically. 
 
i EARLY FORMS OF WATER ELEVATORS 9 
 
 Another flash -wheel, which raises water from the river 
 Seine into the basin that forms a harbour at St. Quen near 
 Paris, is shown in Fig. 6, in ^-J^ of its natural size. It 
 is operated by a steam-engine, and lifts about 1 cub. m. 
 [35 cub. ft.] of water per second in a chase built of stone 
 and having a height of 4 m. [13 ft.] The driving is accom- 
 plished by means of a small pinion C on the engine -shaft 
 
 Fig. 6. 
 
 engaging a large internal gear attached to the rim BB of the 
 flash- wheel A, which makes three revolutions per minute while 
 the engine makes eighteen. A circular sluice-board surrounds 
 the wheel on the side of the lower water-level, and when 
 raised or lowered by means of a gear segment, serves to 
 regulate the quantity of water lifted. 
 
 5. Scoop -Wheels differ from flash- wheels in that they 
 raise the water in receptacles or buckets, while the flash- 
 
10 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 wheels simply make use of paddles, 
 between 
 
 We can distinguish 
 
 (1) Scoop-wheels with movable receptacles, 
 
 (2) Scoop- wheels with fixed receptacles, 
 
 (3) Scoop-wheels with buckets, and 
 
 (4) Scoop-wheels with spiral ducts. 
 
 A simple scoop-wheel with movable receptacles, as described 
 by Belidor, is shown in Fig. 7. The vessels E, Ej are sus- 
 pended from iron rods 
 A, secured to the side 
 of the rim or between 
 two rims of the wheel. 
 As a rule, the water- 
 wheel which gives 
 motion to the appara- 
 tus is attached directly 
 to the shaft C of the 
 scoop -wheel. When 
 the latter revolves 
 there are always a 
 few of the receptacles 
 immersed in the water 
 HR, and, after being 
 filled, these ascend on 
 
 one side, discharging their contents at the top into a trough 
 T, after striking against the edge of the trough by means of a 
 lifter cam or projection B. 
 
 The scoop -wheels with fixed receptacles are of various 
 forms. 
 
 In Fig. 8 the so-called Chinese scoop -wheel is illustrated. 
 The water is here lifted in pails E, E (in China made of 
 bamboo) secured in inclined positions in the circumference of 
 the wheel. Motion is imparted to the wheel by the current 
 of the water HE acting on the floats A, which are firmly 
 secured to the rim. Also here the water is discharged into 
 a trough located at the upper end, and evidently a portion of 
 the total lift is thereby lost. Wheels of this kind are still in 
 use in Europe. A peculiarity of the arrangement as found in 
 Tyrol consists in mounting the wheel in a framework provided 
 

 
 i EARLY FORMS OF WATER -ELE^ 
 
 1 "^rLti 
 
 with a counter-weight, thus enabling the wheel to be adjusted^ 
 
 at different heights, according to the variationskof the water-level. v ' 
 
 The so-called Prankish scoop -wheel, as employed on the 
 river Eednitz at Erlangen, is shown in Fig 9. It consists of 
 
 Fig. 9. 
 
 a wheel ACB hanging freely in the river and provided with 
 tapering vessels E, E X . . . secured to the shroudings in such a 
 
12 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 manner that their axes are parallel to the chords of the 
 segments covered. During the motion of the wheel the vessels 
 are filled to the greater portion with water at HE and dis- 
 charge the latter into the conduit T closely beneath the crown 
 A of the wheel. In order to obtain the maximum effect, the 
 wheel is placed in the water at such a depth that the inclina- 
 tion to the horizon of the axis of the vessel E, when the latter 
 emerges from the water HE (Fig. 9), is equal to the inclination 
 of the axis of the vessel E 2 at the point where discharge 
 commences. 
 
 In other constructions of scoop-wheels the receptacles are 
 made of box shape, being put together of boards and located 
 either in inclined position as in Fig. 8, or tangentially as in 
 Fig. 9. As a rule the boxes are then enclosed on all sides, 
 having only an opening at one side for taking in and pouring 
 out the water. This is made clear from Fig. 10, where, as in 
 Fig. 9, E is being filled, Ej_ is ascending, 
 and E 2 is discharging the water contained. 
 The well-known bucket-wheels may also 
 serve as scoop -wheels when revolved in 
 the opposite direction to what is the case 
 when they are used as prime movers. A 
 scoop-wheel of this type, which was con- 
 structed by Laurenz and Thomas for the 
 irrigation of meadows at Soissons, 1 is illus- 
 trated in y^-Q of its natural size in Figs. 
 11 and 12. As the wheel revolves, the 
 buckets immersed are filled with water 
 through the outside circumference, and, 
 after lifting it to a certain height, they 
 discharge it through openings in the sole of the wheel into the 
 conduits BD and CE which embrace the latter. The three 
 sets of arms F, together with the rims which are inserted 
 between them and serve to connect the "buckets rigidly with 
 the shaft, are confined to the central portion of the wheel in 
 order to leave a clear space for the heads BB and CO of the 
 water conduits (Fig. 12). A breast- wheel located somewhat 
 lower down gives motion to the bucket-wheel from the shaft 
 G through the gears HK. 
 
 1 See Bulletin de la Soctite cl' encouragement, 1848 ; also Der Ingenieur, vol. ii. 
 
 Fig. 10. 
 
EARLY FORMS OF WATER E 
 
 Fig. 1 3 represents a vertical section of a 
 may be seen at Eanstedt in the district of 
 
 Fig. 11. Fig. 12. 
 
 -^j. The left half AAA of the cut shows an ordinary breast- 
 wheel, and the right half BBB the scoop-wheel which is attached 
 
 Fig. 13. 
 
 directly to the former. The outside circumference of the scoop- 
 wheel is entirely closed, and the buckets are formed by inclined 
 
14 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 partitions. Water is admitted to the buckets at E from a side- 
 channel, and the discharge takes place at F. 
 
 The drum-wheel or tympanum, according to Vitrumus, con- 
 sisted of a hollow drum AB, Fig. 14, with a hollow shaft C, 
 and divided by radial partitions into sector-shaped compart- 
 ments. Each compartment had 
 an opening a at the circumference 
 for the reception of the water, and 
 was also placed in connection with 
 
 IB the interior of the hollow shaft 
 
 HI HaRlSS through an orifice b at the side of 
 
 the latter. When now the wheel, 
 which was partly submerged, was 
 set in motion, each section carried 
 up a small quantity of water to 
 the level of the axis of the wheel 
 
 and discharged it into the hollow shaft, from where it was con- 
 ducted through other side-outlets into reservoirs. 
 
 The spiral-wheels do not differ in principle from the drum- 
 wheels, as they also admit the water through openings in the 
 periphery and deliver it through the hollow shaft, only the 
 radial partitions are replaced by spiral ducts. In De La/aye's 
 wheel, pipes wound in the shape of spirals are made use of for 
 conducting the water from the circumference to the interior 
 of the shaft, whereas Perronet's wheel is provided with spiral- 
 shaped partitions, the sides being plane surfaces. 
 
 In Figs. 15 and 16 a spiral tympanum ACB, designed by 
 Cave, is illustrated in -3-^-5- of its natural size. It is made 
 entirely of iron, the shaft CC and the two sets of arms D-f) 
 being of cast-iron, and the spiral partitions, which are given 
 the shape of an involute of a circle, as well as the sides, are 
 made of iron plate 3 mm. [-J- in.] in thickness. Motion is 
 transmitted to the wheel from the shaft w through the gears 
 K and L, and during the slow rotation the elevated water 
 flows away at both sides through the passages contained 
 between the arms and the funnel-shaped rim which surrounds 
 them. 
 
 Such spirally wound partitions are often arranged in the interior 
 of the steam-heated drying-cylinder of finishing machines for the 
 
EARLY FORMS OF WATER ELEVATORS 
 
 purpose of raising the condensed water from the bottom of the 
 cylinder to the level of its axis, from where it is afterwards removed 
 through the hollow gudgeons. 
 
 6. Mechanical Effect of Scoop-Wheels. The effect of 
 scoop -wheels may be calculated simply as follows. Let V 
 deiiote the quantity of water contained in each bucket or 
 receptacle, n the number of receptacles in the circumference 
 of the wheel, u the number of revolutions of the latter per 
 minute, and li the vertical distance through which the water 
 
 Fig. 15. 
 
 is to be lifted. We then obtain as the quantity of water 
 raised per second 
 
 . . . . ax 
 
 and consequently the work required per second will be 
 
 L = Qh = VA (2) 
 
 60 
 
 where 7 is the weight of water per unit of volume. 
 
 Evidently both formulae are also applicable to the flash- 
 wheels, if n denotes the number of paddles and V the water 
 raised by each paddle. 
 
 Owing to the wasteful resistances, however, it is necessary 
 
16 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 to increase the value of L, both for flash- and scoop-wheels 
 by a considerable amount. 
 
 The velocity of the elevated water at the point of discharge 
 being equal to the velocity v of the scoop-wheel, it is evident 
 
 v 2 
 that an additional amount of work equal to ^-Qy has been 
 
 ~*y 
 
 absorbed in overcoming the inertia of the water, and besides, 
 in order that the latter may be discharged conveniently, it is 
 necessary to lift it to a certain height \ above the upper 
 water level, which requires the further expenditure of an 
 amount of work = Qhfl. Thus, if we take these two sources 
 of loss into account, the total amount of work required for 
 turning the scoop- wheel will be 
 
 (3). 
 
 In order to compute, by the aid of this formula, the power 
 necessary for driving a scoop-wheel, we must determine in the first 
 place the volume of water contained in each bucket or vessel. This 
 is done for each particular case from the drawing or by calculation. 
 
 Fig. 17. 
 
 In the case of a scoop- wheel with conical vessels, Fig. 17, for 
 instance, this volume is equal to the difference between a cone 
 FGS with circular base FG and a cone KLS with elliptical base. 
 
i EARLY FORMS OF WATER ELEVATORS 17 
 
 Denoting the height SM by s, and half the angle at the apex FSM 
 = GSM by a, then the volume of the first cone will be 
 
 Vj = ^Trs 3 tan 2 a. 
 
 If the base KL of the second cone intersects the axis SM at an 
 angle SNK = /?, and at a distance SN = s x from the apex S, the 
 longer axis of the base will be 
 
 2ft = KL = KN + NL = ^-fL. + - * sin a 
 sin (ft + a) sin (/3-a) 
 
 3! sin 2a sin ft 
 ~~ sin (ft + o) sin (ft -a) ' 
 and the shorter axis 
 
 2b=2s 1 tan a. 
 
 Since the height of this cone is SR = s 1 sin /3, its volume will be 
 
 y^ygfr*! si - n = *V8 sin 2 asin 2 ft j^V 
 
 3 3 sin 03 + a) sin (ft -a) cot* a - cot* ft ' 
 
 The volume contained in each vessel will now be given by 
 
 In the tympanum with spiral partitions the vertical section of 
 the body of water in each compartment is a segment, and its 
 volume will therefore be approximately expressed by 
 
 when a, b, and I respectively denote the height, width, and length 
 of the mass of water contained. 
 
 EXAMPLE. A scoop-wheel has twelve conical receptacles of the 
 following dimensions : radius at the bottom r = 0*16 m. [0*52 ft.], 
 radius at the top r 1 = 0'08 m. [0'26 ft.], height of receptacle a = 
 0*64 m. [2'1 ft.] ; the inclination of the axis of the vessel when the 
 latter emerges from the water is fi = 25 degrees. How much water 
 does the scoop-wheel deliver per minute, and how much power does 
 it absorb, when running at u = 5 revolutions per minute and 
 raising the water to a height of 4 m. [13*12 ft.] 1 
 
 For the angle 2 a at the apex of the cone we have 
 
 a 0-64 
 
 further, the total height of the cone (Fig. 17) is 
 
 MS=s = r cot a = 0-16x8 = l-28 m. [4 -2 ft.], 
 and the length of the axis NS of the supplementary cone is 
 
 s 1 = ri (cot a + cotft) = 0'08x 10-1445 = 0-812 m. [2-666 ft] 
 C 
 
18 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 Consequently we have for the volume of the whole cone 
 
 V 1 =^7rr 2 s = ^0-16 2 .x 1 -28 = 0-0328-, 
 3 3 
 
 and for that of the supplementary cone 
 
 * gl3 y ' 8123 
 
 v . 
 
 : 3 cot 2 a - cot 2 j8 3 8 2 - 2-1445- 3 
 
 The volume of water in each vessel will therefore be 
 
 V = V!-V 2 = (0-0328 -0-0090) - = 0-0249 cub. m. =24 '9 litres [0 "879 cub. ft] 
 3 
 
 The quantity of water raised per minute is 
 
 ?MtV = 12x5V = 60V = 1-494 cub. m. [52762 cub. ft.], 
 and the work required per second 
 
 L = ^74 = 24 -9x4 = 99-6 m. kg. [720'4 ft. Ibs.], 
 
 or, when the friction at the journals is included, about 1J horse- 
 power. 
 
 7. Chain-Pumps. In place of securing the receptacles 
 for the water directly to a revolving wheel, an endless chain is 
 sometimes employed to which they are attached. The lower 
 end of the chain is submerged in the water and its upper end 
 is passed around a sprocket-wheel ; when the latter revolves, 
 water is thus raised and discharged at the top. Pistons or discs 
 are frequently used in place of actual receptacles or buckets, 
 a tube being then required for the discs to ascend in. Appar- 
 atus of this class are commonly termed chain-pumps (pater- 
 noster-pumps), and the special types are called chain -bucket - 
 pumps, when the water is elevated in buckets ; chain -disc- 
 pumps, when discs or pistons are made use of; and rosary- 
 pumps (or cliaplets), when the chain is provided with pallets or 
 buttons approaching the spherical shape. 
 
 A description of the simplest form of chain-bucket-pump, or 
 the so-called noria, may be found in the volume on Hydraulics. 
 It is there represented as a prime mover, the machine ABD, 
 Fig. 18, being assumed to derive its motion from the weight 
 of the water admitted to the buckets at the top and allowed 
 to descend on one side. If, however, the upper wheel be 
 revolved by some other force in the opposite direction and the 
 
EARLY FORMS OF 
 
 "/45f 
 
 C 
 
 Li i 
 
 19 
 
 apparatus be immersed in the watelr^^isufficient depth, th< 
 
 bucket D will be filled with water at 
 
 discharge it when it arrives at the top, 
 
 in passing over the wheel C. This may, 
 
 at first sight, appear to be a very perfect 
 
 mode of raising water, but the objections 
 
 to its application are numerous. For 
 
 instance, when the buckets are dipped 
 
 into the water vertically, the air con- 
 tained in them opposes the entrance of 
 
 the water, and, besides, it is difficult to 
 
 empty the receptacles without losing a 
 
 large portion of their contents. It is 
 
 also necessary to lift part of the water 
 
 to a considerable height above the point 
 
 where it is collected, and the machine 
 
 must be run at a very slow rate of speed 
 
 in order to effect properly the filling 
 
 and emptying of the buckets and cause 
 
 the chain-links to occupy their correct 
 
 positions on the wheels or drums. 
 
 The manner of driving a noria by 
 
 means of a revolving wheel provided 
 
 with studs, and the means employed for 
 
 collecting the discharging water, are evi- 
 dent from Fig. 19, I. and II., where AB 
 
 is the wheel revolving with the shaft C, D are the driving 
 
 studs projecting from the side of the former, E the box-shaped 
 L jj receptacles, and F the 
 
 E_ trough where the 
 
 water is gathered, 
 while Gr represents 
 the chute for its 
 further conduction. 
 
 Spouts made of 
 sheet-iron are some- 
 times introduced be- 
 tween the driving 
 
 studs or the arms of the wheel for the purpose of collecting 
 
 the discharging water and conducting it to a chute at the side. 
 
 Fig. IS. 
 
 Fig. 19. 
 
 
20 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 Fig. 20. 
 
 The upper end of such a scoop-machine is illustrated in Fig. 20. 
 
 The apparatus consists of two chains 
 carrying the vessels A, B, etc. between 
 them, the joint-pins being supported 
 by the forked ends of the arms 1), E, F 
 of the wheels. Between each adjacent 
 pair of arms, and extending between 
 the two wheels, sheet-iron spouts are 
 placed, which receive and carry off 
 the water. 
 
 In Fig. 21 another form of noria 
 is shown, which was first constructed 
 
 by Gateau and is very commonly used in France. It consists 
 
 of sheet-iron buckets A, etc., 0'3 m. [1 ft.] high, 0'15 m. [6 ins.] 
 
 wide, and 0'24 m. [9| 
 
 ins.] long, the upper end 
 
 being somewhat oblique 
 
 and provided with a large 
 
 opening a at the side for 
 
 the admission and dis- 
 charge of the water, and 
 
 the lower end having a, 
 
 small hole b fitted with a 
 
 flajvvalve and serving as 
 
 an in- and out-let for the 
 
 air. When the receptacles 
 
 ascend, the valves are, of 
 
 course, closed ; but when 
 
 the former have passed 
 
 over the top of the wheel, 
 
 the valves open by the 
 
 action of their own weight 
 
 and admit the air required 
 
 to allow of the efflux of the 
 
 water. Moreover, when 
 
 the buckets are dipped into 
 
 the water at HE at the 
 
 lower end of the chain, 
 
 the air contained in them 
 
 is forced out through the valves by the pressure of the entering 
 
 Fig. 21. 
 
i EARLY FORMS OF WATER ELEVATORS 21 
 
 water. In order that the discharging water may be collected 
 more readily, a guide- wheel D is located below the upper wheel 
 B, the chain being thereby pushed back sufficiently to allow 
 of the chute being placed almost directly beneath the discharg- 
 ing bucket. 
 
 NOTE. The application of bucket-chains to the hoisting of grain 
 or other loose material in elevators for flour mills, as well as to raising 
 sand, slime, etc., in dr edging-machines, is treated of in the volume on 
 
 Hoisting Machinery. 
 
 8. Chain -Pumps (continued). As pumps of this class 
 work satisfactorily also with muddy water and are easily made 
 portable, they are frequently made use of for moderate lifts 
 of from 2 to 3 in. [6 to 10 ft.] One form of water- 
 elevator of this kind consists essentially of a double, endless 
 chain to which, at the middle of the links, are secured rect- 
 angular boards of 20 to 40 mm. [f to 1-J- in.] in thickness, 
 0-3 to 0-4 m. [1 to 1-3 ft.] long, and 0-15 to 0'20 m. 
 [6 to 8 ins.] high. The length of the chain links, and conse- 
 quently also the distances apart of the boards, are likewise 
 0*15 to 0*20 m. [6 to 8 ins.], and the chain wheels over which 
 the double chain runs usually have either 6 studs or 8 or 
 more radial prongs on which the links are supported. The 
 ascending part of the chain travels through a trough of 
 rectangular section, the boards having a clearance at the top 
 and sides of about 8 to 12 mm. [ T 5 ^ to |- in.]; for support- 
 ing the descending part either a plain board or an open 
 trough is used, having a length sometimes reaching 10 m. [33 
 ft.], and an inclination to the horizon of from 10 to 30 degrees. 
 Motion is given to the apparatus through the upper chain- 
 wheel shaft, usually by the turning of cranks. If it is desired 
 to operate the machine by horse-power or by a water-wheel or 
 a windmill, this may be done by the use of an upright shaft 
 provided with a bevel-gear engaging another bevel on the chain- 
 wheel shaft. 
 
 An apparatus of the above description is shown in Fig. 22, 
 partly in elevation and partly in longitudinal section. A is 
 the ascending, B the descending chain, and C shows the chain 
 wheel provided with only four studs, and operated by means of 
 a crank D. There are further visible at EE the rising chute, 
 
Fig. 23. 
 
niF*fi 
 
 CHAP, i EARLY FORMS OF WATER E^^ATORS 23 
 
 and at FF the carrying trough, also at G trie tli^eliaigd cdnduit, 
 and at EF the frames for coupling the twjD inclined troughs to 
 each other. At the lower end a frame^ffl is applied whiflJr v 
 receives the bearings for the lower crraaE 
 suspended by means of a rope or chain from a drurrTM pro- 
 vided with a ratchet, in order that the inclination of the machine 
 may be adjusted to suit the position of the water-level. To 
 provide a means of giving the proper tension to the chain, the 
 bearings of the upper chain wheels are arranged in a sliding 
 piece 1STN", which is connected to the head S of the chute E by 
 means of a rack and pawl. 
 
 Such chain -pumps are sometimes used for dredging slimy 
 bottoms. A very good example of a steam dredge of this kind, 
 built at IFaltjen's works in Bremen for the harbour of Geestemunde, 
 is found in Wiebe's Skizzenbuch f. d. Ing. u. Maschinenbauer, parts 
 32 and 33. 
 
 In the chain-disc-pump, shown in Fig. 23, the chain is 
 fitted with circular discs or pistons, and ascends in a vertical 
 pipe AB. The discs consist of a wooden piece a, a packing- 
 ring b of leather soaked in a mixture of tallow, oil, and tar, an 
 iron plate c, and a spindle or bolt passing through the whole, 
 and attached to the chain at each end. Both at the top and 
 bottom the disc chain is held by the forked ends of the arms of 
 the wheels C and D, of which the upper one is rotated by means 
 of a crank K. Motion is thus imparted to the chain in the 
 direction of the arrow, and the water raised by the discs from 
 the box F through the vertical pipe to the point of discharge 
 A. The vertical pipe or barrel is given a diameter of 0'12 to 
 O'lo m. [4f to 6 ins.], the leather discs being made about 
 3 mm. [^ in.] smaller, so as to reduce the friction, and located 
 at intervals of '80 to 1 m. [2^- to 3^ ft.] In order to pre- 
 vent the water, as far as it is possible, from leaking by the 
 discs, without materially increasing the' frictional resistances 
 in the barrel, the latter is frequently made of iron instead of 
 wood, or at least its lower end is formed by an iron tube in 
 which the leather discs are made to fit accurately. 
 
 9. Mechanical Effect of Chain-Pumps. The effect of a 
 chain -pump may be computed as follows. Let V be the 
 volume of water carried by each bucket or disc, etc., let further 
 
24 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 n denote the number of studs, arms, or forks of the upper- 
 wheel for the support of the links of the chain, and let u be 
 the number of revolutions of this wheel per minute ; then, the 
 volume of water raised by the machine per second will be 
 
 If the vertical height to which the water is raised be 
 denoted by h, and all hurtful resistances be omitted, the work 
 required per second will be 
 
 nu 
 
 As a rule, the volume V may be calculated as that of 
 a body of prismatic shape. In the case 
 of the pump with rectangular lifting 
 boards, the volume depends to a great 
 extent on the inclination of the machine. 
 Letting d denote the height AH (Fig. 
 24) of each board, b the width, and e 
 the distance AB between the boards, 
 Fig 24 then, for an angle of inclination ACH = 
 
 EHD = a of the chute to the horizon, 
 we have the volume of water carried by each board 
 
 V = 6(AB.AH-HD.DR.) 
 
 = b(d .e-^e.e tan a) = be(d - \e tan a). 
 
 This formula, however, is only applicable when the water- 
 line HE intersects both boards ; were it to terminate, on one 
 side, at the bottom wall of the chute (at C), that is, were 
 AC<AB or d cot a<e, then the section of the volume of 
 water between the boards will no longer be a trapeze AHEB, 
 but a triangle AHC having the base AC = d cot a, and conse- 
 quently we should have 
 
 V = d 2 b cot a. 
 
 In a chain -disc -pump with a vertical barrel, the volume 
 will be V = Qe, if G is the area of each disc and e the distance 
 between the discs, 
 
i EARLY FORMS OF WATER ELEVATORS 25 
 
 The actual volume elevated, however, is always somewhat 
 smaller, since we must deduct in the .first place the space V T 
 occupied by the chain links between the two boards or discs, 
 and in the second place the volume which leaks through in the 
 clearance space between the latter and the chute or barrel. 
 This latter loss is to be computed for one board or disc only, 
 namely that at the top, as the water lost from the spaces below 
 is replaced by that flowing down from above. 
 
 For the chain-disc-pump this loss may be calculated as 
 follows : If r is the radius of the disc and i\ the inside 
 radius of the tube, then the area of the clearance space will be 
 
 in place of which, however, we can put approximately 
 
 if s = i\ r denotes the width of the clearance space. 
 
 Let z designate the varying height of water above the dis- 
 charging disc (at the top), and JJL the coefficient of efflux (0'7) 
 corresponding to the area F, then the quantity of water passing 
 through during an element of time dt will be 
 
 If the chain moves with a velocity c, and the distance be- 
 tween the discs is e, we have 
 
 z = e - ct, hence dz = - cdt, and di - 
 
 C 
 
 From this we obtain 
 
 and hence 
 
 W = - \2g . \ + const., 
 c 
 
 or, since z decreases gradually from e to 0, the total leakage 
 for each disc will be 
 
26 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 /? 
 
 Now is, however, - equal to the time of discharge t for each 
 
 
 
 disc, and consequently we can place 
 W = 
 
 and the leakage per second 
 W 
 
 In a chain -pump with rectangular lifting -boards we can 
 assume that leakage takes place only at the two sides of the 
 latter, as the water-line reaches the top of the lowest board 
 only, and the bottom of each board slides on the bottom of the 
 chute. For an angle a of the chute to the horizon, the vari- 
 able head of the water above the top board will be 
 
 z sin a, 
 
 and the variable height of the orifice 
 
 z tan a. 
 
 If therefore the clearance between the board and the chute at 
 each side is denoted by s, we shall have 
 
 = - 2/x - tan a 
 
 c 
 
 = JJL . 2sz tan a V 2^ sin a . c 
 and hence 
 
 W = -2p- tan a \/2g sin a . f ^ + const. 
 
 c 
 
 The definite integral between the limits z e and z = will 
 then give 
 
 W = 2 p - tan a *J%g sin a . f e* 
 
 C 
 
 = 2 . -f- /x - se tan a v 2#e sin a, 
 c 
 
 and consequently the water which returns through leakage per 
 second : 
 
 W We 
 
 Q = = = 
 
 * s 
 
i EARLY FORMS OF WA 
 
 Friction of the boards at the bottoms of ^he two* troughs 
 also materially increases the force Required for moving the 
 chain. If R is the weight of the chain and boards, and <f) the 
 coefficient of friction, this frictional resistance, will be = <R 
 cos a (we may here assume < = ^). 
 
 To this must be added the journal friction of the two wheels, 
 and the friction generated when the chain winds on and off 
 the latter. Both resistances may be computed from the 
 formulae deduced in Weisbach's Mechanics, vol. i. and vol. iii., 1 
 [Machinery of Transmission]. 
 
 If the hurtful resistances were neglected, the force required 
 in the axis of the chain would be 
 
 _ 
 ~7~60 c 7 ' 
 
 and consequently, since the distance 
 
 60 mi c . L ~Vhy 
 e = d = c, or - = - and = - , 
 nu ' 60 e c e ' 
 
 when the friction of the boards is taken into account, and 
 further the length of the crank is assumed = a and the radius 
 of the driving wheel = &, the turning force necessary at the 
 crank 
 
 a\c 
 
 NOTE. For a given length I of the machine there is always a 
 certain inclination a which gives a maximum useful effect, that is, 
 makes the product of the water delivered Q into the head h = I sin a 
 a maximum. Placing, in accordance with the above, the quantity 
 of water delivered per second equal to 
 
 we shall obtain 
 
 Q/& = bcl sin a(d - \e tan a). 
 
 This expression obtains its greatest value when d sin a - 
 \e tan a sin a becomes a maximum, and the corresponding value of 
 a is therefore, according to the calculus, obtained from the equation 
 
 v, s sin a 
 
 d . cos a - - tan a cos a + 
 
 -10 
 
 O I 
 
 cos *aj 
 or 
 
 tan 3 a + 2 tan a = 
 
28 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 Hence, if d = e, for instance, we have tan 3 a + 2 tan a = 2, and 
 consequently a = 37 38'. 
 
 EXAMPLE. In an inclined chain-pump the lifting-boards have a 
 width b = 0'3 metre [0'98 ft.], a height d = 0'15 metre [0'49 ft.], and 
 are placed 6 = 0*20 metre [0*66 ft.] apart; further, the inclination 
 of the chain to the horizon is a = 20, the height to which the water 
 is lifted is h=l'o metre [4 '9 2 ft.], the clearance of the lifting-boards 
 at each side in the chute is s= 10 mm. [0'39 in.], the number of 
 driving studs or arms in the .upper wheel is n = 6, and the number 
 of revolutions of the latter per minute is u = 40. Find the volume 
 of water which can be lifted by the machine and the power required 
 to drive it. 
 
 Neglecting all losses, we should have the volume of Avater raised 
 per second : 
 
 Q = ^be (d-letsn. a] =^^ x 0'3 x 0'2(0'15 - O'lO tan 20) 
 
 ou \ 2 / oU 
 
 = 0-24(0 -15 -0-0364) = 0-02726 cub. metre [0*9697 cub. ft.] 
 
 Under the assumption that the portion of chain included 
 between two adjoining lifting -boards displaces 0*2 litre [0*0071 
 cub. ft.] of water, the volume raised per second will be decreased 
 
 by 0-0002^ = 0-0008 cub. metre [0-0283 cub. ft.], and if we 
 further take into account the leakage 
 
 Q!=|/MW tan a\/2gesin a=|o'7 x O'OIO x 0'2 tan 20\/2 x 9 '81 x 0'2 sin 20 
 
 D O 
 
 = 0-00047 cub. metre [0'0166 cub. ft.], 
 we shall obtain the volume of water actually raised 
 
 Q = 0-02726 -0-0008 -0-00047 = 0-026 cub. metre [0'918 cub. ft.] 
 
 TLU 
 
 The velocity of the chain is given by c = e, in which formula 
 
 e represents the distance from centre to centre of the lifting-boards, 
 i.e. the distance between the boards 0'2 metre [0-656 ft.] plus the 
 thickness of board 0-025 metre [0'082 ft.], or in all 0*225 metre 
 [0738 ft.] Accordingly we have 
 
 c - 4 x 0-225 = 0-9 metre [2 '95 ft. ] 
 The work consumed is 
 
 L = Q/i7 = 0-02726 x 1'5 x 1000 = 40*9 metre kilograms 
 [L = 0-9627 x 4-92 x 62-5 = 296 ft. Ibs.], 
 
 and consequently the force 
 
i EARLY FORMS OF WATER ELEVATORS _': 
 
 It would be sufficient to make the length of each part of the 
 
 7, 1 .K 
 
 chain equal to - = . =4*38 metres [14'37 ft.], but let us 
 
 sin ot sin ZU 
 
 assume that this length be made 6 metres, or the whole chain 12 
 metres [39 '3 7 ft.] ; then the total number of lifting-boards will be 
 
 12: 0-225 = -^54. 
 
 If the weight of each board together with the piece of chain belong- 
 ing to it is 2 kg. [4-41 Ibs.], the weight of the whole chain will be 
 E = 2 x 54 = 108 kg. [222-26 Ibs.], and the corresponding friction 
 at the bottoms of the chutes 
 
 0R cos 20 = x 103 x 0-940 = 25-4 kg. [56 Ibs.] 
 The total load is therefore 
 
 45-5 + 25-4 = 70-9 kg. [156*3 Ibs.], 
 
 and if the ratio - of the radius b of the driving-wheel to the length 
 
 3 
 a of the crank is = - , there will be required at the crank a force 
 
 P=|70-9 = 53-2 kg. [117-24 Ibs.] 
 Since the velocity of the crank is 
 
 -c=. 1 0-9 = 1-2 metre [3'94 ft.], 
 o 6 
 
 the total work expended will be 
 
 L = 53-2 x 1-2 = 63-8 m. kg. [461-5 ft. Ibs.], 
 and the efficiency 
 
 10. Archimedean Screw or Water- Snail. This is one 
 of the oldest water -raising machines known. It consists 
 essentially of a tube wound spirally around an inclined shaft 
 AB (Fig. 25), and taking part in the rotation of this shaft. 
 The pitch of the screw and the inclination of the shaft are so 
 chosen that a portion of each thread will always point down- 
 wards ; a certain quantity of water V may then be contained 
 in the lower part of each thread, the number of pockets or 
 receptacles thus formed being equal to the total number of 
 threads. The volumes of water contained in the latter may 
 be regarded as an equal number of nuts of the screw, and 
 
30 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 hence it follows that for each revolution of the shaft all these 
 volumes of water are elevated, in the direction of the axis, a 
 distance equal to the pitch s of the screw. If, therefore, the 
 screw is so placed that the lower orifice A of the tube, which 
 is submerged to a certain depth in the water HE, can, for 
 each revolution, admit the volume V required to fill one of the 
 pockets, it is evident that when the shaft is rotated there 
 must be discharged at the upper orifice B a quantity of water, 
 which for each revolution equals the volume Y contained in 
 each pocket. The value of V depends, not only on the 
 sectional area F of the tube or worm, but also on the length / 
 of the arc in which the water is contained ; when the diameter 
 
 Fig. 25. 
 
 of the tube is small, as compared with that of the cylinder 
 around which it is wound, it is sufficiently accurate to place 
 V = FJ. 
 
 If the machine consists of one helix only, and makes u 
 revolutions per minute, the volume elevated per second will be 
 
 while for a screw with n spiral tubes or threads the volume is 
 
 nu ^ nu _, 
 Q = 60 V= 60 F/ ' 
 
 and the corresponding work expended, theoretically, 
 
 nu nu ^T, 
 
 -VA 7 = -F%. 
 
i EARLY FORMS OF WATER 
 
 Here h denotes the total lifi 
 number of threads of each heli 
 of inclination of the shaft to the 
 
 To determine the length I of 
 is contained, let r be the radius of 
 axis of the tube, and a the constant 
 
 in which the water 
 . /described fyy.the 
 thread 
 
 makes with a plane normal to the shaft (plane of rotation). 
 If the screw were placed vertically this angle a would 
 represent the inclination of the thread to the horizon at every 
 
 Pig. 26. 
 
 point. Inclining the screw until its axis AB (Fig. 26) makes 
 an angle BOE = /3 with the horizon HE will alter the in- 
 clination of the helix to the latter to a different degree at 
 different points. At a certain point D, the projection of 
 which in the plane of cross-section may be designated by d, 
 the helix can therefore assume a horizontal direction, and we 
 will now determine under what conditions such is the case. 
 Let 8 denote the angle cad, showing how far the point D is 
 removed from the line CO' imagined at the upper side of the 
 cylinder, and let DT> 1 be an infinitely small element of the 
 
32 MECHANICS OF PUMPING MACHINERY CHAP, 
 
 screw-line, the projection of which in the plane of cross- 
 section is dd : = r . 38. Assuming now through the point D a 
 plane DD at right angles to the axis of the cylinder, it is 
 evident that the rise D^i axially of the element is 
 
 D D 1 = dd l tan a. 
 
 But on account of the assumed horizontal position of the 
 element DD X we also have 
 
 D D 1 = dd 2 cot ft = dd l sin 8 cot ft, 
 
 as may be easily seen from the figure. From the equality of 
 these two expressions for D "D } we obtain 
 
 tan a = sin 8 cot ft, 
 or 
 
 sin 8 = tan a tan ft . . . (I). 
 
 For a given screw, i.e. for a given angle a of the thread, 
 and an assumed inclination fi to the horizon, this expression 
 will give two adjacent angles 8, provided that tan atan/3<l. 
 In the limiting case tan a tan ft = 1 it is apparent that 
 g=90, i.e. the horizontal direction of the helix will be 
 obtained in the point M. As, therefore, the helix would 
 ascend on one side of this point M and descend on the other, 
 it is easily understood that for the limit tan a tan $=1, or 
 for a-f-/3=90, the screw is unsuited for the elevation of 
 water, since the pockets serving to receive the water then 
 entirely disappear. The first requirement of a water-screw is, 
 therefore, that the sum of the angle of the thread and the angle 
 of inclination of the shaft should be less than 90. 
 
 Assuming then that this requirement is fulfilled, we obtain 
 from tan a tan /3 = sin 8 two angles 8 and 180 8, at which 
 the tangents of the helix are horizontal. These two points are 
 designated by D and E in the figure, and it is evident that at 
 these places the screw line rises on one side and falls on the 
 other. From these considerations it follows that when the 
 screw is submerged up to the point D the helix will form 
 a bag -shaped arc for the reception of the water, the arc 
 beginning at D and having its lowest point at E. If C F 
 represents the lower end of the screw, we obtain for the 
 
i EARLY FORMS OF WAT 
 
 vertical height of the extremity 
 the expression 
 
 C D cos /? = ?(! - cos 
 
 The arc in which the water is contained extends to the 
 point G where the level HE of the water intersects the helix. 
 To compute the length I of this arc DMEFG, let the corre- 
 sponding angle dag at the centre be designated by o>. As 
 above in the case of D D 1 we now obtain two expressions for 
 the rise G G of the arc axially, namely, 
 
 Gr G 3 = deg tan a = ra> tan a, 
 in consequence of the angle of the thread, and 
 
 GjjGj = d Q g cot /3 = r [cos 8 - cos (o> + 8)] cot /:?, 
 
 on account of the inclination of the shaft. 
 
 From the equality of these values, and by paying attention 
 to (1) we therefore obtain 
 
 cos 8 - cos (to + 8) = o> tan a tan /3 = w sin 8 . (2). 
 
 For any given screw, i.e. for a known value of , the angle 
 ft> may be determined by approximation from this equation, 
 and, referring to the figure, the length I of the arc DEG will 
 then be found to be 
 
 COS a 
 
 During the rotation of the screw around its axis both the 
 length and the shape of this arc will remain unchanged, since 
 the latter gradually advances upward in such a manner that 
 all its points, and consequently its extremities as well, move 
 along lines DD', GG' . . . which are parallel to the shaft AB. 
 
 2-77T 
 
 As of the total length -- of each thread only the portion 
 cos a 
 
 is filled with water, the air will occupy the remainder of 
 cos a 
 
 the arc 
 
 2?rr cor 2-TT o> 
 L= ---- = - - r. 
 
 1 COS a COS a COS a 
 D 
 
34 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 In each revolution the orifice of the tube describes an arc 
 2cd = 28r only in the air, and therefore it takes in a volume 
 
 O * 
 
 of air corresponding to the arc - only. 'After the orifice 
 
 cos a 
 
 has re-entered the water this volume can expand only at the 
 expense of the density of the enclosed air. Such expansion 
 or decrease in density is necessarily combined with a reduction 
 in the pressure, and therefore the state of equilibrium of the 
 water arc is disturbed and a portion of the water must return 
 through the air space. To avoid such disturbances in the 
 regular ascent of the water, the tube is either provided with 
 a large number of small holes along its whole length for the 
 admission of the air needed to fill the arc l p a small quantity 
 of water being hereby lost, however, through the arc /, or it 
 is made of such a width that all the air spaces will com- 
 municate with each other, and accordingly the air which is 
 lacking below may be supplied from above. In this case the 
 width d must be at least equal to the perpendicular height 
 EJ of the water arc DEG, and from the figure it is thus found 
 to be 
 
 = 2r cos 8 cos /3 - r(ir - 28) tan a sin /?. 
 
 When this or a greater width is chosen, it is evident that 
 the sectional area F of the water arc must not be placed equal 
 
 to - , but a mean value must be deduced from which the 
 
 capacity may be computed. In this calculation Simpson's rule 
 may be utilised to advantage after the surface of the cylinder 
 has been rectified ; the water arc DEG and the horizontal 
 water line DJG may then be transferred to the paper and 
 the distances between these two lines measured at various 
 points. 
 
 In order that the arc DEG may actually become filled with 
 water, it is necessary to revolve the screw very slowly. 
 
 EXAMPLE. If a water-snail be placed at an angle of j3 = 35 
 and the angle of thread be a = 30, then the most advantageous 
 angle of submersion 8 will be obtained from 
 
 sin 5 = tan a tan j8 = tan 30 tan 35 = '4043, 
 
EARLY FORMS OF WATER ELEVATORS 
 
 35 
 
 which gives 8=23 5 1/; for the angle w at the centre, correspond- 
 ing to the water arc, we have 
 
 w sin 5 + cos (8 + w) = cos 5, 
 w sin 23 51'+ cos (23 51' + w) = cos 23 51', 
 
 that is, 0'4043o> + cos (23 51' + o>) = 0-91461. Hence follows w = 
 211 4', and the length of the water arc 
 
 cos a cos 30 
 
 The angles 8 and w may also be easily obtained by a construc- 
 tion, if the surface of the cylinder, the elliptic outline of the water- 
 level, and the helical axis of the tube be developed on the paper. 
 
 ,--Ei 
 
 Fig. 27. 
 
 In Fig. 27, let AB represent the base, CD the axis of the cylinder, 
 and BE the elliptic section formed by the water-level in cutting 
 the cylinder around which the tube is wound (this .section making 
 with the base an angle ABE = 90 - = 90 - 35 = 55). Now, 
 make BE = irr equal to half the circumference AFB of the base 
 of the cylinder, further, divide both the semicircle AFB and the 
 straight line BE in (6) equal parts and erect perpendiculars from 
 
36 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 the points of division (1, 2, 3 . . .) of both lines, and finally, 
 through the points of intersection of the first system of lines (1, 2, 3 
 . . .) and the section BE draw horizontal lines ; then, the intersec- 
 tions of the latter with the second system of perpendiculars will 
 form a curve BM 1 D 1 E 1 G 1 , which will represent the development of 
 the elliptic water-line, and the shape of which is that of the sinus 
 curve. If we now draw a straight line KjLj intersecting the base 
 AB at the given angle of thread a (30), and touching the curve in 
 the point M p this line will be the desired development of the helix, 
 from which the projection MNOL of the helix is determined by 
 drawing horizontal lines M 1 M, N X N, 1 0, LjL . . . from the intersec- 
 tions M p Np Op L x . . . of the line KjLj and the developed system of 
 perpendiculars to where they intersect the system of perpendiculars 
 drawn from the periphery of the cylinder AFB. The line MpLp 
 extending from the point of tangency M T to the point of intersec- 
 tion Lj of the developed water-line and the developed helix, is the 
 true length of the arc in which the water is contained, and there- 
 fore a rectangle drawn on this line with a height M 1 P 1 = L 1 Q 1 = the 
 diameter of the tube will represent the development of the vertical 
 section through the axis of the latter, while the space between 
 M 1 N 1 1 L 1 and M 1 D 1 E 1 L 1 is the development of the vertical section, 
 axially, through the body of water enclosed in the tube. The distances 
 of the points D p E p etc., from M X L X are the heights of the circular 
 segments forming the cross-sections of this body of water. We are 
 therefore able to determine the volume of the latter by taking the 
 mean of all the cross-sections and multiplying it by the length 
 M 1 L 1 = / of the water arc. From the drawing, which is made accur- 
 ately to scale, we thus get 
 
 = 3 -30r + '95r = 4 -25r, 
 
 which is approximately the same value as was obtained by calcula- 
 tion. The greatest depth S^ of the screw below the surface of 
 the water is E, 1 S 1 =l*lr. In order to establish communication 
 between all the air spaces, we give the same width to the screw, 
 consequently making d = M 1 P 1 = L 1 Q 1 = 1'lr. Dividing the arc 
 M 1 K 1 in four and the arc R^ in three equal parts, and through 
 the dividing points thus obtained drawing additional ordinates be- 
 tween MjDjEjLj and M 1 N 1 1 L 1 parallel to I^Sp we shall have the 
 necessary data for the determination of the volume of water con- 
 tained in each thread of the screw. The inserted heights are : 
 
 between Mj and RjSj between R 1 S 1 and Lj 
 
 0-'20r; Q'55r ; 0'90r l'04r; O'SOr 
 
 or, if we take as unit the radius of the tube ?\ = - = -^ = 0'55?-, 
 0-3647-! ; 1'OOOrj ; l'636ri and l'891ri ; 1 '4547V 
 
i EARLY FORMS OF WATER 1 ' 
 
 - 
 
 The areas of the segments having these" Jieights will be found to 
 
 be respectively 
 
 ^^>.- .o/fj. 
 
 0-3757V ; 1 -5717Y 2 ; 2-751^ and 3'075r 1 2 an^*46r,-. -"H. v " 
 
 By using Simpson's rule we now get the volume of water in the 
 tube M^R lt 
 
 3'30r(0 + 4x 0-375 + 2 x 1-571 + 4 x 2-751 + 3-142) ^L 
 
 12 
 
 and in the tube 
 
 0-95r(3'142 + 3x 3-075 + 3 x 
 
 and consequently the total volume of water in each thread, 
 
 = 7-507xO-3025r 3 =2-27?- 3 . 
 
 If the screw has w = 4 threads and is revolved 20 times per 
 minute the volume of water elevated per second will be 
 
 Assuming, for instance, that the screw has a radius of r = 0'15 
 metre [0'459 ft.], we should have Q-0'01023 cub. m. [0'36128 
 cub. ft.] If the axis of the screw has a length of 6 metres [19 '685 
 ft.], which for an angle of inclination /3 = 35 corresponds to a 
 vertical lift of h= 6 sin 35 = 3-441 metres [11-289 ft.], the 
 theoretical work absorbed per second would be 
 
 L = Q7&7=10-23 x 3 '441 = 35 '2 metre kilograms 
 [L = 0-36128 x 11-289 x 62'5 = 254'9 ft. Ibs.] 
 
 11. Water-Screws. As it is difficult to produce a snail 
 having circular cross -sections, threads of rectangular section 
 are almost exclusively employed at the present day in water- 
 screws, being wound on the spindle and enlosed by a cylin- 
 drical casing. When the casing is fixed to the screw the 
 machine assumes the appearance of a long barrel or drum. It 
 is more common, however, as in the so-called Dutch water- 
 screw, to make the casing stationary, in the shape of a trough, 
 and allow it to surround the screw only at the bottom side. 
 The trough may be made either of iron or wood, or it may be 
 constructed of brick and cement. In order to reduce the 
 leakage through the clearance space to a minimum, it is not 
 only necessary to make the latter as small as possible (from 
 
MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 2 to 4 mm. [0*08 to 0*16 ins.]), but the whole trough should 
 be constructed very accurately and substantially. In Holland, 
 where water-screws are used for draining of low lands, the 
 troughs are constructed with great care of vitrified brick 
 or clinker. The water -screws with revolving casings are 
 usually portable and operated by hand, while the Dutch water- 
 screws are rotated by windmills. In the latter machine the 
 screw shaft is provided with a gear which is driven by another 
 gear placed at the lower end of the upright windmill shaft. 
 
 Fig. 28 shows the arrangement of a water-screw with 
 revolving drum and triple thread. The journals C and D of 
 
 Fig. 28. 
 
 the shaft are supported in a wooden frame which at the top 
 rests on a horse A, and at the bottom is held by a guide beam 
 B suspended by chains from a windlass E by means of which 
 the screw can be given the proper inclination. The crank K 
 is not rotated directly by hand, but is turned by means of rods 
 attached to the wrist pin and pulled back and forth by four or 
 six labourers. In the figure the lower half of the machine is 
 shown in section; at G, G r G 2 are seen the threads which 
 wind around the shaft WW, while at M in the upper portion 
 the casing, bound with iron hoops, is visible. 
 
 Fig. 29, I, represents a Dutch water-screw also having a 
 triple thread, and in which the trough is made of wood, the 
 
EARLY FORMS OF WATER ELEVATORS 
 
 39 
 
 upper half of the latter being cut away in the engraving. The 
 trough BB rests on the cross timbers E, E . . . between the 
 posts F, F . . ., which are joined into the former, and the 
 whole apparatus is supported by a portable framing GHK. 
 Also here the crank K at the upper bearing C is put in 
 motion by means of push rods ; the step for the pivot D at 
 the lower end is secured to a cross girt which is inserted 
 between two posts. A cross - section of the screw together 
 with its trough and the supports for the latter is shown in 
 Fig. 29, II, where W is the shaft and S 1 , S 2 , S 3 sections 
 
 Fig. 29. 
 
 through the three threads. After the water has been elevated, 
 it is removed through the discharge conduit Z, which is secured 
 to the trough and also rests on the framing. 
 
 NOTE. The Dutch screw is occasionally used for transporting 
 loose material, as, for instance, in flour mills for taking the mixture 
 of meal and bran to the elevator ; in this case the screw is, as a 
 rule, placed horizontally. 
 
 It is quite common in practice to make the water-screws 
 entirely of wood ; the threads may, however, just as easily be 
 made of iron-plate sectors as of wooden ones. When made of 
 
40 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 wood they have a thickness of about 25 mm. [1 in.], and 
 the shaft or stem of the screw is provided with helical grooves 
 about 25 mm. [1 in.] deep for the reception of the boards. 
 The adjoining boards are tied together firmly by irons, and no 
 further fastening to the shaft is necessary. When the casing 
 is to be secured to the screw, the former is also provided with 
 grooves for the boards to fit into, and iron hoops are driven on 
 the outside at intervals of about 0'6 metre [2 ft.] Usually 
 the whole machine is coated with tar. 
 
 When the threads are put together of sections made of 
 iron plate, a cast-iron shaft is used, which in place of the 
 grooves is provided with screw-shaped flanges to which the 
 sections are riveted. If the casing also is of iron plate it is 
 most suitably fastened to the thread by means of angle irons. 
 To get the shape of the sections, a prismatic block of wood 
 ^ (Fig. 30) is cut out, the base AB X = CD 1 of which is 
 
 a sector of a circle form- 
 
 Bl ing the projection of each 
 
 section in a plane at 
 right angles to the axis 
 of the screw. The out- 
 lines BD and B 1 D 1 of the 
 thread are then marked 
 on the two cylindrical 
 ends AC and A 1 C 1 , and 
 finally the block is sawed 
 through along these 
 curves with the blade of 
 the saw always kept at the same height a, a x or b, b 1 at both 
 ends ; the side surface Ba&DD 1 6 1 a 1 B 1 will then give the curva- 
 ture of each section. 
 
 If now the concave surface of the block ABDD 1 B 1 A 1 be 
 placed on the plate from which the sections are to be made, 
 the outline of the latter is easily obtained. When the thread 
 is to be made of wood it is necessary to increase the height of 
 the wooden prism by the thickness CF = DG of the thread in 
 the direction of the axis of the screw. By making a second 
 cut EGG 1 E 1 parallel to the concave surface BDD 1 B 1 and at a 
 distance BE = B^ from it, the desired section BGG 1 B 1 will 
 be produced. 
 
 Fig. 30. 
 
EARLY FORMS OF WAT 
 
 In place of curved sections, plane Rectors may W Wed, il. 
 they are made to overlap each other alaced at right angles 
 to the axis. A step -shaped thread 
 
 , ,, 
 winding stairway. 
 
 The ordinary water-screws have a length of from 3 to 6 
 metres [10 to 20 ft.], the diameter of the shaft is from 
 O'lo to 0*30 metre [6 to 12 ins.], and that of the screw 
 from ^ to 1 metre [1'6 to 3^ ft.] The angle of the thread 
 at the outside circumference is usually from 10 to 30, and 
 an inclination of from 30 to 35 is given to the shaft. At 
 the shaft the angle of the thread is evidently much greater, 
 
 q 
 
 since, according to the formula tan a = - , the tangent of the 
 
 angle a varies inversely as the distance r from the axis of the 
 screw. If, for instance, the diameter of the shaft is -J- of that 
 of the screw, and the angle of the thread at the outside circum- 
 ference were 15, then the angle at the shaft would be deter- 
 mined by tan a = 3 tan 15 = 0'80385, which gives a = 38f . 
 In orfler to admit and discharge the water as uniformly 
 as possible, the distance between the threads is usually made 
 only 0'15 or 0'20 metre [6 or 8 ins.], and from two to four 
 separate threads are instead employed. If s is the pitch of 
 the screw, n^ the number of separate threads, and s l the 
 distance from centre to centre of the latter measured in the 
 direction of the axis, then we have 
 
 s = STTT tan a = n : s v 
 and hence 
 
 2?rr tan a 
 
 for instance, if r=0'5, 1 =0'18 metre [r=l'64 and s x 
 = 0-59 ft], and a =12 , 
 
 For a length I of the screw each thread will wind around 
 the shaft 
 
 I 
 
42 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 times; for instance, if ^ = 4, s 1 = 0'18, and /=6 metres 
 [^ = 0-59, 1= 19-685 ft], we have 
 
 NOTE. Water-screws may be classed among the most perfect 
 types of water -raising machines, their efficiency being at least 
 0'75. According to Mallet's observations, nine men operating a 
 water -screw of the drum type, having triple thread, can raise 
 1480-2 cubic feet of water per hour to a height of 10'S feet, the 
 screw making thirty -five revolutions per minute. The corre- 
 sponding hourly effect is therefore 1480'2 x 10'8 x 62'5 - 999150 
 foot pounds = 138130 m. kg. ; or, for each man, 111017 foot 
 pounds = 15350 m. kg., which, with an actual working day of six 
 hours, is equal to a daily effect of L = 6 x 111017 = 666102 foot 
 pounds = 92100 m. kg. In France L is estimated at 100,000 m. kg. 
 
 12. Water-Screws (continued). It is a matter of some 
 complication to determine geometrically the volume of water 
 raised in each revolution of a water-screw, because we no 
 longer have a water arc to deal with, but instead solids of 
 peculiar shape, being bounded by cylindrical and helical 
 surfaces and one horizontal plane. The development method 
 is the quickest, the screw lines being transformed into straight 
 lines and the elliptic outlines of the water-level into sinus 
 curves. 
 
 In Fig. 3 1 let CX be the axis of the screw placed vertically, 
 let AFB be a half transverse section of the screw shaft, and 
 AjFjBj one of the screws, both unfolded in the vertical plane of 
 the drawing. Further, let AO represent half the pitch of a 
 thread, and BMGOH the vertical projection of the thread on 
 the shaft or stein, as constructed in accordance with well- 
 known rules, and let KMDE be the tangent of the curve 
 representing the vertical projection of the level of the water in 
 the thread. Making BL equal to the semicircle AFB = TT . CB, 
 and LOj = half the pitch, we shall have the developed screw line 
 represented by the straight line BOj, while KMjDjNP is the 
 development of the ellipse along which the surface of the water 
 intersects the stem of the screw. The two lines MJ^NP and 
 MjP enclose the surface of contact between the stem of the 
 screw and the water contained in one division ; this surface is 
 
EARLY FORMS OF WATER ELEVATORS 
 
 43 
 
 one of the elements necessary to determine the desired volume, 
 and its area may easily be calculated by means of Simpson's 
 
 rule. The section KE corresponding to the water-level in the 
 thread intersects the outside surface of the water-screw in a 
 second ellipse whose transverse axis is E^Ej = 2DE X = 2DK 1; 
 
44 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 and which may be developed into a sinus curve K^QTBUS 
 intersected at two points Q and S by the developed helix BjQS 
 at the outside surface of the screw. Were the screw provided 
 with single thread only, the area QTEUS between the sinus 
 curve QTEUS and the straight line QS would now represent 
 the surface of contact between the inside of the casing or drum 
 and the water contained in one thread. On the other hand, 
 if the screw has double thread, then the sinus curve is inter- 
 sected by a second line TU which is parallel to QS and at a 
 distance from it equal to half the pitch AO ; the zone QTUS 
 between these two parallel lines will then be the desired element 
 for the determination of the volume of water in the thread. 
 
 If now other cylinders be inserted between the stem, above 
 AFB, and the outer surface, above A^Bj, and the same 
 proceeding be repeated as was applied to the outside cylinder, 
 additional surface elements for determining the volume of 
 water will be obtained, as, for instance, VWZ, which corresponds 
 to the cylinder that has a radius CA 2 = CB 2 equal to the mean 
 of the radius of the stem and that of the screw. After com- 
 puting the areas of all these elements by the use of Simpson's 
 rule, the required volume of water in each thread may be 
 obtained by taking the mean of all these surface elements, also 
 by the aid of Simpson's rule, and multiplying it by the normal 
 distance between the casing or drum and the shaft or stern. 
 
 EXAMPLE. In the water-screw shown in Fig. 31, let the radius 
 of the shaft be CA = CB = r=0'15 metre [0'49 ft], the radius of 
 the drum CA 1 = CB l = r l = '45 metre [1-48 ft.]; let half the pitch 
 be AO = ^s = 0'3 metre [0'98 ft], the number of individual threads 
 be n = 2, and the angle of inclination of the axis of the screw to the 
 horizon be 40, which must be <EDX. We then have for the 
 angle of the inside helix (at the stem) 
 
 tan a = = = = 0-6366 ; hence a = PBC = 32 29' ; 
 for the outside helix (at the drum) we have, further, 
 
 tan o 1= |^ = ^-0-2122 ; hence o 1 = QB 1 C = ll 59', 
 and for an intermediate angle ZB 2 C = a 2 , 
 
 tan 0,5 = ^-=- = 0-3183, consequently a 2 = 17 39'. 
 
i EARLY FORMS OF WATER EL^VATORg 45 
 
 1\ 'y 1 1 \ 
 
 Vv^ 
 
 Drawing, in accordance with these values,Me^raight lines BP, 
 BjQS, and B 2 VZ to represent the developed sfc^e^lin^s^ and con- 
 structing in addition the sinus curves KNP, ] 
 corresponding to the developed elliptic water-lines in a 
 finally, lying off at a distance s = 0'3 metre [0'98 ft.] above QS 
 the developed helix TU of the next thread, then we obtain the 
 surface elements MjNP, QTUS, and VWZ, and it is now an easy 
 matter to calculate the volume of water in a thread. 
 
 We shall find the surface 
 
 F =M 1 NP = 0-0289 sq. in. [0-311 sq. ft] 
 F x = QTUS = 0-3358 sq. m. [3 -61 3 sq. ft.] 
 F 2 = VWZ =0-1609 sq. m. [1731 sq. ft.] 
 
 and consequently the mean of these 
 
 As the width r^ - r = AA X = BB X of the water space is 0'3 metre 
 [0'98 ft.], we get the desired volume 
 
 V = F(- 1 -r) = -1681 x 0'3 = 0'0504 cub. m. = 50'4 litres [178 cub. ft.] 
 
 The screw being double threaded will therefore deliver 2V = 
 0*101 cub. m. [3 '5 6 cub. ft.] of water per revolution. For a length 
 1= 6 metres [19*68 ft.] of the screw the water will be lifted to an 
 approximate height 
 
 h=l sin /3 = 6 sin 40 =6 x '6428 = 3 -857 metres [12 '65 ft.], 
 and consequently the work absorbed per revolution will amount to 
 
 VA7=101 x 3-857 = 389-6 m. kg. 
 [Vfry = 3-56 x 12-65 x 62'5 = 2815 foot pounds]. 
 
 With a speed of u 30 revolutions per minute, the theoretical 
 work expended will be 
 
 Of) 
 
 389-6 = 194-8 m. kg. =2 -6 p.c. 
 
 |Q 2815 = 1407-5 ft. pounds = 2 -56 h.p.~l 
 
 With reference to journal friction, which is greater for screws of 
 the drum type than for those revolving in a trough, and to the 
 hydraulic resistances, an increase of 20 to 25 per cent must be 
 made in this result, and therefore the amount of power absorbed 
 must be placed at about 3 '2 5 horse-power. 
 
 For further information on water-screws and the literature per- 
 taining to the subject, see Riihlmann, Allgemeine Maschinenlehre, 
 vol. iv. 
 
CHAPTER II 
 
 ELEMENTARY ACTION OF RECIPROCATING PUMPS 
 
 13. Reciprocating Pumps are the most common water- 
 raising machines in use. They elevate water by means of a 
 reciprocating piston fitting closely in a cylinder to which are 
 attached the requisite pipes and regulating apparatus. The 
 principal parts of a pump of this description are 
 
 (1) The pump cylinder or pump barrel; 
 
 (2) The piston moving in this cylinder ; 
 
 (3) The pipes through which the water is conducted to or 
 from the barrel ; and 
 
 (4) The valves by means of which communication between 
 the pump barrel and the pipes is alternately established 
 and interrupted. 
 
 As a rule two valves are employed, one admission and one 
 delivery valve, the former governing the entrance of the water 
 into the barrel and the latter regulating the discharge. Accord- 
 ing as both valves have immovable seats, or one seat only is 
 fixed while the other is arranged in the piston, two different 
 types of pumps may be distinguished 
 
 I. Pumps having solid pistons, or plunger pumps. 
 II. Pumps having hollow valved pistons, or bucket pumps. 
 
 The pipe which conducts the water from the barrel is 
 called the delivery pipe, and that through which the water is 
 led to the barrel is termed the supply or suction pipe, according 
 as the reservoir which supplies water to the pump is located 
 above or below the latter. Occasionally one of these pipes is 
 dispensed with, the pump cylinder being placed either directly 
 
CHAP, ii ELEMENTARY ACTION OF RECIPROCATING PUMPS 
 
 47 
 
 in the water to be lifted, or just above the upper level to which 
 it is to be delivered. 
 
 Pumps having a suction pipe but no delivery pipe are 
 called suction pumps, and those having a delivery but no suction 
 pipe are named force or lift pumps, according as the delivery 
 pipe is attached to the barrel below or above the piston, i.e. 
 according as the piston acts with its lower or its upper surface 
 on the water column, thus exerting either a forcing or a lifting 
 action on the water. In most cases either combined suction 
 and lift or combined suction and force pumps are employed. 
 
 II. 
 
 III. 
 
 Fig. 32. 
 
 Fig. 33. 
 
 14. Bucket Pumps. The manner in which bucket pumps 
 operate can be seen from Figs. 32 and 33, where sections of 
 three pumps are shown, the pistons being indicated in their 
 up strokes in Fig. 32, and in their down strokes in Fig. 33. 
 The sections at I. represent a lift pump, those at II. a suction 
 pump, and those at III. a combined suction and lift pump. In 
 all three pumps C is the barrel, K the valved piston, V the 
 suction or admission valve, UU the lower and 00 the upper 
 level of the water. Moreover in I. and III. S is the delivery 
 
48 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 pipe, and in II. and III. E is the suction pipe. During the up 
 stroke (Fig. 32) the piston valves are closed and the suction 
 valves (V) are open, owing to the pressure of the atmosphere 
 on the lower level. A portion of the water above the piston 
 is therefore discharged, and the volume below it is increased 
 by the influx from the lower level. On the other hand, during 
 the down stroke (Fig. 33) the piston valves are open and the 
 suction valves closed, and consequently no fresh supply is 
 taken in. The volume below the piston then simply flows 
 through it to the space vacated above, and the amount delivered 
 merely equals the displacement of the piston rod. 
 
 Theoretically, these three pumps are identical both as 
 regards the power absorbed and the effect delivered. Letting 
 b denote the height of the water barometer, A 2 the height of 
 the water column above the piston, and h L the height of the 
 column below it, measured from the lower level UU. Further, 
 letting F designate the area of the piston, and 7 the weight of 
 a unit volume of water, or of the fluid which is to be lifted, 
 then during the up stroke of the piston we have : 
 
 (1) For the downward pressure of the air and water acting 
 on the upper side of the piston K, 
 
 E 2 - F(6 + A 2 )y, and 
 
 (2) For the upward pressure of the air and water acting 
 on the piston from below, 
 
 The difference of these pressures gives the force required 
 for lifting the piston 
 
 P = E 2 - Ej = F(6 + h. 2 - b + hjy = F(A 2 + A^y, that is, P = FAy, 
 
 where h is the total vertical lift 7^ + Ji 2 measured from the 
 lower level to the upper surface of water in the pump. 
 
 It is thus evident that the force necessary to lift the piston of 
 a bucket pump is constant, and does not depend either on the 
 position of the piston or on the pressure of the atmosphere, 
 being simply equal to the weight of a water column having the 
 piston area F as a base and a lift h for its height. 
 
 As the air pressing on the lower level UU can only balance 
 a column of water of the height I (10'336 m. [33'9 ft.]), the 
 water can follow the rising piston only as long as the height h 2 
 

 ELEMENTARY ACTION OF RECIPR 
 
 o/" tf/te foz#e?* e?i^ of the piston above the 
 than the height b of the water barometer. 
 
 If s represents the stroke of the piston, the 
 charged during the up stroke is 
 
 Neglecting the sectional area of the piston rod and all the 
 hurtful resistances, it is easily seen that the pressure of the 
 water above and below the piston is the same during the down 
 
 stroke, as the piston valves are then open, consequently the 
 force needed to push down the piston and the quantity of 
 water discharged on the down stroke are both equal to zero. 
 
 It follows that the work needed to lift the volume of water 
 V to the height h by means of these pumps is 
 
 A = Ps = Fhys = Fshy = Vyh ; 
 
 or if G = Vy represents the weight of the lifted water, the 
 work per stroke will be 
 
 15. Plunger Pumps. The action of the plunger pumps 
 can be seen from Figs. 34 and 35, the first representing the 
 
 E 
 
50 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 up stroke of the plunger, and the second (Fig. 35) the down 
 stroke. In the pump shown at I the suction pipe A is a 
 continuation of the pump barrel C ; at II the suction pipe is 
 a continuation of the delivery pipe B. Otherwise the action 
 of the two pumps is the same. During the up stroke of the 
 piston K the suction valve V is open, and the delivery valve 
 W is closed. On the other hand, during the down stroke the 
 former is closed and the latter open. In the first case the 
 empty space left by the piston on its up stroke is filled with 
 
 Fig. 35. 
 
 water that is driven into the suction pipe A by the atmos- 
 pheric pressure ; in the second case the piston presses this 
 water out of the cylinder into the delivery pipe, and thus 
 causes the discharge of an equal quantity of water into the 
 catch basin 00. 
 
 Let F again represent the area of the piston, ~b the height 
 of the water barometer, and 7^ the height of the piston K 
 above the lower level, then, during the up stroke the downward 
 pressure of the atmosphere on the piston is 
 
 The upward pressure of the atmosphere and the water acting 
 on the piston from below is 
 
ii ELEMENTARY ACTION OF RECIPROCATING PUMPS 51 
 
 From this follows the force needed to lift the piston when 
 hurtful resistances are neglected : 
 
 P! = R - Rj = F(6 - b + hjy = F/* l7 . 
 
 Moreover, if A 2 is the height of the upper level of the water 
 in the delivery pipe B above the piston K, the pressure of the 
 water on the piston, from below upward, is 
 
 consequently the total force needed to push down the piston is 
 P 2 = E 2 - E = F(6 + A 2 )y - Fby = FA 2 y. 
 
 As the heights 7^ and k z are continually changing during 
 the piston motion, the piston forces Pj and P 2 are not constant, 
 and therefore 
 
 are only average values when h 2 is the height of the point of dis- 
 charge from the average piston position (at half stroke), and h l 
 the height of the average piston position above the lower water- 
 level. If s is the stroke of the piston, then during the up 
 
 stroke the force P : gradually increases from F( h^ -- hy to 
 
 s\ 
 -f- W, and during the down stroke the force P 2 varies 
 
 The work that must be expended per double stroke is again 
 A = Pj* + P 2 s = (FA l7 + Th 2 y)s = F(A X + h 2 )y = Fshy = Vhy = G/* 
 
 where again h = h l + h 9 is the total lift, V = Fs is the volume 
 discharged per double stroke, and G = V<y the weight of the 
 water discharged. 
 
 Consequently in plunger pumps the work is distributed 
 over both piston strokes, while in bucket pumps the work is 
 only performed during the up stroke of the piston. 
 
 16. Plunger Pumps (continued). When the open end of 
 the pump barrel points downward, the piston rod must either 
 be guided through a stuffing box or it must also be pointed 
 
52 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 downward. The former arrangement is shown in Fig. 36 and 
 the latter in Fig. 37. The first figure represents a combined 
 suction and lift pump, the solid piston causing the work 
 to be distributed over the up and down stroke, which is not 
 the case with the lift pumps shown in Fig. 32. E is the 
 suction pipe with the suction valve V, and S the delivery pipe 
 with the delivery valve W. During the down stroke of the 
 piston K water is sucked in through E, and during the up 
 stroke it is lifted through' S ; in the first case, of course, the 
 
 Fig. 36. 
 
 valve V opens, and in the second, which is shown in the 
 figure, the valve W opens. In Fig. 37 a force pump having 
 the supply pipe E is represented in its down stroke. The 
 peculiarity of this arrangement is that the piston operates 
 below the lower water-level, while in pumps with suction 
 pipes its place of action is above this level; consequently 
 in pumps with supply pipes, the perpendicular distance 7^ 
 between the lower water-level and the average piston position 
 will be negative if it be regarded as positive in pumps with 
 suction pipes. If h 2 again represents the height of the upper 
 water level B above the average piston position, and F the 
 
ii ELEMENTARY ACTION OF RECIPROCATING PUMPS 53 
 
 area of the piston, then for the pump with suction pipe (Fig. 
 36) pushing down the piston will require a force 
 
 on the other hand, in the pump with supply pipe (Fig. 37) the 
 same force will be 
 
 while the force needed to lift the piston in both cases is 
 
 The work needed per double stroke is, therefore, in the first 
 pump, 
 
 A = P x s + P 2 s = Fs^ + A 2 ) 7 = V(^ + A 2 ) 7 , 
 
 and in the second pump 
 
 A = P lS + P 2 s - Fs(A 2 - hjy = Y(A 2 - hjy ; 
 
 but as the difference of level in the first case is 
 
 h = h 1 -t'hp 
 and in the second case 
 
 h = h 2 ~ h v 
 
 the work in each of the pumps per double stroke will be 
 expressed by 
 
 The pump barrels are not always vertical, but frequently 
 horizontal or inclined ; it is quite evident, however, that this 
 does not alter the mode of action nor the driving force. 
 
 17. Double Pumps. In order to obtain a continuous 
 discharge of water we may employ either one double-acting pump, 
 or a combination of two single-acting pumps. 
 
 A double-acting suction and force pump is shown in Fig. 
 38. It has a suction pipe E and a delivery pipe S, like most 
 single-acting pumps ; but the pump barrel C is connected at 
 each end with the two pipes E and S, and there are, therefore, 
 four communicating pipes leading off from the barrel C, the 
 pipes containing two suction valves V and V 1} and two delivery 
 valves W and W T . As the suction valves open inward and 
 the delivery valves outward, it is easy to see that during 
 each stroke a suction valve will be open on one side of 
 
MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 the piston and a delivery valve on the other. The figure 
 shows the piston on the up stroke, during which the valves 
 Y and W x are open. On the other hand, when the piston 
 is on the down stroke the valves V 2 and W are open ; but in 
 both cases the water is sucked in through K and driven up 
 through S. 
 
 The same object is attained by a combination (Fig. 39) of 
 
 Fig. 38. 
 
 two single-acting pumps whose pistons K and Kj alternately 
 move up and down. In the pump shown the four valves V 
 and V r W and W l are in the same valve chamber GGr l5 and 
 their seats are in two planes at right angles to each other. 
 The figure shows the machine with the left piston K moving 
 downward and the right piston K x moving upward, conse- 
 quently the valves V and W T are open while V x and W are 
 closed, and as a result the water passes from A through E to 
 C, and from C^ through S to B. The two systems of pumps 
 
HO Tlf,.- 
 
 ELEMENTARY ACTION OF RECIPROf^rfrG ^UMPS 55 
 
 * M v/ j" i_ k \ 
 
 (Fig. 38 and Fig. 39), besides a continu\^usrplischarge, possess 
 
 the advantage that the force to be exerted^Hfo^ piston K is 
 the same for the up and the down stroke, narnely, P = F//7, 
 where li again represents the total lift or different 
 and F the area of the piston. 
 
 In bucket pumps (Fig. 32 and Fig. 33) the same condition 
 can also be brought about by using a piston rod of correspond- 
 ingly large diameter. Let F.,^ be the sectional area of this rod, 
 then during the down stroke it displaces the volume of water 
 FjS, and consequently during the up stroke only the volume 
 (F F x )s is discharged ; therefore, if the same quantity of water 
 is to be discharged during the down as during the up stroke, 
 we must make 
 
 F! = F - F 1? that is, F x = JF. 
 
 Accordingly, if d represents the diameter of the piston and 
 d l that of the piston rod, we have 
 
 d^ = %d 2 , therefore d^d \/| = 0'707d. 
 
 Such distribution of the discharge is of course accompanied 
 by a corresponding distribution of driving force. In this case 
 the force necessary to lift the piston is 
 
 on the other hand, the force needed on the down stroke, since 
 the water acts with a head \ on the lower surface F and 
 with the same head on the upper surface F F 1 , will be 
 
 or for the case that F X = 
 
 In case we should have \ = h, that is, \ = (Fig. 32, I.), we 
 should get Pj = P 2 = -J-F/^. In general, if we wish to expend 
 the same force for the up and the down stroke, we place 
 
 R = P 9 and obtain the ratio of the cross-sections -J= = - ; 
 
 2fi 2 
 
 in this case the discharge is of course unequal for the two 
 strokes. 
 
 In order to maintain a practically uniform discharge from 
 
56 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 the delivery pipe, as is necessary in fountains and fire-engines, 
 for instance, air chambers are introduced, the mode of action 
 of which will be described hereafter. 
 
 18. Pump Cylinder and Pipes. The pump cylinder or 
 barrel is the vital part of every purnp, and its proportions are 
 of prime importance to the performance of the machine. 
 Pump cylinders are usually made of cast-iron, though occasion- 
 ally for small diameters brass or even zinc is employed ; 
 wooden pump barrels are only used for small lifts in hand 
 pumps for agricultural or building purposes ; in such cases 
 oak or maple is usually the material chosen. Occasionally, in 
 the crudest forms of pumps employed for building purposes, 
 the barrels are made square, being put together of four boards ; 
 with this exception, however, pump cylinders are always made 
 of circular cross-section. This form is not only most easily 
 produced, but also best suited for making the piston water- 
 tight. With the latter object in view, the cylinder must 
 always be bored accurately, whereas the inside of the water 
 pipes is never finished. The diameter of the pump barrel, of 
 course, ranges within very wide limits, according to the 
 quantity of water to be lifted. For example, in pumps which 
 supply hydraulic presses or feed accumulators or steam boilers, 
 the plungers are often only 20 mm. [0'79 in.] in diameter, 
 while in those used for draining low lands they may reach 
 2 m. [6 '5 6 ft.] or more. 1 The length of the cylinder is, as in 
 steam engines, at least equal to the length of stroke plus the 
 depth of piston ; the stroke must be determined for each 
 particular case, in accordance with the prescribed piston speed 
 and the desired number of strokes. As a rule, the thickness 
 of the walls of the pump barrel cannot be determined accord- 
 ing to the formulae for strength from the pressure of the fluid, 
 for by this method such slender dimensions would be obtained 
 in most cases that the practical execution would be impossible. 
 But, in order to furnish ample resistance to the great torsional 
 stress accompanying the boring process, and to make re-boring 
 possible when they are worn, the walls of cast-iron cylinders 
 are seldom made less than 20 mm. [0*79 in.] thick; for 
 greater pressures and diameters we can use the formula given 
 
 1 The pumps used in draining the low lands near Bremen have cylinders 8 ft. 
 in diameter ; see Berg, Die Entwdsserung des Blocklaiides, 1864. 
 
ii ELEMENTARY ACTION OF RECIPROCATING PUMPS 57 
 
 in Weisbach's Mechanics, vol. ii., under the head of Water- 
 Pressure Engines, for the thickness of cylinder walls : 
 
 e = 0-0025 pd + 32 mm. [e = 0*00017 pd + 1'26 ins.] 
 
 where p is the pressure in atmospheres [Ibs. per sq. in.], d the 
 diameter of the cylinder, and c the thickness of the cylinder 
 wall. 
 
 In all the better pumping arrangements the suction and 
 delivery pipes are of metal, either cast-iron, wrought -iron, 
 copper, or lead. It is only in small wells that we find pipes 
 made of wood. The diameter of the pipes depends on the size 
 of the pump barrel and on the piston speed, which latter 
 is commonly chosen at 0'3 or 04 metre [1 to 1J ft.], although 
 in mining pumps with long strokes the piston velocities may 
 reach 1 m. [3 '2 8 ft.] or more. 1 Usually, the pipe diameters are 
 so proportioned as to give the water a velocity of about 1 m. 
 [3'28 ft.] per second. The pipes are made in lengths of from 
 3 to 4 m. [12 to 16 ft.], and either provided with flanges for 
 bolting the sections together or with a socket at one end 
 to receive the adjoining pipe, the joint in this case being made 
 by pouring in molten lead and then calking. 
 
 Special care should be taken to make the joints as staunch 
 and tight as possible, particularly in the suction pipes, as 
 a very small opening in the latter may endanger the entire 
 suction by admitting air ; in delivery pipes the only effect of 
 poor joints is the loss of water due to leakage. It is, of 
 
 1 In modern steam pumping machinery these speeds have been considerably 
 exceeded, experience having proved that advantages can be gained by increasing 
 the speed of the plunger. The principal advantage is that smaller steam cylinders 
 can be used for a given amount of work to be done, thus reducing the losses due to 
 radiation, and increasing the efficiency of the machine, which latter will occupy 
 less space and be cheaper to procure. In an article entitled "A Few Examples 
 of High Grade Pumping Engines," by E. D. Leavitt, in the Journal of the New 
 England Waterworks Association, a number of modern pumping engines pro- 
 duced by able builders both in Europe and America are enumerated, in which the 
 velocity of the plunger ranges from 1'28 to 2'29 m. [4 '2 to 7'5 ft.] per second. 
 The latter is the plunger velocity in a large pumping engine built by I. P. Morris 
 and Co. of Philadelphia for the Calumet and Hecla Mines. Velocities of more 
 than 2 m. [6 '56 ft.] are likewise used in pumping engines built by the Quintard 
 Iron Works of New York for Boston, Mass. ; by the Hannov. Maschmenbau A. 
 Gesellschaft for Barmen, Germany ; by Ehrhardt and Schumo of Saarbriicken 
 for Eschweiler, Germany ; and by L. Lang of Buda-Pesth for the latter city. 
 THE TRANSLATOR. 
 
58 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 course, evident that suction pipes are from without subjected 
 to a pressure that tends to collapse them, whereas delivery 
 pipes are acted upon from within by a pressure which strives 
 to burst them. 
 
 The thickness of metal in pipes is not generally determined 
 from considerations of strength, but with reference to the pro- 
 cesses of manufacture. For cast-iron pipe it varies from 10 
 to 20 mm. [0'4 to 0'8 in.], according to the diameter of the 
 pipe, and for drawn wrought-iron pipe from 3 to 5 mm. [0*12 
 to 0'2 in.] for diameters varying from O m 04 to 0*2 m. [T6 to 
 8 ins.] Pipes of larger diameter are sometimes made of 
 riveted plates like steam boilers, but are not in favour because 
 of their rapid corrosion when used with pumps. The smallest 
 pipes are of sheet-copper soldered, or are pressed out of lead. 
 Wooden suction pipes have a thickness varying from 50 to 
 80 mm. [2 to 3^- ins.] ; their inside diameter rarely exceeds 
 0*10 m. [4 ins.] When the pressure is considerable the 
 thickness & can be determined from the following empirical 
 formulae : 
 
 For cast-iron 8 = Q'00'25pd + 12 mm. [8 = O'OOOlv pel 
 
 + 0-47 ins.] 
 wrought-iron 8 = Q'OQOQpd + 4 mm. [8 = O'OOOQGl pd 
 
 + 0-16 ins.] 
 ,, lead 3 = 0-0040X J - 8mm. [8= 0*00027 X 
 
 + 0-315 ins.] 
 wood 8 = 0-0050 pd + 50mm. [8= 0'00034 pd 
 
 + 1-97 ins.] 
 
 where p is expressed in atmospheres [Ibs. per sq. in.], and d is 
 the inside diameter expressed in millimetres [inches]. 
 
 In order to facilitate the influx of the water from the 
 sump or lower level into the suction pipe, the inlet of the latter 
 is rounded so as to diminish the contraction of the entering 
 water ; this orifice is also provided with a strainer to prevent 
 impurities and foreign bodies from entering the pump. The 
 total area of the holes in the strainer is usually equal to two 
 or three times the cross-section of the suction pipe. When 
 the delivery pipes discharge into an open basin their upper 
 end is provided with a special discharging piece or nozzle 
 of suitable form. 
 
ELEMENTARY ACTION OF RECIPROCATING PUMPS 
 
 19. Pump Valves. Pump valves are placed in special 
 valve chambers, which communicate directly with the suction 
 and delivery pipes, and are provided with lateral openings 
 ordinarily closed by bungs, plates, or doors, in order that the 
 valves may be examined or repaired. In simple suction 
 pumps only one chamber is needed, for the suction valve, 
 since the delivery valve, which is here located in the piston, 
 can be seen and repaired from the discharging orifice ; in 
 the suction and lift pumps, on the other hand, there must 
 be a second chamber directly above the pump barrel, in 
 order that the piston may be reached when repairs are to be 
 made. 
 
 Pump valves are either simple or compound ; the latter are 
 used chiefly in large pumps in order -to obtain a large inlet 
 area together with prompt action. The simple valves are either 
 clack valves or lift valves. The clack valves are fastened at 
 one edge, and, when opening and closing, work like a trap- 
 door on its hinges ; lift valves move along their geometrical 
 axis when they open and close ; to this class belong cone 
 (poppet) valves and loll valves. Cone valves have the form of 
 a low frustum of a cone, and ball valves are perfect spheres. 
 In the former case the valve seat is of course conical, and 
 in the latter it is spherical. Balance valves have been proposed 
 by Belidor ; these operate like balanced sluice gates, being 
 divided into two unequal parts by their horizontal axis, and 
 when they open one part is raised above the seat while the 
 other recedes below it. 
 
 Valves must be so arranged as to offer the least possible 
 resistance to the passage 
 of the water. For this 
 reason the valve opening 
 must be of a size corre- 
 sponding to the cross-section 
 of the valve chamber, and 
 the lift of the valve must 
 correspond to its diameter. 
 Let r represent the radius 
 CD of the valve chamber or 
 pump barrel N (Fig. 40), 
 r^ the mean radius CB of a lift valve BB, this being equal to 
 
 Fig. 40. 
 
 Fig. 41. 
 
60 MECHANICS OF PUMPING MACHINERY CHAP, 
 
 the mean radius of the passage A A, and let s be the lift AB of 
 the valve, then the area of the circular orifice AA is 
 
 the area of the annular space between BB and DD is 
 
 *(r--r*), 
 and that of the cylindrical surface ABBA 
 
 Now, in order that the water may pass through these aper- 
 tures with equal velocity, we must have Tny = 7r(r 2 ?y) = 2-Tn'jS, 
 which gives 
 
 r 2 = and s = -l, 
 
 1 2 2 
 
 i.e. 
 
 r^r vj = 0'707r and s = f *^J = 0'35r. 
 
 If the clack valve BS (Fig. 41) is open and makes the 
 angle ASB = /3 with the valve seat, its projection on to a plane 
 at right angles to the axis of the pipe is an ellipse with the 
 semi-axes i\ and i\ cos ft, and the average height of the open- 
 ing is EC = r-L/3, which gives for the cross - sections of the 
 current 
 
 Trfj 2 , 7i-r 2 - Tr^ 2 cos P, and 2;rr 1 2 /?. 
 By placing 
 
 7T? 1 ! 2 = :r(r 2 - r x 2 cos P) = 2-n-r^p 
 we now obtain 
 
 P = , i.e. P = 28 J and r*(l + cos /?) = r\ 
 or 
 
 r 
 
 r, = 
 
 + cos p 
 or approximately 
 
 Hence we can derive the following constructive rules : the 
 mean radius of the valve and its orifice should be fully ^ of 
 the diameter of the valve chamber or pump barrel ; moreover, the 
 
irf 
 
 n?i 
 
 " 
 
 ELEMENTARY ACTION OF RECIP1 
 
 61 
 
 ttf> 
 
 , - 
 ..J^fTOP 
 
 lift of a lift valve should be equal to half \ 
 and finally, the angular motion of the 
 
 20. Pump Valves (continued). The a 
 simple lift valves is shown in Figs. 42 and 43. 
 A is the valve seat, B the conical valve disc, M the pipe 
 through which water is led to the valve, and N the valve 
 N 
 
 Fig. 42. 
 
 Fig. 43. 
 
 chamber. In order that the valve may shift itself exactly in 
 its geometrical axis it is either provided with a stem CD (Fig. 
 42), or with three or four radial wings as in safety valves, or 
 it receives a cylindrical guiding surface with perforations or 
 passages, as at D (Fig. 43). 
 
 In the first case the stem is guided through two lugs, 
 C and D, rigidly united to the valve seat by the arms E and 
 
 Fig. 44. Fig. 45. 
 
 F ; in the other two types the cylindrical surface EE under the 
 valve seat serves to guide the valve. To prevent the valve 
 from lifting too high it is provided with a projection K, which 
 strikes against a stop ; for example, in Fig. 42 against the 
 yoke EE, and in Fig 43 against a lug L on the cover of the 
 valve chamber. 
 
 Clack valves are shown in Figs. 44 and 45. The simple 
 clack valve in Fig. 44 is of leather, so cut out as .to form a 
 
62 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 D 
 
 circle, with a radial lapping piece B, so that it not only covers 
 the orifice A of the pipe M, but can be fastened between M 
 and N by means of this lap. In order that the leather clack 
 may have the necessary stiffness, it is covered with two iron 
 plates, the upper C being the larger, and, like the leather disc, 
 projecting 20 to 30 mm. [0'8 to 1'2 ins.] beyond the edge of 
 the orifice A. The lower plate D is somewhat smaller than 
 the orifice, so that it can enter the latter without obstacle. 
 One or more rivets or bolts firmly unite the plates and the 
 intermediate leather. 
 
 In very large pipes, instead of a single circular plate, two 
 semicircular or segment-shaped plates are em- 
 ployed, as in Fig. 45. Here the leather clack 
 CC rests on a diametral bar, to which it is 
 fastened by a second cross bar SS, the clack as 
 before being covered above and below by iron 
 plates. 
 
 To facilitate the opening of heavy valves, 
 they are placed in an inclined position, par- 
 ticularly if they cover orifices in horizontal 
 pipes. Such valves are often provided with 
 special hinges, and then work exactly like trap 
 doors. The cross-section of such a valve for 
 closing a rectangular pipe is shown in Fig. 46. 
 Here AB is the clack, AD an ear attached to 
 it, EF an ear attached to the pipe, and C the pin passing 
 through both, and constituting the axis of rotation. 
 
 In large pumping engines double- seated 
 valves, resembling double-seated steam valves, 
 have recently come into use. The wide end 
 of the bell-shaped valve BDE (Fig. 47) rests 
 on the ring-shaped seat A, and the contracted 
 end on the disc-shaped seat F. Consequently, 
 when the valve opens, the water can flow 
 through two cylindrical orifices ABBA and 
 FEEF. Let r and i\ represent the radii CD 
 and CE of the valve orifices, and s = AB = FE the lift of the 
 valve, then the area of the passages will be given by 
 
 Fig. 46. 
 
TI ELEMENTARY ACTION OF RECIPROCATING PUMPS 63 
 
 Also let z represent the height of a water column measuring 
 the difference between the pressure of water on the upper and 
 lower surface of the valve, then the force with which the water 
 tends to lift the valve is given by 
 
 and if this force is greater than the weight G of the valve, 
 i.e. if 
 
 the lifting will actually take place. 
 
 In suction valves z = b h 2 , that is, equal to the height b 
 of the water barometer less the height of suction h 2 measured 
 from the valve seat to the lower water-level. 
 
 The arrangement of such a double -seated pump valve is 
 shown in Fig. 48. Here also BDE is the movable bell or 
 valve proper, A the wide ring-shaped valve seat, and F the 
 narrow disc-shaped seat. The 
 ring-shaped surfaces of con- 
 tact must be made to fit ISi^^ 
 accurately ; sometimes the 
 valves are allowed to strike 
 against rings a and / which 
 are of wood or some soft 
 metal. The wings L support 
 the disc F and guide the 
 valve, the latter purpose 
 being also served by the 
 
 cylinder C resting on F, the valve enclosing this cylinder 
 with a ring ; the disc k bolted to C prevents too great a lift of 
 the valve. 
 
 Ordinary double-seated valves require considerable excess 
 of pressure in order to open, and unless their lift is small they 
 strike hard against their seat at the end of the strokes. To 
 overcome these objections and also lessen the resistance to the 
 passage of the water, other valves have more recently been 
 designed. Among these are those designed by ffosking, Jenkin, 
 Simpson, and others, and provided with several passages. 
 
 Hashing* 8 valve, of which a vertical section is given in Fig. 
 49, deserves special attention. This valve consists of a series 
 
64 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 of ring-shaped valve seats A, B, C . . ., which lie over each other 
 in the form of a pyramid, and are covered with ring-shaped 
 valve clacks a, b, c. . . . The clacks are of leather or rubber, 
 either in the form of complete rings or sections of rings. Each 
 clack is held in position by the valve seat above it, and all 
 the valve seats are clamped together to a rigid whole by means 
 of a bolt DE. Instead of clacks, rubber balls a, I, c have been 
 employed, 1 the balls resting in conical seats which are enclosed 
 by chambers of the kind shown in Fig. 50. In the large 
 
 Fig. 49. 
 
 Fig. 50. 
 
 "box pumps described below ( 24), a series of valves are like- 
 wise employed for the admission and discharge of the water. 
 
 NOTE. The manner in which the excess of pressure necessary 
 to open the valves is obtained is explained in Weisbach's Mechanics, 
 vol. iii. 1, ch. ix. 
 
 21. Pump Pistons. The solid pump pistons, like the 
 driving pistons in water -pressure engines, consist of a low 
 cylinder called the piston head, with its surrounding packing ; 
 or they have the form of a long cylinder, without packing, 
 called the plunger, the requisite tightness being then obtained 
 by a stuffing box on the pump barrel. The piston head is 
 either made of wood which has been boiled in oil, or it is cast of 
 iron or bronze. In ordinary pump pistons the packing is simply 
 
 1 See article on "Improvements in Pump Valves," in the Artizan, vol. xvi., 
 May 1, 1859. 
 
ELEMENTARY ACTION OF EECIPEOTHG PUMPS 65 
 
 a strip or disc of leather, or several strips 
 iu air and hot- water pumps of steam engines, where leather' 
 would be rapidly injured by the heat, hempen packing is em- 
 ployed. The width of the packing ring may be taken equal 
 to 6=50 mm. -f Old [6=1'96 in. + 0'ld], where d is the 
 diameter of the piston. Evidently pistons for double-acting 
 pumps must have two packing rings. Such a piston is shown 
 in Fig. 51. Here A is the piston head proper, BC its piston 
 rod, D one packing ring or cup leather, and F the other ; E the 
 upper cover of the packing, and G the lower ; and S a nut at 
 the lower threaded end of the piston rod, by means of which 
 all these parts can be pressed against the collar E on the 
 
 Fig. 52. 
 
 piston rod, and thus become firmly united. In valved pistons 
 the heads are provided with rectangular holes for letting the 
 water through, and are fitted with clack valves covering the 
 upper ends of these holes. In order to facilitate as much as 
 possible the passage of the water, the latter are made as large 
 as is practicable, and are rounded off at the end where the 
 water enters. When the end of the piston rod is straight 
 and not forked, the head receives two passages and two clack 
 valves. 
 
 A wooden valved piston, with forked rod and one passage, 
 is shown in Fig. 52. Here A is the piston head, CBC the 
 fork constituting the end of the piston rod, and CS the tines 
 of the fork passing through the piston head and bolted to the 
 latter as at S. Moreover, D is the sewed leather packing 
 
 F 
 
66 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 fastened to the piston head by an iron ring E driven on from 
 below ; F is a second iron hoop which, together with the first, 
 protects the piston head from injury. Finally, V is the leather 
 clack covered with sheet-iron, and secured by nails or screws 
 to the piston head at N. To prevent the ring E from slipping 
 off, wooden or leather pieces G are nailed into the groove 
 occupied by the ring before it was driven in place. 
 
 in. 
 
 
 Fig. 54. 
 
 An iron valved piston, with straight rod and two passages, is 
 shown in Fig. 53. Here A is the cast-iron piston head, B the 
 packing which is secured to the conical outer surface of the 
 head by the bevelled wrought-iron ring C. Moreover, DE is 
 the piston rod with the cross-piece F forged on, and GG is a 
 slotted piece slipped on the end of the piston rod, while H is 
 
II 
 
 ELEMENTARY ACTION OF RECIPROCATING PUMPS 
 
 a key by means of which the head is wedged in firmly between 
 the two cross-pieces, and thus rigidly united to the piston rod. 
 Finally, KK are two leather clack valves stiffened by iron 
 plates, and covering the upper ends of two segment -shaped 
 passages in the piston. 
 
 In the air and hot-water pumps of steam engines, rubber 
 clack valves have proved most satisfactory, since they close more 
 perfectly than metal valves. A pump piston with such rubber 
 valves is shown in Fig. 54, I. The piston head here consists 
 of a ring A, connected by four arms to the hub B, through 
 which the end of the piston rod CS passes. Hempen packing 
 D is employed as in the earlier forms of steam pistons. The 
 rubber disc V, constituting the valve, rests on a gridiron frame 
 E, supported by the arms of the head, and, when lifting, strikes 
 against a curved stop or 
 disc F attached to the piston 
 rod. In Fig. 5 4, II., is shown 
 the foot or suction valve V r 
 which is arranged exactly 
 like the piston valve ; and 
 in Fig. 54, III., the gridiron 
 plate E 1 is visible. To pre- 
 vent the valve discs from 
 stretching, a layer of cloth 
 is embedded in the rubber. 
 
 Pistons for air and hot- 
 water pumps sometimes 
 have metallic double valves, 
 as in Fig. 55, where the 
 piston head A is formed like that in Fig. 54, but the valve V 
 is a dished cast-iron or brass plate, with a hub C movable along 
 the turned portion DE of the piston rod, up to the shoulder D. 
 The valve seats are formed by two brass rings and inserted 
 in the piston head, and ground to make a tight joint with the 
 dished plate. 
 
 Metallic piston packing, such as is now generally used in steam 
 pistons, is never applied to pumps, because experience has shown 
 that it is rapidly destroyed by the sand and other solid particles 
 carried along by the water. On this account rubber and leather 
 valves are to be preferred to metallic valves when dirty water is 
 
 Fig. 55. 
 
68 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 pumped, as that which collects in excavations, for instance ; but for 
 high pressures or temperatures neither rubber nor leather valves 
 can be used. 
 
 22. Suction and Lift Pumps. The arrangement of a 
 suction pump, as used in mines, is shown in Figs. 56 and 5*7. 
 
 Fig. 57. 
 
 The pump barrel here consists simply of a cast-iron pipe 
 resting in a socket on the valve chamber AB, which is at 
 the top of the suction pipe B, and at the upper end fitting 
 into another socket, which is a part of the discharge pipe DE. 
 Both valve chamber and discharge pipe are supported by 
 timbers F and G, and the hand hole through which the 
 suction valve V can be examined and repaired is closed by 
 
ELEMENTARY ACTION OF RECIPROCATING PUMPS 
 
 69 
 
 D 
 
 a wooden bung S ; the piston rod KL is attached to an arm 
 
 LM, which is bolted to the main rod MX, 
 
 that passes down the shaft. To prevent this 
 
 rod from bending in consequence of the 
 
 eccentric action of the pump, it is guided 
 
 between two rollers EK. The lifted water 
 
 is discharged at D into the tank 0, into 
 
 which the next higher suction pipe T enters. 
 
 In case the pump MOB discharges more 
 
 water into the tank than the next pump 
 
 is able to lift, the surplus is returned through 
 
 an overflow pipe UZ to the lower tank, 
 
 from which the suction pipe B draws its 
 
 supply. 
 
 In some mines pumps are employed which 
 differ from that just described, chiefly in that 
 a series of pipes are placed on the top of the 
 barrel, thus together with the latter forming 
 a very long delivery pipe. The vertical sec- 
 tion of such an arrangement is shown in 
 Fig. 58. Here C is the pump barrel, AB 
 the suction pipe, DE the delivery pipe, B 
 the chamber for the suction valve V, and S 
 the plate covering the hand hole. In order 
 that the piston and its valve may be readily 
 repaired, a second chamber D is placed over 
 the pump barrel, and has a lateral opening 
 which is likewise covered by an iron plate T. 
 The lower end of the suction pipe is enlarged 
 and provided with a number of small perfora- 
 tions, so as to exclude solid matter. 
 
 In bucket pumps the delivery pipe may 
 also be connected to the side of the barrel, 
 provided the piston rod is passed through a 
 stuffing box. A vertical section of such an 
 arrangement is shown in Fig. 59, where C 
 is the pump barrel, with a lateral pipe D on 
 which the delivery pipe is placed, and B is 
 the valve- chamber to which is attached the 
 pipe A that connects with the suction pipe. 
 
 S 
 
 Fig. 58. 
 
 The whole rests 
 
70 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 on the cast-iron base E supported by the beams S. The valve 
 seat consists of two rectangular frames G, which are inclined 
 at an angle of 45 to the vertical partition BF ; W are brass 
 clack valves with lugs cast on that strike against the vertical 
 sides of the chamber when the valves are open. The piston 
 head K shown in half section is a short brass cylinder provided 
 
 with a groove for the packing L, 
 and with a vertical partition M, 
 in which the semicircular valve 
 plates WW are hinged. To render 
 the discharge as uniform as pos- 
 sible, the piston rod OP ter- 
 minates in a hollow plunger NO, 
 to which the bucket is attached 
 by means of a yoke and a bolt 
 H. If the sectional area of the 
 plunger is equal to half that of 
 the barrel, the pump will dis- 
 charge as much water on the 
 down as on the up stroke ; and 
 if at the same time the height of 
 suction is small compared with 
 the height of delivery, the driv- 
 ing force needed during the up 
 stroke of the piston will not be 
 much greater than that required 
 on the down stroke (see 17). 
 
 In place of the ordinary 
 valved piston there may be sub- 
 stituted an externally finished 
 pipe provided with an internal 
 valve, and guided by stuffing boxes located in the ends of the 
 suction and delivery pipes. 
 
 The telescope pumps designed by Althans and Rittinger are 
 of this class. The former were employed in the mine Pfingst- 
 wiese near Ems, and were driven by a water-pressure engine. 
 Their peculiarity consists in having a piston composed of two 
 pipes, one within the other, so arranged that, according as the 
 service may require, either both pipes or the inner alone may 
 be reciprocated. The arrangement of a Rittinger pump as 
 
 Fig. 59. 
 
II 
 
 ELEMENTARY ACTION OF EECIP 
 
 71 
 
 r L.ii 
 
 einintz 
 
 employed at the mines near Joachirnstl^J, and 
 
 shown in the vertical section ^^in Fig. 60. 
 V is the suction valve at the eta 
 E [^ E pipe ; W the delivery or piston valve in the 
 
 piston CD ; B the pump barrel proper ; E the delivery 
 pipe ; C is the stuffing box on the pump barrel B, 
 which guides the lower end of the tubular piston ; 
 D and D is the stuffing box at the upper end of the 
 latter, surrounding the turned end of the delivery 
 pipe E. The manner in which the tubular piston 
 CD is connected to the pump rod is clearly shown 
 by the sections I. and II., Fig. 61. Here also W 
 is the piston valve, G- the pump 
 rod, arid K a flanged bracket 
 cast on the valve chamber and 
 bolted to the pump rod. The pet- 
 cock H serves to let the water 
 out of the valve chamber. 
 
 In Althans' pumps the tubu- 
 lar piston is connected to the 
 pump rod by means of two 
 brackets and auxiliary piston 
 rods, thus rendering the action 
 of the driving force perfectly central. 2 In order 
 that this pump may discharge as much water on 
 the up as on the down stroke, the area of the outer 
 cross-section of the delivery pipe is made equal to 
 half that of the tubular piston, i.e. the diameter of 
 B|^^g|B the former = x/-J-= 0'707 of the diameter of the 
 latter. In common with the plunger pumps, these 
 constructions possess the advantage of being easily 
 taken care of and lubricated, and besides they are 
 well adapted for pumping water containing slime or 
 sand. 
 
 An excellent suction and lift pump with solid 
 Flg ' 60 ' piston is shown in Fig. 62. It is in operation at 
 Huelgoat in Brittany, and is driven by a water-pressure engine at 
 
 1 See Polytechn. Centralblatt, 1851 ; also Rittinger's Erfahrungen im Berg- und 
 hutten- mdnnischen Maschinenwesen, etc., 1856. 
 
 2 See Prechtl, Technolog. Encydopadie, Bd. 11, Art. on Pumps. 
 
 Fig. 61. 
 
 Cfe C 
 
72 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 Gig 
 
 the rate of five and a half double 
 strokes per minute, the length of 
 stroke being 2*3 m. [7'54 ft.] The 
 aforesaid water-pressure engine has a 
 fall of 61 m. [200 ft], and a driving 
 piston 1'2 m. [47'24 ins.] in diameter, 
 while the pump driven by it has a 
 piston 0-422 m. [16 '61 ins.] in dia- 
 meter, and lifts the water to a height 
 of 230 m. [750 ft.] In the figure, 
 AB is the suction pipe, which has a 
 diameter of 0'275 m. [10'83 ins.], 
 B the chamber for the suction valve, 
 E that for the delivery valve, and 
 FG the lower portion of the delivery 
 pipe. The entrance to the suction 
 pipe is about ^ m. [1'64 ft] below 
 the lower water-level, and is provided 
 with two clacks A, acting as foot 
 valves. The height of suction is about 
 6 m. [19 '7 ft], and consequently the 
 height of delivery is 230-6 = 224 
 m. [734-7 ft] Through the short 
 pipe D the valve chamber B com- 
 municates directly with the pump 
 barrel CD, which is open at the 
 bottom, and, like the piston head 
 and rod KS, is made of brass. In 
 order to make both piston and 
 piston rod air- and water-tight, the 
 former has leather packing both 
 at the top and bottom, and the 
 latter is guided through a stuffing 
 box S, filled with leather discs. The 
 connection between the delivery pipe 
 and the valve chamber E is also 
 effected by a leather -packed joint, 
 so that, after unscrewing the 
 bolts, the distance pipe E may be 
 pushed upward, and the cham- 
 
ii ELEMENTARY ACTION OF RECIPROCATING PUMPS 73 
 
 ber B removed whenever it is necessary to put in new 
 valves. 
 
 The pump is also provided with a small pipe MNO, by 
 means of which, without opening the pump valves, the space 
 between the latter can be connected with the delivery pipe as 
 well as with the suction pipe, and thus the whole apparatus 
 be filled with water before starting. If the delivery pipe is 
 full, and the cocks M and 0, as well as the pet-cock that 
 connects the chamber B with the atmosphere, be opened, then 
 the water will flow by way of MO into the suction pipe AB, 
 and the air enclosed in the latter will lift the valve and flow 
 through the pet-cock into the atmosphere. To fill the pump 
 cylinder and valve chamber BE with water, the cock N is also 
 opened and kept so until water flows out of the pet-cock. 
 Finally, there is attached to the suction pipe a small branch 
 pipe closed by a sort of safety valve by which leakage of the 
 valves is indicated. When the suction valve leaks the suction 
 pipe will be in communication with the delivery pipe during 
 the up stroke of the piston, and, as a consequence, the excess 
 of pressure in the suction pipe will raise the test valve U, and 
 allow water to flow out. The same would be the case when 
 the delivery valve leaks, provided the cocks N and are 
 opened when the pump is at rest. 
 
 As long as it is perfectly filled with water, the pump runs 
 smoothly, the piston speed at the beginning of each up and 
 down stroke being equal to zero, then gradually increasing 
 until about half stroke, and finally diminishing until it again 
 becomes zero. But if air has collected in the valve chamber 
 BE in consequence of leakage through the packing, then the 
 delivery valve fails to open until the air has been compressed 
 to a certain degree and the piston has assumed a considerable 
 velocity. The whole mass of water in the delivery pipe must 
 then suddenly assume this velocity, with the result that a 
 severe shock is experienced by the apparatus. 
 
 23. Suction and Force Pumps. The force pumps press 
 the water upward during the down stroke of the piston, and 
 consequently they cannot be directly driven by long piston 
 rods, which would be apt to bend ; they are therefore employed 
 only when the pump is near the prime mover, or when the water 
 can le pressed upward by the weight of the descending rod. At 
 
74 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 the present day plungers, as at A, Fig. 63, are mostly em- 
 ployed in force pumps, owing to the ease with which their 
 packings can be maintained. In the pump here shown the 
 delivery valve C is composed of one, and the suction valve B 
 of two, inclined clacks. During the up stroke of the plunger 
 the pressure in the pump barrel is below that of the atmo- 
 sphere, and, as a consequence, the water drawn in is partially 
 
 Fig. 63. 
 
 Fig. 64. 
 
 freed from the air it contains. To prevent the air from 
 accumulating in the cylinder, which would materially reduce 
 or perhaps destroy the suction, the diameter of the pump 
 barrel is made no larger than that of the plunger. As, how- 
 ever, a small quantity of air is liable to collect under the 
 stuffing box, the plunger is, for its removal, provided with a 
 narrow passage D, which connects the interior of the pump 
 with the atmosphere whenever the cock E at the upper end is 
 
ii ELEMENTARY ACTION OF RECIPROCATING PUMPS 75 
 
 open. Evidently this cock must be opened only during the 
 down stroke of the piston if the air in the cylinder is to be 
 removed, for in case it were open during the up stroke merely 
 air would be sucked in instead of water. Occasionally an air- 
 cock of this description is placed on the pump barrel, and it is 
 then possible by opening the cock to destroy the action of the 
 pump without interrupting the motion of the piston. A 
 simple means of preventing air from collecting in the barrel 
 consists in placing the valve chest close to the stuffing box, as 
 in the boiler feed-pump shown in Fig. 64. Here no space 
 exists for the air to collect in, for as soon as it is freed it 
 passes through the delivery valve C to the delivery pipe G-. 
 The water drawn from the suction pipe F through the suction 
 valve first fills the cylinder D, and then, during the down 
 stroke of the piston, is forced through the delivery valve to 
 the delivery pipe. Consequently the piston A must not 
 exactly fill the cylinder D, since there must be sufficient space 
 between the piston and the wall of the cylinder to enable the 
 water to pass from the latter to the valve chamber. A special 
 advantage of the construction just given is, that by removing 
 the cover H both valves are at once accessible, the delivery 
 valve C being so large that the suction valve B below it can 
 be taken out through the seat of C. Also in leading the 
 suction pipes from the pump-well it is necessary to carefully 
 avoid leaving high places in the pipes where air can collect, 
 the best plan being to so arrange the suction pipe that it shall 
 everywhere slope up- 
 ward toward the pump 
 in order that the air 
 may be continually re- 
 moved by the latter. 
 
 For the automatic 
 and continual removal 
 of air from a pump 
 barrel, the air -escape 
 designed by Reuleaux 
 can be used to ad- 
 vantage. This device is shown in Fig. 65, and consists 
 essentially of a double-seated ball valve V, having a lift of but 
 3 to 4 mm. [0*12 to 0'16 in.] The apparatus is attached to 
 
76 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 the pump by means of the screw C, and its cock A is left open. 
 On its inward stroke the piston drives the air from the pump 
 barrel into the pipe cb, and this air lifts the ball valve Y from 
 its lower seat, the ball falling back to the seat during the 
 return stroke. On the following inward stroke the ball is 
 again lifted, and thus receives an oscillating motion, which 
 continues until the pipe cb becomes filled with water, which 
 
 will keep the ball pressed against its upper seat during both 
 strokes of the piston. 
 
 24. Double -Acting Pumps. The so-called box pumps, 
 designed by the Dutch engineer Fynje, have been employed 
 to advantage for draining low lands. They differ from 
 ordinary pumps in having their valves located outside the 
 barrel on a separate box. The vertical section of such a 
 double-acting box pump is given in Fig. 66. Here AB is the 
 pump barrel, open above and below, and resting on deck 
 
ii ELEMENTARY ACTION OF RECIPROCATING PUMPS 77 
 
 beams, KK is a solid piston packed with rings of wood, and 
 CDC 1 D 1 is a sheet-iron box surrounding the pump barrel, and 
 divided into two chambers by a partition EF fitting around 
 the barrel. The piston rod NO is connected to the piston by 
 a pin LL, and is surrounded by a pipe rigidly attached to the 
 piston head, and passing through a stuffing box S in the cover 
 CD of the pump box. The open sides CD l and Cf) of this 
 box are provided with cast-iron frames, on which the cast-iron 
 valves, covered with wood, are hung inclined. On one side 
 C 1 D the space enclosed by the box is in communication with 
 the lower water-level, and on the other CD.,^ with the upper 
 level, consequently the valves hanging at the first -mentioned 
 side are made to open inward, while those on the other side 
 open outward. This construction offers the great advantage 
 of a large valve area for admission and discharge of the water, 
 the velocity of which in the valve passages need be no greater 
 than that of the piston. The speed of the latter can therefore 
 be taken much greater than in ordinary cylinder pumps, in 
 which the sectional area of the valve passages is only a small 
 fraction of the piston area. 
 
 The piston therefore is allowed to work with an average 
 velocity of 1*5 m. [5 ft.] per second. 1 
 
 Another advantage peculiar to this type of pumps, and one 
 which renders them particularly adapted for draining low lands, 
 which always involves the raising of large quantities of water to 
 small heights, lies in the fact that they always lift the water to a 
 height h, representing the exact difference between the upper level 
 A (Fig. 67) and the lower B, without being affected by the varia- 
 tions of the two levels. This is accomplished by placing the pump 
 box K in a break in the dam enclosing the low land to be drained, 
 and at a sufficient depth to cause the lowest position of the level B 
 to remain above the valves. In this manner all unnecessary lift is 
 avoided, since the loss which is caused in some pumps by elevating 
 the water into a conduit placed at sufficient height above the upper 
 water-level to discharge into it does not here exist. This advantage 
 is of particular importance in drainage works, where every un- 
 necessary lift, no matter how small, even that due to the depth of 
 the discharging jet or stream, causes a noticeable loss of work. An 
 
 1 See article by Kriiger in Erbkam's Zeitschrift fur das Bauwesen, 1858, 
 "Die Trockenlegung von Landereien und die Kastenpumpen " ; also Polytechn. 
 Centralblatt, 1858. 
 
73 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 excellent plant of above description, constructed by Berg for 
 draining the Bremer Blocklands, is described in his pamphlet : Die 
 Entwasserung des Blocklandes. 
 
 Fig. 67. 
 
 A double-acting pump of more ordinary construction is 
 shown in Fig. 68. The pump barrel C has a diameter of 
 0'135 m. [5 '30 ins.], and is cast in one piece with the valve 
 chests and the short pipes B and D for admitting and dis- 
 charging the water. The piston rod is operated by a rotating 
 crank by means of a connecting rod L, the crank having a 
 length of 0*1 m. [3'94 ins.], and consequently the piston K a 
 
II 
 
 ELEMENTARY ACTION OF RECIPROCATING PUMPS 
 
 79 
 
 stroke of 0'2 m. [7*88 ins.] According to the position of the 
 two-way cock H, the water can be led to the pump either 
 through the pipe A or another pipe A : leading from some 
 other reservoir. The valve chambers are accessible from above, 
 
 ^nOIESFtf^ 
 
 Fig. 68. 
 
 through hand holes provided with removable covers. During 
 the up stroke of the piston the valves a and d are open, and 
 during the down stroke the valves a-^ and d l ; water is there- 
 fore drawn in at each stroke and forced into the delivery 
 pipe DS. 
 
CHAPTEE III 
 
 THEORY OF RECIPROCATING PUMPS 
 
 25. Quantity of Water Delivered. If F designates the 
 area and s the stroke of the piston, then the theoretical quantity 
 of water lifted by a single-acting pump per double stroke is 
 
 V = F S; 
 
 consequently when there are n double strokes per minute the 
 quantity discharged per second will be 
 
 __!L Fs - - Fv 
 ^~6(T l ~ 60 " 2' 
 
 2ns ns 
 
 where v = -^r = 7:7; represents the average piston velocity. 
 60 30 
 
 On the other hand, in a double-acting pump we have 
 
 But the quantity of water actually lifted is much smaller than 
 the theoretical quantity corresponding to the space swept 
 through by the piston (sometimes called piston displacement), 
 because even in the most perfect pumps an assignable quantity 
 of water runs back during each stroke. This is partly due to 
 leakage at the packing and valves, and partly to the gradual 
 and not instantaneous closing (slip) of the valves. If a small 
 leak exists in the packing or valves, the water will flow back 
 through it with a velocity w = *Jlgli, where h is the head or 
 lift; if /is the area of the opening, the quantity of water thus 
 lost per second will be 
 
 q =f w =f 
 
CHAP, in THEORY OF RECIPROCATING PUMPS 81 
 
 and the loss relatively to the quantity discharged 
 
 Consequently the loss of water due to leakage at the packing 
 and valves becomes greater the smaller the area F and 
 velocity v of the piston, and the greater the lift h. For this 
 reason pumps which are less perfectly made are run faster 
 than the more perfect ones, and several smaller pumps are 
 employed in preference to a single machine that lifts the water 
 to the same height as the several combined. In plunger pumps 
 leakage at the piston has the additional disadvantage that 
 during suction air is drawn into the pump barrel through the 
 packing, thus preventing the cylinder space from being filled 
 with water. 
 
 The quantity of water that runs back during the closing of 
 a valve can be determined approximately as follows. If V a is 
 the volume and e the density of a body, and 7 the weight of a 
 unit volume of water, then the body will fall under water with 
 the acceleration 
 
 force Vjcy ~ ^i7 e 1 
 mass ^i e 7 e 
 
 and such is also the case with an open valve which on both 
 sides is acted on by water of the same pressure. If s 1 is the 
 vertical drop of the valve and ^ the time of its fall, we have 
 
 and therefore 
 
 = /A.i. 
 V-i 9 
 
 Now if Fj is the sectional area of the passage when the valve 
 is open, and if we assume its average value for the time ^ to 
 be -J-Fj, then the quantity of water running back in this time 
 will be 
 
 V, = 
 
82 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 and its ratio to the total quantity discharged will be 
 
 Q - V - ~ 1 
 This loss increases directly with the ratio of the areas 
 
 in 
 
 ^, with the head h and with the lift of the valve s lt but in- 
 
 
 versely as the piston stroke s. For this reason it is well to 
 employ small valve openings, smaller heads, and greater piston 
 strokes, and above all the valve lift should not be unnecessarily 
 large. On this account therefore multiple valves, for instance, 
 as shown in Figs. 47 to 50, are to be recommended, for with 
 these the requisite valve lift is small. 
 
 In the best pumping plants executed these losses amount to 
 5 per cent, in fairly good pumps to 10 per cent, and in many 
 cases they reach 15 per cent and more of the theoretical or 
 geometrically determined quantity of delivery V = ~Fs. It is 
 therefore advisable, in order to provide a safe margin, to place 
 V = //,Fs = 0'85Fs, or in other words to assume a coefficient of 
 discharge //,= 0"85. Under this supposition we obtain for the 
 quantity discharged per second by single-acting pumps 
 
 and consequently for the area of piston corresponding to a 
 required discharge Q 
 
 and the necessary diameter of piston, therefore, is 
 
 d= = 1-128 VF = 1-731 /^m. [ft] 
 
 \ TT \J V 
 
 On the other hand, in double-acting pumps we have 
 
 therefore 
 
 ^= 1-176?, 
 
 JJiV V 
 
in THEORY OF RECIPROCATING PUMPS 83 
 
 and 
 
 m. [ft.] 
 
 The average piston speed v and the number n of double 
 strokes depend on various items, namely, on the ratio of the 
 sectional area of the pipes to that of the pump barrel, and on 
 the height of suction, concerning which further information 
 will be given in the following paragraph. Usually the 
 velocity of the piston is not over 0'4 m. [1*31 ft.], the common 
 value ranging between 0'2 and 0'3 m. [0*66 and 1 ft.], though 
 piston velocities of 1 m. [3'28 ft.] per second sometimes occur, 
 for instance in mine pumps. 1 
 
 EXAMPLE 1. If a pump valve of brass whose specific gravity is 
 e = 8-5 has a lift of 0'03 m. [0'0984 ft.], the stroke of the piston 
 being s= 1-2 m. [3'936 ft.], the head h= 12 m. [39'36 ft.], and the 
 
 "R 1 
 ratio of the sectional areas -^T = T, then the quantity of water 
 
 running back through the valves is 
 
 FI \/hs, ~ /S-5 t Vl2x0'03 _ A . 
 
 : F Q= v ri* * x ~^2 Q=0 ' 106 Q ' 
 
 i.e. more than 10^ per cent of the theoretical discharge. 
 
 EXAMPLE 2. If a single-acting pump has an average piston 
 velocity v = 0'3 m. [0-984 ft.], and is to lift the quantity Q = 25 
 litres [0'883 cub. ft.], it will require a diameter of piston 
 
 = 1731 ^=0-5 m. [1'64 ft.], 
 
 and if the water is to move with a velocity of 1/2 m. [3*94 ft.] in 
 the suction and discharge pipes, the necessary diameter of these 
 pipes will be 
 
 m. [0-82 ft.]. 
 
 26. The Suction. To ensure the ascent of the water 
 in the suction pipes it is not only necessary that the height of 
 suction should not exceed a certain limit, but the sectional 
 area of the suction pipes should not fall below a certain 
 minimum value. To determine these relations let b again 
 represent the height of the water barometer and 7^ the height 
 of suction or the distance between the lower water-level and 
 
 1 Compare note on p. 57. 
 
84 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 the average piston position. This suction height /^ must, of 
 course, always be less than the height of the water barometer, 
 partly because of the resistances to motion of the water in the 
 suction pipe and partly because a certain head must be avail- 
 able to accelerate the water continually entering the suction 
 pipe, and cause it to follow the motion of the piston. 
 
 Let F be the area of the piston, and let us assume the 
 usual case, that the piston is driven by a crank of length r, 
 which makes the piston stroke equal to 2r, and let this crank 
 make n revolutions per minute. Then the velocity of the 
 
 fi> 
 crank pin is given by u = 2-Trr, and that of the rising 
 
 piston at any instant by v = u sin <z, where a is the angle of 
 rotation of the crank estimated from the lower dead centre. 
 The piston begins its motion at the lower end of the stroke 
 with a velocity -0=0, and its acceleration for any crank angle 
 a is expressed by (see Weisbach's Mechanics, vol. iii., 1, ch. 6) 
 
 dv da u 2 
 
 consequently the acceleration at the beginning of the up 
 stroke is 
 
 Now if/ is the sectional area of the suction pipe, the velocity 
 and consequently the acceleration in the pipe at any instant 
 
 F 
 
 must be greater than that of the piston in the ratio - ; hence 
 
 the velocity v l of the water in the suction pipe is expressed by 
 and the acceleration by 
 
 v 1 = w sm a, 
 
 Pi = ~f COSa > 
 
 if the condition is to be satisfied that the water shall always 
 remain in contact with the piston. A driving force must 
 therefore act upon the water sufficiently great to impart to it 
 at every instant this acceleration. Otherwise the piston will 
 
in THEORY OF RECIPROCATING PUMPS 85 
 
 move ahead of the water at the beginning of the motion, when 
 
 U 2 
 
 its acceleration p = is greatest, i.e. a separation will take 
 
 place of the piston and the water. As a consequence, a shock 
 will occur during the upper half of the up stroke when the 
 water has caught up with the retarded piston. Such shocks 
 would interfere with the smooth running of the pump and 
 cause severe stresses in all its parts, and therefore they must 
 be carefully avoided. In order that the piston may not 
 separate from the water at the dead centre when it has its 
 
 U 2 
 
 maximum acceleration , the force driving the water up the 
 r 
 
 suction pipe must always be at least sufficient to generate the 
 
 F u 2 
 acceleration . Now if ^ represents the whole length of 
 
 the suction pipe, and consequently//^ is the weight of water 
 in this pipe, then the acceleration imparted to this mass at 
 the first instant of motion by the excess f(b /h)7 of atmos- 
 pheric pressure is given by 
 
 force f(b h^y b li^ 
 
 mass 
 
 The limit at which no separation will occur at the dead centre 
 is therefore given by the equation 
 
 2 F 
 
 -o-oii r v . 
 
 from which we obtain the maximum permissible number of 
 revolutions of the crank per minute, 
 
 or the minimum sectional area of the suction pipe 
 
 If instead of the piston area F we have given the theoretical 
 discharge Q per minute, which in a single-acting pump is 
 
86 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 we have only to substitute -2_ for F in the above expression 
 
 2nr 
 
 and then obtain 
 
 On the other hand, in a double-acting pump we have 
 
 and substituting - for F, we obtain the minimum area of 
 4nr 
 
 the suction pipe, 
 
 (4*). 
 
 From this we see that for a given discharge Q , other things 
 being equal, the permissible number of revolutions n is directly 
 proportional to the sectional area/; therefore, the smaller the 
 suction pipe the smaller must be the number of revolutions 
 
 of the pump, and the greater, of course, the volume 9 = F2r 
 
 n 
 
 of the pump barrel. If the suction pipe of a single-acting 
 pump has an area of cross-section /, which at least equals the 
 value determined from (3) or (4), there will be no separation 
 of the piston from the water at the dead centre ; the question 
 then arises whether such a separation may not take place after- 
 
 wards during the up stroke of the piston. As the acceleration 
 u % 
 
 cos a of the piston continually diminishes during the first 
 
 quarter of a turn of the crank, becoming zero for a= 90, a 
 separation of the piston is only possible if the acceleration 
 imparted to the water by the atmospheric pressure decreases 
 more rapidly than the piston acceleration. Now, the general 
 expression for the acceleration of the water at the angle a, 
 where the velocity of the water in the suction pipe is already 
 
 F 
 
 u sin a, is 
 
 mass ^ 
 
 for the excess b h of atmospheric pressure is expended partly 
 
"**m 
 
 in 
 
 THEORY OF RECIPROCATING PUMMCl 87 
 
 !I III 3' . 
 
 in overcoming the frictional resistance^tojhe suction pipe, 
 represented by a head of water <f>, and paro&43f imparting the 
 
 F ^fcSIciSCD ^" V 
 
 velocity u sin a (already existing in the suction piie) to the 
 
 water continually entering the pipe, the head needed for this 
 
 /~rA 2 2 2 
 
 , . / FV tr sin" a ~ , , ,, , , ,, , 
 
 purpose being I - 1 - . On the other hand, the accelera- 
 
 \ t/ / c/ 
 
 tion which the water must possess in order to keep up with 
 
 F^ 2 
 the piston is p k = -- cos a. Therefore, if p w is always to be 
 
 / 
 
 greater than p kJ the decrement of p wt i.e. the absolute value of 
 ejp^, must always be smaller than the decrement of p k , or the 
 absolute value of dp k . Hence we have the condition 
 
 or 
 
 2 2w 2 sin a cos a~ F % 2 . - 
 
 da^ -7 sin a9a, i.& Ff COS a ^/^ (5). 
 
 *fl / r 
 
 This condition is always fulfilled under ordinary circumstances, 
 for the quantity of water fl^ in the suction pipe is always 
 considerably larger than the half cylinder volume Fr. Con- 
 sequently no separation of the piston from the water can take 
 place except at the beginning of the stroke, and no separation 
 whatever will occur if we satisfy condition (4), which requires 
 that the sectional area / of the suction pipe shall increase 
 directly as its length l lt 
 
 When this length is considerable the area of the suction 
 pipe may evidently become inconveniently large. To avoid 
 this difficulty, it is advantageous to apply an air chamber to the 
 suction pipe, as close to the pump as possible. The action of 
 such an air chamber will be understood from the following. 
 Let us suppose the chamber W (Fig. 69) to be inserted in the 
 suction pipe S, a certain quantity of air being contained in the 
 space L ; then it is evident in the first place that when the 
 pump is at rest the tension of this air must be less by the 
 head AB = h f than that of the outer atmosphere represented 
 by a water column of a height AC = b. If therefore b { denotes 
 the height of water column corresponding to the air enclosed 
 in the chamber, we have when the pump is at rest, 
 
88 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 Now assume the piston K to move upwards from its lowest 
 position, then water from the air chamber will evidently follow 
 
 it, since the pressure ^ 
 in the latter will act in 
 the same manner as the 
 atmospheric pressure l> 
 when the suction pipe has 
 no air chamber. As a 
 result the air in L is ex- 
 panded to a pressure BE, 
 for instance, smaller than 
 BC. Owing to this reduc- 
 tion in pressure, water will 
 now enter the suction pipe 
 S, the rate of motion being 
 more rapid the greater the 
 diminution of pressure in 
 L, or in general, the smaller 
 the air chamber in com- 
 parison with the volume 
 of water withdrawn from 
 it by the pump piston. In 
 order that the piston shall 
 not separate from the water supplied to it from the air chamber 
 through the pipe H, the condition expressed by equation (4) 
 must again be complied with, i.e. we must have 
 
 Fig. 69. 
 
 \30 
 
 where f is the sectional area and l f the length of the pipe H, 
 while h" represents the height of suction between the air 
 chamber and pump. Under the supposition that this con- 
 dition as well as that expressed by (5) is fulfilled, the water 
 will remain in contact with the piston K during the up stroke, 
 and at the end of the stroke the air chamber will have sup- 
 plied the quantity of water 2Fr to fill the cylinder. Now, in 
 the meantime a certain quantity of water must have reached 
 the air chamber from the suction pipe S, though it is easily 
 seen that during the first stroke this quantity will be smaller 
 than that which has flowed out of the air chamber, because at 
 
in THEORY OF RECIPROCATING PUMPS 89 
 
 the start the force 5 ^ A', available for acceleration of the 
 water in S, is equal to zero, and it assumes a definite value 
 only when the pressure \ in the air chamber becomes smaller, 
 i.e. when more water is withdrawn from the latter by the 
 pump than is supplied to it by the suction pipe. After 
 the piston has reached its highest position and reversed its 
 motion no water is withdrawn from the air chamber during 
 the down stroke, but the upward motion already begun in the 
 suction pipe S continues, since the excess b-rh' of the atmo- 
 spheric pressure at the lower water-level is greater than the 
 diminished pressure 5 1 in the air chamber. Therefore while 
 the motion of the water in the pipe H between pump and air 
 chamber is periodical, the flow into the air chamber through 
 the suction pipe S is continuous. It is evident that after a 
 short while a certain normal condition will maintain in the 
 action of the pump, characterised by the relation that the air 
 chamber during a whole revolution of the crank receives the 
 same volume of water 2Fr from the suction pipe S as is with- 
 drawn from it by the piston during one half of a revolution. 
 On account of this difference in the supply and discharge of 
 the water, there arise in the air chamber certain periodical 
 fluctuations of pressure, which evidently will be more marked 
 the smaller the volume of the air chamber in comparison with 
 the cubic contents of the pump barrel. By giving a large 
 volume to the air chamber these fluctuations can be reduced, 
 but they cannot be wholly avoided, as that would require the 
 air chamber to be made of infinite size. There is therefore 
 a certain resemblance between the regulating action of air 
 chambers and that of fly wheels. 
 
 Assuming that the air chamber is of such large proportions 
 that we may neglect these variations in pressure, we can 
 determine the internal pressure \ as follows. Supposing the 
 water to be regularly supplied to the piston so that no separa- 
 tion can take place, then the condition (4) must be fulfilled, 
 
 where h" is the height of the piston above the water-level in 
 the air chamber, I' the length, and f the sectional area of the 
 communicating pipe H. 
 
90 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 From this follows 
 
 and if we here substitute the value for n given by (2), namely, 
 
 30 
 
 we get 
 
 60 /F-rra 
 ^-^ V J g ~T' 
 
 Now, in order that no separation of the piston from the 
 water may occur, condition (5) Fr cos a < fl' must be satisfied, 
 and we may therefore place Fr =f'l f , then getting 
 
 ") <) 
 
 In the suction pipe S the water moves with a uniform 
 velocity given by *J%g(b 5 1 h f $), when < is the frictional 
 resistance in the pipe, expressed as a head of water ; therefore 
 the quantity discharged per minute is also given by 
 
 (& -&!-#-*) (8). 
 
 If we assume the cross-sections of the pipes S and H to be 
 equal, that is, /=/', we get by equating (7) and (8) 
 
 &! - h" = 2;r 2 (& - ^ - h' - <), 
 from which we deduce the pressure in the air chamber, 
 
 _ h , _ + 
 
 With this value of \ we can now determine from (8) the 
 minimum area of the suction pipe, 
 
 Jmin ~ 
 
 As this value represents the minimum area of the suction 
 
 60 */2gx 0-05(6- h'-^-h"} 
 Qo 
 
in THEORY OF RECIPROCATING PUMPS 91 
 
 pipe, it is advisable, for the sake of safety, to choose a larger 
 dimension. If, with Fink, we take double the above value, we 
 should have 
 
 (10) 
 <f>) ' 
 
 where, in place of h f + h f/ t the total height of suction ^ is 
 introduced. The value <f> of the frictioiial resistance in the 
 suction pipes (according to Weisbach's Mechanics, vol. L | 7, 
 ch. 3) is given by 
 
 where d is the diameter of the suction pipe. 
 
 When the pump is double-acting, we have from (4 a ) the 
 equation 
 
 / .a- 
 
 /mm ~ V30/ i^g^-h")' 
 which also gives 
 
 19Q _ 
 
 Qo= /VM-A') - (7 a ). 
 
 Equating this and (8), and assuming /=/', we get 
 
 \-A'-y (-,-*'-*), 
 
 from which follows 
 
 b - y - + 2 
 
 
 _ h , _ ^ + Q . m . (9a) _ 
 
 With this value of &j we now find from (8) the minimum 
 area of the suction pipe, when the pump is double-acting and 
 provided with an air chamber for the suction, to be 
 
 f 
 
 60 v/2#0-l 7(6 -A' -/&"-<) 24-74 J(b - h' - h" - <j>)2g ' 
 or, if here also we double this area, 
 
 12-37 ^/2g(b -h'- h" - <) 
 As the air chamber, however, is comparatively small, the 
 
92 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 pressure b : is not constant, as was assumed in the preceding 
 investigation, but is subject to certain fluctuations, which 
 somewhat modify the action; nevertheless, equations (10) and 
 (10 a ), for single- and double-acting pumps respectively, may 
 serve as starting-points when the suction pipe is provided 
 with an air chamber, the volume of which, in accordance with 
 Fink, is taken equal to the volume F2r swept through by the 
 piston during one stroke. 
 
 On the other hand, when the pump works without an 
 air chamber on the suction pipe, we must determine the 
 diameter of the latter so as to satisfy equations (4) and (4 a ) 
 respectively, in order that no shocks may take place during 
 the influx. It should here be noticed that everywhere in the 
 present investigations Q represents the theoretical discharge, 
 nY2r and 2nY2r respectively, which, according to 25, may 
 
 Q 
 
 be placed equal to, say r r^r= 1'18Q, where Q is the actual 
 
 U'o o 
 
 discharge of the pump. Usually this actual discharge Q is 
 given, and then 1'18Q is to be substituted for Q in all the 
 preceding formulae. 
 
 27. The Suction (continued). When the piston has 
 attained its maximum velocity v = u at the middle of the 
 stroke, i.e. when the crank (always presupposing a very long 
 connecting rod) is 90 from the lower dead centre, the retarda- 
 tion of the piston begins ; from zero it increases to the value 
 
 u 2 
 - at the upper dead centre, and for any crank angle a it is 
 
 u* 
 expressed by cos a. Now, if the water ascending the suction 
 
 pipe is to continue to follow the piston without any tendency 
 to get ahead of it, it must, by the action of its own weight, be 
 
 TT 2 
 
 subjected to a retardation not less than -r . If the retarda- 
 tion should have a smaller value, p w for instance, the water 
 will, at a certain crank position, tend to move ahead of 
 the piston. This crank position is given by the equation 
 
 m 2 
 
 p w - cos a, where a is the crank angle estimated from the 
 lower dead centre. In consequence of this tendency, the water 
 
in THEORY OF RECIPROCATING PUMPS 93 
 
 will exert a pressure on the delivery valve, and cause the 
 latter to open. In this case water will discharge from the 
 delivery pipe also during the up stroke, and thus the quantity of 
 water lifted will exceed the cubic contents of the pump cylinder. 
 
 In order to investigate under what circumstances this 
 action occurs, we will first assume that the pump is a suction 
 and lift pump, with hollow, valved piston, and that the 
 sectional area / of the delivery pipe is the same as that of the 
 suction pipe. In this case, while the piston is rising, the 
 water in the delivery pipe at every instant moves with the 
 same velocity as that in the suction pipe. Now, if the case of 
 premature opening of the delivery valve occurs, the weight of 
 a water column having a height equal to the total head 
 Ji^ -\-h^ = h will retard the water rising in the pipes, and 
 therefore the retardation will be expressed by 
 
 where I = ^ + 1 2 is the sum of the length ^ of the suction, and 
 1 2 of the delivery pipe. If this premature opening of the 
 delivery valve occurs at the crank angle a, where the retarda- 
 
 u* 
 
 tion of the piston is cos a, we have the equation 
 
 Fu* h 
 
 --cosa= -gj . . (11). 
 
 It is here assumed that no air chamber is applied to the 
 suction pipe ; if the reverse were the case, the force retarding 
 the water between the air chamber, where the pressure is b v 
 and the point of discharge would be represented by a water 
 column of the weight/(6 ^ + h 2 )y. Now, since b ^ = A x -j- <, 
 if c/> again designates the head due to the resistance in the 
 suction pipe, the retarding force may be expressed by 
 f(h 1 + h 2 -\-(f))y=f(h + <t))y, the retarded water being merely 
 fl 2 y contained in the delivery pipe. For this case, therefore, 
 the equation corresponding to the premature opening of the 
 piston valve becomes 
 
 h + <h 
 sa= _ (IP). 
 
94 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 In a force pump with solid piston the delivery valve will 
 not open at the instant when the retardation of the piston has 
 diminished to that of the water in the suction pipe, for at this 
 moment the head of the water h 2 still rests on the valve. 
 The force due to the inertia of the water in the suction pipe 
 will instead push the piston ahead, and the delivery valve will 
 not open until this force is greater than that of the head of 
 water in the delivery .pipe. 
 
 From equation (11) we get 
 
 frh 
 
 and hence we can determine the angle a at which the piston 
 valve opens. From this moment on the water will pass 
 upward through the piston valve with a retarded motion until 
 
 F 
 
 its initial velocity ju sin a has been extinguished. The period 
 
 required for this purpose depends on this initial velocity of 
 the water and the retardation p w ; at all events, the ascent of 
 the water will continue until the crank has passed the upper 
 dead centre, for during the time intervening the retardation 
 of the water will be less than the continually increasing 
 retardation of the piston. Consequently, the suction valve 
 will not at once close when the piston begins its down stroke, 
 but will remain open as long as the ascending motion of the 
 water continues. It may happen that this ascending motion 
 will last beyond the time needed for the crank to move from 
 the upper to the lower dead centre. When this is the case, 
 the suction valve does not close at all, since the new up stroke 
 of the piston causes suction. To ascertain under what con- 
 ditions this state of inactivity of the suction valve will occur, 
 we first determine the time needed, by virtue of the retarda- 
 
 F^ 2 F 
 
 tion p w = j cos a, to destroy the velocity ju sin a, and find 
 
 it to be 
 
 velocity u sin a r 30 
 
 t = - , . = -5 - = - tan a = tan a, 
 retardation u* u irn 
 
 cos a 
 r 
 
in THEORY OF RECIPROCATING PUMPS 95 
 
 since 
 
 Placing this time equal to that needed by the crank to 
 
 pass through the angle 360 a, i.e. equal to -- 
 
 360 n 
 
 seconds, we obtain the equation 
 
 30 360-a60 
 
 tana = ^7- -- ; 
 Trn 360 n 
 
 and hence 
 
 loU 
 
 This equation is satisfied by a =10 2 34', and thus we see 
 that the suction valve of a pump remains inactive when the 
 retardation p w of the water caused by the weight of the latter 
 
 F 
 is only - times as large as the retardation of the piston when 
 
 j 
 
 the crank is at the angular distance a =102 34' from the 
 lower dead centre. If the retardation p w is greater, the 
 premature opening of the piston valve will not take place until 
 the crank has described a greater angle, and the suction valve 
 will close during the return stroke. No premature opening of 
 the delivery valve will occur when the retardation p w of the 
 
 F 
 
 water is equal to or greater than times the piston acceleration 
 
 F u 2 
 
 -- a at the dead centre. 
 / r 
 
 When there is a premature opening of the delivery valve, 
 a greater volume of water is discharged during every revolution 
 than would otherwise be the case. The quantity discharged 
 can be determined as follows : Let a represent the angle at 
 which the premature opening of the delivery valve begins. 
 While the crank has turned through the angle a, the piston 
 has advanced the distance r(l cos a), and therefore has lifted 
 a volume Fr(l cos a) of water. The water then moves 
 through the open delivery valve with the initial velocity 
 
 "C 1 "C 1 2 
 
 u sin a, under the influence of the retardation --- cos a. 
 / / r 
 
96 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 If we regard this motion as a uniformly retarded one, we find 
 the distance s through which the water moves, according to the 
 law of uniformly retarded motion, to be 
 
 F . v 
 u sin a J 
 
 Fr sin 2 a 
 
 F u 2 f 2 cos a 
 
 2 T COS a ' 
 
 / r 
 
 Therefore the amount of water that passes upward after the 
 delivery valve opens is equal to the volume of a cylinder 
 having the sectional area / of the pipes for base and the length 
 
 s, that is, equal to the volume fs= Fr -- In this 
 
 2 cos a 
 
 manner we obtain the total quantity discharged during one 
 revolution of the crank : 
 
 (12). 
 
 2 COS a 
 
 Introducing in this equation the above value a= 102 34', 
 at which the suction valve is entirely out of action, we get 
 
 V = Fr(l+ 0-217 + 2-190) = 3'407Fr; 
 
 that is, about 1/7 times as great as the cylinder volume 2Fr. 
 Of course this increased discharge is accompanied by a corre- 
 spondingly greater expenditure of work. 
 
 The numerical values found for a and V in the preceding 
 investigations are in reality modified by the influence of the 
 frictional resistances of the water in the pipes, which were 
 neglected in the above discussion, as was also the hydraulic 
 resistance due to the imparting of a velocity to the water 
 originally at rest, and entering the suction pipe while the 
 aforesaid upward motion through the delivery valve is taking 
 place. In consequence of these resistances the motion of the 
 water is not uniformly retarded, as was assumed. Neverthe- 
 less, the above discussion explains the peculiar result, often 
 observed in practice, that sometimes the actual discharge of a 
 pump is greater than the theoretical discharge. It is likewise a 
 fact that has been practically demonstrated that water can be 
 pumped without any suction valve, as is done by the well- 
 
Ill 
 
 THEORY OF RECIPROCATING PUMPS 
 
 97 
 
 known device 1 shown in Fig. 70. It consists of a pipe open 
 at the top and bottom, and pro- 
 vided at the lower end with a 
 delivery valve. By rapidly moving 
 this pipe up and down water can 
 be made to rise and discharge from 
 the spout c. During the upward 
 motion the valve is kept closed, 
 and on the downward stroke it is 
 opened by the inertia of the water 
 ascending in the pipe. 
 
 A satisfactory investigation and 
 explanation of the occurrences that 
 take place during the suction was, 
 so far as our knowledge goes, first 
 presented by Fink? whose investi- 
 gations have formed the basis of the 
 present article and the following one. 
 
 Remark. The action of the forces of inertia of the water during 
 suction, just analysed, can be clearly shown by a diagram like 
 that employed in Weisbach's Mechanics, vol. iii. 1, chap. vi. for the 
 investigation of the crank train. For this purpose let the axis of 
 abscissae A X A 2 (Fig. 71) be taken equal to the piston stroke 2r, and 
 let a parallel BjB 9 to this axis be drawn at the distance A 1 B 1 = A 1 . 
 Then the constant ordinates included between A 1 A 2 and B^ can 
 be regarded as the load on the piston due to the column of water 
 in the suction pipe. Now if we suppose the force needed to pro- 
 
 F u z 
 duce the acceleration -=- cos a of the water in the suction pipe to 
 
 /. r 
 
 be expressed by the weight of a water column having the height x, 
 we can determine x from 
 
 which gives 
 
 fxy = "" 
 
 FJ, M 2 
 
 = r L cos a. 
 fff r 
 
 Laying off this height from every point of the axis A 1 A 2 , we shall 
 obtain a line C 1 C 2 , which will represent the forces of inertia of the 
 water in the suction pipe. 
 
 1 Ruhlmann, Allgem. Maschinenlehrc, Bd. 4. 
 
 2 C. Fink, Theorie und Construction dcr Kolben- und Centrifugalpumpen, 
 Berlin ; also Zeitschr. dcutsch. Ing. 1863, p. 177. 
 
 H 
 
98 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 It is readily seen that when we assume a very long connecting 
 rod, these forces of inertia will be represented by the straight line 
 CjCg cutting the axis at the middle A , and also that the ordinates 
 
 ~Fl u 2 
 at the dead centres A l and A 2 are given by j 
 
 Now, if we suppose the ordinates of the two lines, B for the 
 suction and C for the acceleration, to be combined by drawing 
 through the end B of the ordinate at A the straight line 'D-flz 
 parallel to C 1 C 2 , we shall get in the diagram A 1 D 1 D 2 A 2 a graphical 
 representation of the forces acting on the piston, ordinates on 
 opposite sides of the axis A 1 A 9r of course, representing forces of 
 opposite directions. At the same time the algebraic sum of the 
 areas of this diagram is a measure of the work which must be 
 performed by the piston during an up stroke, provided the pump 
 has a solid piston or plunger, and consequently the head h of the 
 
 Fig. 71. 
 
 pump does not act on the pump piston during the up stroke. 
 Apparently a separation of the piston from the water will take 
 place whenever the ordinate A X D X is greater than the height b of the 
 water barometer. In order that such a separation may not occur, 
 the line D]D 2 , representing the resultant piston pressure, must not 
 cut the atmospheric line E^Kg drawn parallel to the base line A at 
 a distance A^ = b. The figure further shows that at the point a, 
 where the base line intersects the line of resultant piston pressures, 
 the driving force exerted by the crank on the piston is equal to 
 zero, and that for the subsequent movement the force of inertia of 
 the water in the suction pipes even exerts a driving action on the 
 piston. Now, laying off the head h. 2 of the water column resting on 
 the delivery valve equal to A^Ej, and drawing through E x the 
 straight line EjEg parallel to the base line A, we see that at the 
 instant when the piston reaches position e the delivery valve is 
 pressed upward by the force of inertia, so that during the remainder 
 of the movement of the piston from e to A 2 the water rises through 
 
in 
 
 THEORY OF RECIPROCATIN 
 
 99 
 
 TRCf 
 
 ~ * . , 
 
 the delivery valve, and increases the discharge as calculated above. 
 While the piston travels from a to e it is 3&(efr ^pward by the 
 inertia of the water, the force of which is 
 becomes equal to E <? at the piston position e. 
 to the end A. 2 , while from e onward the excess of the force ot iner 
 is expended in forcing the water through the valve and up the 
 delivery pipe. As the ordinates of the diagram are proportional to 
 the forces exerted on the piston area, we see that the corresponding 
 areas of the diagram can be regarded as measures of the various 
 amounts of work performed. Accordingly, the work transmitted to 
 the piston from the crank during the up stroke is represented by 
 the area A 1 D 1 , which may be placed equal to A 1 B 1 B 2 D 2 aA 1 , because 
 the triangles B 1 B D 1 and B 2 B D 9 are equal. Of this work a part 
 
 Fig. 72. 
 
 represented by the area rtA. 7 E E # is given back to the crank, so 
 that the whole amount of work performed by the crank on the 
 piston during an up stroke is represented by A 1 B 1 B 2 A 2 + E E 2 D 2 . 
 It is easy to see that the rectangle A 1 B 2 represents the work needed 
 to lift the volume of water F2r through the suction height h v while 
 the area of the triangle E E 2 D 9 gives us the work which must be 
 expended to lift the aforesaid extra water through the whole height 
 
 h = 
 
 ^ 
 
 h . The weight of this extra water is given by ^ where 
 
 Lj is the work represented by the triangle E E 2 D 2 . 
 
 The diagram on p. 98 applies to a suction and force pump, i.e. 
 to a pump with solid piston ; for a suction and lift pump, with 
 hollow, valved piston, the diagram looks somewhat different, for 
 during the up stroke a resistance corresponding to the whole 
 lift h = h^ + h.-, must be overcome. In Fig. 72 is shown the diagram 
 for such a pump, and it will be easily understood after what has 
 
100 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 preceded. Here also A X A 2 = 2r represents the base line, and the 
 parallels B 1 B 2 and E]E 2 are drawn at the distances A 1 B 1 = /^ and 
 AjEj h 2 from the base. If in the same manner as before we draw 
 the straight lines C 1 C 2 and F^ for the accelerating forces of the 
 water in the suction pipe and in the delivery pipe, so as to have 
 
 ,5 n FJj. w 2 F L 'ii- 
 
 BiQ = -r 1 and E, -, = --, 
 
 fgr l / g r ' 
 
 we first get the condition under which a separation of the piston 
 from the water will not take place, namely, that the line C 1 C 2 
 corresponding to the height of suction shall not reach the line K X K 2 
 representing the atmospheric pressure. If we also draw the line 
 to represent the resultant pressures, by making A 1 D 1 = A 1 C 1 
 j and A 2 D 2 = A 2 C 2 + A 2 F 2 , the intersection a of this line with 
 the base will give the piston position at which the premature open- 
 ing of the delivery valve must occur, and the area aA D 2 again re- 
 presents the work needed to lift the extra quantity of water. The 
 work performed by the crank on the piston is again represented by 
 the area 
 
 AjDja = A 1 G 1 G 2 A 2 + A 2 D 2 , 
 
 which two surfaces are to each other as the volume of the pump 
 barrel to the volume of the extra quantity of water. For example, 
 if the point a were so situated that the piston travel A^ corre- 
 sponded to a crank angle of 102 34', then, according to the above 
 determinations, 
 
 EXAMPLE. A single-acting suction and lift pump, whose piston 
 has a diameter of 0'3 m. [11 '81 ins.] and a stroke of 0'6 m. [23'62 
 ins.] makes 30 revolutions per minute with a height of suction of 
 6 m. [19-68 ft.]; it is required to determine the cross-section of a 
 suction pipe which shall be free from shocks caused by the water, 
 without the use of an air chamber. 
 
 If the whole length of the suction pipe is assumed to be / x = 
 10m. [32*8 ft.] we have from equation (3) 
 
 0'011Fx30 2 xO-3- 
 
 tib-hj 9-81(10-34-6) 
 
 = 0-698F = 0'698x 0-0707 = 0-0493 sq. m. [76'4 sq. in.] 
 
 This requires a diameter of pipe d- *- 0-0493 = 0'251 m. [9*88 
 
 V 7T 
 
 ins.] To avoid the use of such a large pipe let us suppose the 
 suction pipe to be provided with an air chamber whose cubic con- 
 tents is equal to the volume of the cylinder F x 2r = 0'0707 x 0*6 
 = 0'0424 cb. m. [1 5 cub. ft.] Now, if we give to the pipes a diameter 
 d-|D = f x 0-30 = 0-20 m. [7-87 ins.], i.e. make the area/=|-F 
 
in THEORY OF RECIPROCATING PUMPS 101 
 
 = 0-0314 sq. m. [48*5 sq. ins.], we obtain a velocity of the water 
 in the pipe of 
 
 ' 
 
 and from this follows the head due to the resistance in the suction 
 pipe, 
 
 Now, if the water-level in the air chamber is 0'5 m. [1-64 ft.] below 
 the average piston position, that is, h' = 5*5 m. [18'04 ft.] and 
 h" = 0'5 m, [1'64 ft.], we obtain from equation (9) the head repre- 
 senting the average pressure in the air chamber : 
 
 &! = 0-95(6- A' -0) + 0-057i" = 0-9o(10-334 -5'5 -0'030) + 0'05 x 0'5 = 4 '588 m. 
 
 [15 -05 ft] 
 
 Now, if the height of delivery or distance of the upper level from 
 the average piston position is A 2 = 14 m. [45'92 ft.], the total lift 
 h h^ + h^^ 20 m. [65*6 ft.], and if the whole length of the delivery 
 pipe is l z = 36 m. [118-Q8 ft.], we find the crank angle at which the 
 premature opening of the delivery valve takes place from equation 
 (IP), or 
 
 f r _. 20 + 0-030 4 0'3 
 
 ib = - 9 ' 81 85 5 = - ' 820 - 
 
 This gives a = 145, hence if there were no losses of water the 
 quantity discharged per stroke would equal that given by equa- 
 tion (12) 
 
 ie. one per cent larger than the cylinder volume. But on account 
 of leakage at the piston and at the valves, we must, in designing a 
 pump, always assume the actual discharge less than the theoretical 
 one F x 2r. 
 
 28. The Forcing Action in Pumps. The investigations 
 of the preceding articles only referred to the sucking action of 
 the pump piston, and therefore only to the motion of the crank 
 from the lower to the upper dead centre. The second half of 
 the rotation of the crank can be discussed in the same way ; 
 during this part of the revolution the piston, which we will 
 here suppose to be solid, moves downward, forcing the water 
 that has been raised from the pump-well up the delivery pipe 
 
102 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 to the height A 2 . In order that this latter action may take 
 place, it is necessary that the piston be driven by a force not 
 only equal to the weight of the water column pressing against 
 the piston and having a head h. 2 , but also capable, hurtful re- 
 sistances neglected, of imparting to the water in the delivery 
 pipe an acceleration corresponding to the motion communicated 
 to the piston by the crank. 
 
 The force needed for this acceleration may be represented 
 
 ~Fl u 2 
 by a water column of the height ? cos a, where a is the 
 
 'fff T 
 angle of the crank estimated from the upper dead centre, 
 
 / the sectional area, and 1 9 the length of the delivery 
 pipe. The resistance experienced by the piston is therefore 
 equal to the pressure of a water column having the height 
 
 h 9 4- _ cos a, and this resistance, like the action of suction, 
 
 fff r 
 can be represented by a diagram (Fig. 73). Again, make 
 
 A 1 A 2 =2r, and draw EjE 9 parallel to .the base line, at the 
 
 T77 2 ' 
 
 distance A^Ej = h 9 ; also make E.D. = EJD 9 = * , then the 
 
 fff T 
 
 ordinates of the straight line T>f> z again represent the pressures 
 on the piston. As the water is here directly driven by the 
 piston, no assistance being rendered by the atmospheric pressure, 
 as in the case of suction, the initial pressure A 1 D 1 is limited 
 by no condition, since no separation of the water from the 
 piston is possible as long as the latter accelerates the water, i.e. 
 while the crank is passing from the dead centre through the 
 third quadrant. In other respects the same remarks apply 
 to this diagram as to the diagram in Fig. 71. While the 
 piston is travelling from A.,^ to a, the crank acts on the piston 
 with a force that varies from the initial value A 1 D 1 down to 
 zero, and when the latter value is reached, the force of inertia 
 of the water set in motion in the delivery pipe exerts a pulling 
 action on the piston in the direction in which it moves. This 
 pull gradually increases from zero at a to the value B & at the 
 position b, which just corresponds to the suction height Ji l ; 
 from -this point on the moving mass of water in the delivery 
 pipe exerts a constant driving force B & on the piston, and at 
 the same time a certain quantity of water passes through the 
 prematurely opened suction valve, for, at position 5, the driving 
 
Ill 
 
 THEORY OF RECIPROCATING PUMPS 
 
 103 
 
 force of inertia of the water is equal to the weight of the 
 suction column. The work performed by the crank is again 
 represented by the areas AjX^a &A 2 B 2 B = A^EgA^ + B B 2 D 2 . 
 The resemblance between this procedure and that described 
 in the preceding article is readily perceived from the diagrams. 
 We likewise find that the delivery valve becomes entirely inactive 
 when the premature opening of the suction valve takes place at 
 a piston position b, for which the crank is at the angular dis- 
 tance a= 102* 34' from the upper dead centre. 
 
 It must be noted, however, that in the proceeding just con- 
 sidered, no attention was paid to the fact that when no air 
 chamber is applied to the suction pipe the water in the latter 
 is entirely at rest at the moment when the premature opening 
 
 Fig. 73. 
 
 of the suction valve takes place. Now, as this water cannot 
 
 -p 
 instantaneously assume the velocity u sin a which it must 
 
 have in order that it may follow the water in the delivery 
 pipe, the latter will move ahead and there will be a separation 
 of the water at the pump. As a result, a shock (water-blow) 
 will occur as soon as the water from the suction pipe catches 
 up with that in the delivery pipe, for the latter, after its living 
 force has been spent, will fall back into the vacuum created 
 by the separation of the water. Such a separation can, of 
 
 F u 2 
 course, only take place when the greatest retardation of 
 
 . J 
 
 the piston is greater than that g 2 experienced by the 
 
 t- rt 
 
104 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 water from the combined action of the delivery head A and 
 the atmospheric pressure on the orifice of efflux. 
 
 On the other hand, if the suction pipe is provided with an 
 air chamber, such a separation at the pump, and the accom- 
 panying shock, cannot take place, provided that, as is generally 
 the case, the quantity of water between the air chamber and 
 the suction valve is comparatively small. In this case there 
 
 will be an opening of the suction valve when the retardation 
 
 r<2 
 u ... 
 
 cos a reaches the value 
 / r 
 
 for the water in the delivery pipe is pressed downward by the 
 water column b + k 2 and upward by the pressure & x = b h-^ (f> 
 in the air chamber, where </> again represents the head necessary 
 
 FIG. 74. 
 
 to impart to the water taken from the lower reservoir the 
 uniform velocity it possesses in the suction pipe. 
 
 But even if a separation of the water be made impossible 
 at the pump, for instance by employing an air chamber in the 
 suction pipe, it is liable to occur with the accompanying shock 
 at some point in the delivery pipe whenever the retardation at 
 this point, due to the weight of the water and the atmospheric 
 
 F u 2 
 pressure, is smaller than the retardation - - effected by the 
 
 / r 
 
 crank. The possibility of this occurrence depends wholly 
 upon the arrangement of the delivery pipe. In the first place, 
 it is evident that no such separation can take place if the de- 
 livery pipe is entirely horizontal or entirely vertical. Tor, in a 
 pump (Fig. 74) with horizontal delivery pipe AB of the length 
 l. 2> the retardation at the point A near the pump is 
 
 b + h 
 
Ill 
 
 THEORY OF RECIPROCATING PUMPS 
 
 105 
 
 while for a point C at a distance AC = x from the pump it is 
 
 which is greater than at A. No separation can therefore take 
 place at the pump, since the condition 
 
 I + h 9 F w 2 
 a ? > 
 
 k fr 
 
 is satisfied, and the possibility of separation at any point C 
 will be smaller the farther this point is removed from A. In 
 
 B 
 
 Fig. 76. 
 
 Fig. 75. 
 
 like manner we find that with a vertical delivery pipe (Fig. 75) 
 for which I 2 = h 2) while at A the retardation is expressed by 
 
 for a point C at the distance x above the pump it is given by 
 
 ' _ b + h 2 -x 
 
 h 2 x 
 b + h 2 ,. 
 
 As 
 
 is an improper fraction, it is easy to see that pj is 
 
 greater than p w , and that no separation and shock can occur 
 at any point above the pump. 
 
 On the other hand, if the delivery pipe is inclined or partly 
 horizontal and partly vertical, as in Fig. 76, a shock may 
 
106 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 occur in the pipe, for instance at the elbow C, if the retarda- 
 
 tion p w r = g . at this point is smaller than - , which may 
 
 I* / r 
 
 well happen if the length I 2 f of the horizontal portion of the 
 pipe is sufficiently great, even though separation at the pump 
 be impossible because of the fact that the condition 
 
 has been satisfied. As the arrangement of the pipes is deter- 
 mined by local considerations, it is always advisable to examine 
 beforehand in each case whether any shock can occur, and, if 
 so, at what point in the pipe conduit. 
 
 29. Air Chamber on the Delivery Pipe. Separation of 
 water in the delivery pipe, and the consequent shock, can be 
 wholly avoided in every case by placing an air chamber on the 
 delivery pipe as close to the pump as possible ; the pressure 2 
 of the air in this chamber maintains an approximately uniform 
 motion of the water in the pipe, here performing the same 
 function as the suction air chamber does at the suction pipe. 
 The periodic motions caused by the reciprocation of the piston 
 are thus, as in the case of the suction, confined to the short 
 piece of pipe connecting the air chamber and the pump. If 
 this air chamber be made sufficiently large, shocks in the de- 
 livery pipe, and hence all shocks whatever, can be avoided, for 
 we know from what has preceded that separation at the pump 
 can be prevented either by satisfying the fundamental condition 
 
 b + h* F u* 
 
 or by employing an air chamber on the suction pipe. 
 
 But there are other advantages gained by placing an air 
 chamber on the delivery pipe ; one of these is that an approxi- 
 mately uniform discharge is obtained, a matter of importance 
 in fire engines and in pumps that supply fountains ; another 
 advantage, due to the regulating action of the air chamber, 
 is constituted by the materially reduced stresses in the 
 machine parts, for example in the piston rod, connecting rod, 
 crank shaft, etc. For, without an air chamber, the resistance 
 
in THEORY OF RECIPROCATING PUMPS 107 
 
 opposing the piston at the dead centre would be equal to the 
 pressure of a water column having the height 
 
 7 FL u z 
 
 h 2 + 2 - , 
 
 fff r 
 
 and we see that, when the lengh 1 2 of the delivery pipe is con- 
 siderable, the second term, which depends on the inertia of the 
 water in this pipe, may become many times greater than the 
 delivery height h 2 . Consequently all the driving parts of the 
 pump would have to be calculated for this maximum stress at 
 the dead centre, and with long pipes extremely large dimen- 
 sions would become necessary to prevent fractures. On the 
 other hand, if an air chamber is employed on the de- 
 livery pipe, only the inertia of the volume of water con- 
 tained between this chamber and the pump will resist the 
 motion of the piston during the first part of the down stroke, 
 and this quantity is always very small, inasmuch as the com- 
 mon practice, justified by the above, is always to place the 
 air chamber as close to the pump as possible. The water con- 
 tained between the pump and the air chamber is, of course, 
 removed from the regulating action of the latter, being there- 
 fore directly influenced by the motion of the piston. 
 
 As in the case of fly wheels, the equalisation of motion 
 attainable by the use of air chambers can never be complete, 
 for, on account of the variable velocity of the pump piston, 
 water alternately enters and leaves the air chamber, thus sub- 
 jecting the pressure of the air in the latter to continual fluctua- 
 tions having the same periodicity as the discharge from the 
 pump. It is evident that these fluctuations will be greater 
 the greater the ratio of the volume of water periodically enter- 
 ing and leaving the air chamber to the volume of the air space 
 in the latter. The air chamber will therefore have to be 
 made larger when slight variations of pressure are desired, 
 and the more so the greater the irregularity in the delivery of 
 the pump. 
 
 To investigate these relations, let us assume that the velocity 
 7; in the delivery pipe beyond the air chamber is constant, 
 which assumption, though not strictly correct on account 
 'of the variations in pressure of the air, is permissible in the 
 following determinations if the air chamber is of sufficient size. 
 
108 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 Taking then the case of a single-acting force pump having the 
 piston area F and the crank radius r, and supposing the crank 
 to have turned through any angle a from the upper dead 
 centre, the piston velocity will be u sin a and the crank pin 
 
 velocity u ZTTT. Now if / is the sectional area of the 
 
 delivery pipe, then in the element of time dt a quantity of 
 water Yu sin a . dt passes from the pump into the air chamber, 
 while the volume fv . dt passes from the air chamber into the 
 delivery pipe, and therefore, in the interval under consideration, 
 the difference 
 
 dq = Fu sin a . dt -fv . dt 
 
 of these two quantities is taken up or given out by the air 
 chamber, according as this value is positive or negative. During 
 
 rv 
 
 one complete revolution of the crank, i.e. in seconds, the 
 
 n 
 
 volume F2?* is lifted and, when the pump is running normally, 
 passes into the delivery pipe ; hence we have 
 
 or 
 
 which value, substituted in the above formula for water received 
 by the air chamber, gives 
 
 = Fw( sin a \ 
 
 dt. 
 
 This quantity becomes equal to zero when sin a = , i.e. for 
 
 7T 
 
 the crank angles 
 
 04 = 18 35' and <x 2 =161 25'. 
 
 While the crank is turning from the dead centre through 
 the angle ^ = 18 35', water is continually passing from the 
 air chamber into the delivery pipe, as the negative value of dq 
 shows, and while the crank is moving from a x to a 2 = 161 25' 
 the air chamber receives water ; finally, while the angular dis- 
 tance from 161 25'to360 is passed over, water again leaves 
 
" 
 
 109 **~ V < 
 VI i_ , r Ul 
 
 smallest 
 greatest 
 
 determined from 
 
 / 1\ 
 
 oci = ~Fu\ sin a )8/, 
 
 V 7T/ 
 
 by substituting rda for udt, and then integrating, which gives 
 
 i 
 q l = Fr I ( sin a ) da = Fr ( 1 - cos a, -) , 
 
 .' \ 7T/ V 7T/ 
 
 and 
 
 o 
 
 = Fr I ( sin a ) 8a = Fr ( 1 - cos a 9 - ^ ) . 
 
 .' \ 7T/ V ^ 77 / 
 
 Introducing in these expressions the values 0^= 18 35 ; , and 
 a. = 161 25 r , we obtain 
 
 ^ 1= = -0-05 Fr, 
 and 
 
 q 2 = +1-05 Fr; 
 
 hence the quantity of water entering and again leaving the 
 air chamber during each revolution is given by 
 
 22-^=1-10 Fr = 0-55Y, 
 
 where V = ~F2r is the cubic capacity of the pump barrel. 
 
 Knowing this fluctuating quantity of water and the size of 
 the air chamber, we can now determine the variations of pres- 
 sure in the latter. Let W 2 represent the volume of air in the 
 chamber when it contains the most water, i.e. at the crank 
 angle a 9 , and let iv 2 be the corresponding pressure of the air, 
 then the volume W l of the air when the air chamber con- 
 tains the least water, or at the crank angle a v is given by 
 Wj = W 2 + vV, where v is the ratio of the fluctuating volume 
 of water to the volume of the pump cylinder. The minimum 
 air pressure w t is then given by Mariottes law 
 
 W 2 
 
 since the temperature may here be assumed constant. 
 
110 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 When the pump is double-acting the only change to be 
 made in the preceding formulae is due to the fact that the dis- 
 charge per revolution is F x 4r, the crank positions for minimum 
 and maximum water contained in the air chamber being now 
 
 2 
 given by the equation sin a = , which is satisfied by the 
 
 7T 
 
 angle a^ = 39 35' and a 2 = 140 25'. Substituting these values 
 in the formula 
 
 q = Fr ( 1 - cos a ) , 
 
 V 7T / 
 
 we obtain 
 
 J 1= - 0-210Fr and g 2 = O210Fr, 
 
 and consequently the quantity of water entering and leaving 
 the air chamber during every half of a revolution is given by 
 
 ?2-?i = ' 42 Fr=0-21V. 
 
 If we take the frequently occurring case of two double- 
 acting pumps, with cranks set at right angles to each other, 
 the discharge during a complete revolution is given by F x Sr, 
 and it is evident that the quantity of water that has entered 
 the air chamber, when the crank reaches the angle a from the 
 dead centre, is given by 
 
 q = Fr ( 1 - cos a + sin a -- ) . 
 
 \ 7T / 
 
 This expression becomes a minimum and a maximum for 
 
 the respective angles ^=19 10' and a 2 = 70 50', obtained 
 
 4 
 from the equation sin a + cos a . These angles give 
 
 7T 
 
 2i= - 0-042JV and 2 2 = 0'042Fr, 
 and hence the fluctuating quantity of water is 
 
 This volume enters and leaves the air chamber four times 
 during every revolution. The foregoing determinations show 
 that in single-acting pumps the air chamber must be made 
 proportionately larger than in double-acting pumps. Fink 
 
in THEORY OF RECIPROCATING PUMPS 111 
 
 gives for the volume W of the air space of the chamber, when 
 the air is compressed by the delivery head h 2 , the following 
 rules : 
 
 W = 4V for single-acting pumps. 
 W = 1*6V for double-acting pumps. 
 
 W = 0'8V for two double-acting pumps, with cranks at 
 right angles. 
 
 When the pump is at rest (the delivery pipe being filled 
 with water) the pressure of the air in the chamber is deter- 
 mined by the sum h^ + 1 of the delivery head and the atmo- 
 spheric pressure. When the pump is at work this pressure is 
 increased by the head </> 2 , representing the frictional resistances 
 in the delivery pipe. The pressure in the air chamber, when 
 the water is moving uniformly up the delivery pipe, we will 
 call the average pressure, and designate it by w t thus having 
 
 and the volume of air enclosed at this average pressure we will 
 designate by W. As was shown above, the variable delivery 
 of the pump causes the volume W and its pressure w to change 
 continually, in conformity to the periods of discharge, and 
 therefore the average volume W of the air will alternately 
 increase and decrease. Designating the greatest and smallest 
 volumes of air by W l and W 2 respectively, and the correspond- 
 ing pressures by w l and w^ we have, according to Mariotte's 
 law, 
 
 W 1 w 1 = W 2 w 2 . . . (1), 
 
 and according to the above 
 
 Wl -W 2 = vV. . . . (2), 
 
 where i/V represents the fluctuating quantity of water. 
 
 Now the average values of W and w are given by the 
 construction, and enable us to determine approximately the 
 maximum and minimum values as follows. When the maximum 
 pressure w z in the air chamber falls to the average w, the 
 work performed while the air expands is expended in acclerat- 
 ing the water in the delivery pipe. Neglecting all hurtful 
 
112 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 resistances due to contraction, etc., this work will, in accord- 
 ance with well-known laws, be expressed by 
 
 A 2 = Ww hyp log * . 
 
 If the pressure is still further reduced from the average w 
 down to w lt the expanding air will exert a retarding action on 
 the water, which is measured by 
 
 A l = Wiv hyp log . 
 
 Now, when the pump is running normally, we have A 2 = A p 
 and this gives 
 
 , , w, , w 
 
 h yp log ^=kypiog-, 
 
 or 
 
 WjW 2 = v^ . . (3), 
 
 i.e. the average pressure w may be regarded as a mean propor- 
 tional of the minimum pressure w x and the maximum pres- 
 sure w 2 . 
 
 By means of equations (1), (2), and (3) we can now easily 
 determine the maximum and minimum pressures vj 9 and w 1 
 from the given values W, w, and i/V. 
 
 For, according to these equations we have 
 
 w 2 - w Wo W. - v 
 
 = w = w -^~ = w *_== = w 
 
 Ww 
 
 w, w 2 ~W W W 
 
 from which follows 
 
 and this gives 
 
 vV 
 
 in like manner we obtain 
 
 v v 
 
 We may now proceed, in the manner indicated in the pre- 
 
in THEORY OF RECIPROCATING PUMPS 113 
 
 ceding article, to determine whether the minimum air pressure 
 w : is sufficient to prevent the water from separating in the 
 delivery pipe near the pump, and, if this is not the case, we 
 must increase the volume W of the air chamber in order to 
 obtain a sufficiently large value for iv l to exclude the possibility 
 of a waterblow. If the air chamber, as is usually the case, is 
 located as close to the pump as possible, there is generally no 
 danger of a separation of the water. 
 
 The values w 1 and w 2 , determined above, represent the 
 minimum and maximum air pressures when the pump is 
 running normally, but at the moment the pump is started a 
 pressure w" is generated in the air chamber, which exceeds the 
 value w^ and in the like manner when the pump is suddenly 
 stopped the absolutely smallest pressure w' is obtained, as will 
 be shown in what follows. Let us assume that, when the 
 pump is at rest, there exists in the air chamber an average 
 pressure w == (& + 7i 9 )y, the chamber then containing the 
 volume W Q of air. If now the pump be set in motion, the air 
 chamber will receive a volume Q of water per minute, this 
 supply, for the sake of simplicity, being in the following cal- 
 culation assumed to be furnished at a uniform rate, so that the 
 
 water will flow with a velocity V Q = in the supply pipe 
 
 60/ 
 
 leading to the air chamber. This assumption is not exact on 
 account of the variable delivery of the pump, but is sufficiently 
 so for the purpose of the following investigation. The water 
 delivered by the pump first enters the air chamber, compres- 
 sing the air and increasing the pressure from w to a greater 
 value w. In consequence of this increase the air in the 
 chamber imparts to the water fl. 2 y in the delivery pipe an 
 acceleration 
 
 proportional to the excess of pressure w w ; in consequence 
 hereof, the water in this pipe is started from its state of rest 
 and gradually acquires the velocity v corresponding to the 
 normal running of the pump. Now if t represents the time 
 that has elapsed from the beginning of the motion to any 
 assumed instant, and v the velocity at this instant, then 
 
 I 
 
1U MECHANICS OF PUMPING MACHINERY CHAP. 
 
 during the following element of time the quantity of water 
 fv Q dt will pass from the pump into the air chamber, and the 
 quantity fvdt will leave the air chamber and pass into the 
 delivery pipe. Consequently the volume of air in the chamber 
 will be diminished by the amount 
 
 dq=f(v -v)dt . (5). 
 
 The whole diminution of volume during the time t is there- 
 fore 
 
 Now, according to Mariottes law, we have 
 W _w_ 
 
 and from this 
 
 w 
 differentiating, we obtain 
 
 This equation in combination with (5) gives 
 
 and multiplying this by (4) we obtain 
 
 Now when v has reached the value v , the pressure w of the 
 air in the chamber will have increased from its initial value 
 W Q to the required greatest pressure w", hence, integrating as 
 follows, 
 
 V W" 
 
 we obtain 
 
 ;,' - / ftl* ff /)/ \ 
 
 (6), 
 
in THEORY OF RECIPROCATING PUMPS 115 
 
 which equation will enable us to calculate the greatest pressure 
 w" of the air in the chamber at the start while the pump is 
 acquiring its normal speed. 
 
 This value w' is greater than the initial value w = b + 7i 2 , 
 and it also exceeds the average pressure w = b + A 2 + <f> 2 that 
 exists when the pump is running normally ; it will therefore 
 cause a further acceleration of the water in the delivery pipe, 
 where the velocity accordingly will exceed the average value 
 v . As a consequence, water again leaves the air chamber, the 
 pressure falls below w", and after some fluctuation it assumes 
 an average value w, whereupon the variations of pressure are 
 confined within the limits w 1 and w 2 prescribed by the 
 periodical variations in the delivery of the pump. 
 
 On the other hand, when the pump is suddenly stopped, 
 the water in the delivery pipe continues its motion by virtue 
 of its living force, and by thus drawing water from the 
 chamber causes the air space in the latter to increase from 
 W to W', this action continuing until the living force 
 
 fl 9 y-$- of the water is consumed by the work performed by 
 
 the retarding force. This work of retardation is evidently 
 that required for expanding the air from the volume W Q and 
 pressure W Q to the volume W and pressure w' ' . This work, 
 for an increment 3W of the volume W, is expressed by 
 
 consequently when the whole living force of the water has 
 been spent we have 
 
 w 
 
 W 
 
 = Ww - W t0 - W w hyp log =r 
 
 vv o 
 
 W 1 , . W \ 
 ^--1+hyplog^J, 
 
 W w 
 
 or, since -2 , 
 W w' 
 
 w 
 
116 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 By means of this equation we can calculate the minimum 
 pressure w f that will obtain in the air chamber when the pump 
 is suddenly stopped, while the water in the delivery pipe con- 
 tinues its motion by virtue of its living force. Moreover, it is 
 clear that, after the water has entirely lost its velocity, the 
 pressure w' of the air in the chamber being now smaller than 
 the average pressure IV Q , the water will rush back and thus 
 assume, an oscillating motion which is only limited by the 
 internal resistances. 
 
 The results found above are represented by the diagram 
 (Fig. 77), where, on the horizontal base line AJ, the ordinate JH 
 is made equal to the delivery head Ji 9t and HL to the height b of 
 the water barometer. Then the sum JL = AB = A., + b will 
 
 M 
 
 M 
 
 " 
 
 M 
 
 Fig. 77. 
 
 represent the pressure w of the air in the chamber when the 
 pump is at rest. At the beginning of motion the pressure 
 will first rise to the greatest value CC' = w" and then sink 
 below its initial value, the oscillations gradually diminishing 
 until the pump attains its normal condition of running, which 
 is represented by the wavy line MM. During this state of 
 motion the pressure in the chamber oscillates periodically 
 between the smaller pressure NN 1 = ^ 1 and the greater 
 00 1 = w 2 ; the average pressure w is represented by the hori- 
 zontal line DE, at a distance from the base of JE = 6-h/i., + (/>.,. 
 When the pump is suddenly stopped the pressure sinks to 
 FFj = w', and then, after some undulations of the water, it 
 assumes the value JL = w = b + h 2 , which obtains when the 
 pump is at rest. 
 
 It is evident that the fluctuations between OT^ = w^ and 
 OOj = iv z furnish a measure of the uniformity of the motion of 
 
in THEORY OF RECIPROCATING PUMPS 117 
 
 the water, and in fountains are a measure of the fluctuations 
 in the height of the stream. The greatest pressure CC 1 = w" 
 during the starting period forms the basis for determining the 
 stresses to which the separate machine parts are subjected. 
 Finally, the smallest pressure FFj = w r occurring while the 
 pump is being stopped determines the minimum volume "W 7 to 
 be given to the air chamber in order that no air may escape 
 when the pressure falls to the lowest limit. 
 
 As the quantity of air absorbed by a volume of water is 
 directly proportional to the pressure of the former, the reason 
 is evident why the air gradually escapes from the delivery 
 chambers unless care be taken to make good the loss occa- 
 sioned by its absorption. On the other hand, air chambers on 
 the suction pipes will never lack the necessary quantity of air, 
 since the water, being saturated with air under atmospheric 
 pressure, gives up a portion of it when subjected to the smaller 
 pressure in the air chamber. In order to keep the chamber 
 on the delivery pipe filled with air it is customary to place a 
 small air-cock on the suction pipe, through which a small 
 quantity of air may be sucked (or " snifted ") in by the piston 
 and allowed to rise to the chamber, or, after the latter has 
 been filled, to pass off with the water. By this means a 
 certain elasticity is also given to the water, the air contained 
 in the latter serving to moderate any shocks that may arise. 
 
 Finally, as regards the total volume of the air chamber, i.e. 
 the volume down to the place where the latter is attached to 
 the delivery pipe, it is evident that in fire engines and other 
 pumps which have no delivery head h 2 when at rest, the pres- 
 sure in the air chamber for the state of rest can only be equal 
 to that of the atmosphere. Not until the engine is at work 
 will a delivery head h 9 exist, being then equal to the height to 
 which, theoretically, the water can be thrown ; consequently if, 
 for the average pressure w = 6 -f h 9 -f- <f) 9 , we have determined in 
 accordance with the above the volume W of the air chamber, 
 the total volume must, according to Mariotte's law, be equal to 
 
 On the other hand, in pumps which raise the water through 
 a delivery pipe to a height li y the air, for the condition of rest, 
 
118 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 always has a pressure which is less than & + A 9 , and it is there- 
 fore here sufficient to take the total volume of the air chamber 
 eqiial to the greatest volume W occupied by the air after the 
 pump has been suddenly stopped. It will then be impossible 
 for the air to escape, and therefore, when the pump is again 
 started, there will be a sufficient supply on hand to prevent 
 the maximum pressure from exceeding the calculated value 
 of w". 
 
 EXAMPLE. A double-acting force pump has a piston of 0'4 m. 
 [15'75 ins.] diameter, making 12 double strokes per minute, the 
 length of stroke being 1 m. [3 9 '3 7 ins.] ; it forces the water through 
 a delivery pipe having a diameter of 0'25 m. [9 '84 ins.] and a 
 length of 100 m. [328 ft.] into a reservoir located 20 m. [65 '6 ft.] 
 above the pump. Required, the pressures in the air chamber. In 
 the first place, we have for the pressure W Q of the air when the 
 pump is at rest 
 
 w = (b + 7^)7= (10-336 + 20)1000 = 30336 kg. per sq. metre 
 
 [43'15 Ibs. per sq. in.] Assuming the actual discharge to be 0'85 
 of the theoretical, we have 
 
 Q = 0-85 x F x 2r x 2n = O'So x 0-1257 x 1 x 24 = 2*562 cub. m. [90'48 cub. ft.], 
 
 and consequently the average velocity of the water in the delivery 
 pipe, whose sectional area /= -0'25 2 = > 0491 sq. m. [76'1 sq. ins.], 
 
 from this we find the head, due to the resistance in the pipe, to be 
 
 and consequently the average pressure of the air in the chamber 
 during the motion is 
 
 w = (b + h 2 + 0)7 = 30712 kg. [43'68 Ibs. per sq. m.] 
 
 Now, if we assume the volume of air corresponding to this 
 average pressure to be 
 
 W = l-6xFx2r=l-6x 0-1257 = 0-2 cub. m. [7'063 cub. ft.], 
 
 and the fluctuating quantity of water in the double-acting pump 
 to be 
 
 vV = 0-21 x 0-1257 = 0-0264 cub. m. [0'932 cub. ft], 
 
in THEORY OF RECIPROCATING PUMPS 119 
 
 we find the smaller pressure from 
 
 vV \ 2 1 
 2WJ -T' 
 
 If we substitute in this formula the values of v, V, W, and w, 
 we obtain 
 
 -t- 0-066 + 
 
 = 0-93610 = 28746 kg. [40'89 Ibs. per sq. in.], 
 and in like manner we obtain for the greater pressure 
 
 f vV / / vV \ 2 ~| 
 W2= L + 2W + V 1 + (,2w) J^ 1 ' 068 ^ 32800 kg. [46 '65 Ibs. per sq. in.] 
 
 The pressure of the air therefore fluctuates during the normal 
 running of the pump some 6J per cent above and below the 
 average pressure w. At the same time the volume of air in the 
 chamber varies between 
 
 = ' 214 CUb ' m " t 7 ' 56 Cub ' 
 
 and 
 
 W 2 =^!g = 0-187 cub. m. [6-60 cub. ft.], 
 
 or in all about 27 litres [0'95 cub. ft.] 
 
 In order to determine the greatest pressure w" that occurs 
 during the starting of a pump we make use of equation (6) 
 
 in which we can substitute W w = Ww = 0'2 x 30712. This equa- 
 tion can also be written as follows : 
 
 >, l ^ . w o-f l 2Y ^o 2 , T _0'Q491 x 100 x 1000 Q'870 2 
 ^WQW" W w 2g 0-2x30712 2x9'81 + 
 
 = ^0-0386 + 1 = 1-031, 
 
 and it is satisfied by = 1 '3, which gives for the greatest pressure 
 
 w o 
 in the air chamber when the pump is started 
 
 w"=l'B x iv = 1-3 x 30336 = 39437 kg. [56 '09 Ibs. per sq. in.] 
 
 It is this maximum pressure which must form the basis in 
 determining the dimensions of the parts of the pump. In case no 
 air chamber were employed, the initial piston pressure, and 
 consequently the stresses in all parts of the pump, would be much 
 
120 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 greater. The resistance experienced by the piston would then be 
 equal to the weight of a water column having the height 
 
 .- , 
 
 fy r* 
 in which the velocity of the crank pin is 
 
 This would make the height of the equivalent water column 
 equal to 
 
 while the maximum excess of pressure in the air chamber only 
 corresponds to a water column of 
 
 -6 = 39-437 -10 -336 = 29 -101 m. [95 -45 ft] 
 
 The smallest pressure in the air chamber when the pump is 
 suddenly stopped may in like manner be found from equation (7) 
 
 hyp l og ^ + ^ =1 
 w w' 
 
 which equation is satisfied by = 0'79. Therefore the smallest 
 
 u 'o 
 pressure in the air chamber is 
 
 w' = 79w;o = '79x30336 = 23965 kg. [34'09 Ibs. per sq. in.], 
 
 and in order that the chamber may contain the assumed volume 
 W = 0'2 cub. m. [7'06 cub. ft.] of air for the pressure iv, its total 
 volume must be 
 
 W'=W 7 -0-2 ~ = 0-257 cub. m. [9*08 cub. ft.] 
 
 30. Wasteful Resistances. The power required 
 theoretically for driving a pump has already been computed 
 above ; we will now take the wasteful resistances into account 
 with a view to determine the power actually absorbed. 
 
 In pumps with hollow, valved pistons the theoretical force 
 necessary to raise the latter (see 14) is 
 
 as, however, the packing is pressed by the water against the 
 inner surface of the pump barrel with a force represented by 
 
in THEORY OF RECIPROCATING PUMPS 121 
 
 the head b + h. 2 (b hj = \ + h, 2 = h, it is evident that, as in 
 water-pressure and steam engines, the force needed to over- 
 come the piston friction will be 
 
 and consequently that necessary to lift the piston, taking this 
 friction into account, will be expressed by 
 
 where the coefficient of friction is (j>= 0*25, b is the breadth of 
 the piston packing in contact with the barrel, and d the 
 diameter of the pump barrel (see Weisbach's Mechanics, vol. ii., 
 also the volume on Hoisting Machinery, 19). 
 
 The hydraulic resistances are almost exactly like those of 
 water-pressure engines (see Hydraulics and Steam Engines). 
 
 Let f be the coefficient of resistance for the entrance of 
 the water into the suction pipe, d l the diameter of this pipe, 
 v s the velocity of entrance into the suction pipe, and v l the 
 velocity of the ascending piston ; then the head due to the 
 hydraulic resistance at the entrance is 
 
 With a cylindrical opening not rounded we have f = 0*505, 
 while for a smooth and well-rounded opening =0*100 (see 
 Weisbach's Mechanics, vol. i.) 
 
 The head due to the friction of the water in the suction 
 pipe is given by 
 
 where ^ is the length of the suction pipe, and ^ = 0^024 the 
 corresponding coefficient (see the volume just cited). 
 
 If f m is the coefficient of resistance for the passage of the 
 water through the suction valve, the corresponding head due 
 to this resistance is 
 
 Theoretically, the coefficient of resistance f m can be deter- 
 
122 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 mined from the coefficient of contraction <z, the areas F of 
 the piston and F 2 of the valve opening, according to the well- 
 known formula 
 
 Assuming a = 0'6 and = - we get 
 
 -T 2 ^ 
 
 ** 2 
 
 C m =10 and z 2 =l()|-, 
 
 i/ 
 
 which agrees very well with the experimental results obtained 
 by the author. The friction of the water in the pump barrel 
 is further given by 
 
 .1 
 
 where / is the length of the barrel ; the same formula is 
 applicable to the friction in the delivery pipe, and accordingly 
 if f 2 is the coefficient of friction, v r the velocity, 1 2 the length, 
 and d 2 the diameter, we have 
 
 1 11 2 
 
 Finally, for generating the velocity v r of the water in the 
 delivery pipe is required the head 
 
 2g 
 
 The sum of all these resistances constitutes the total 
 hydraulic resistance : 
 
 and therefore the total force needed to lift the valved piston is 
 
in THEORY OF RECIPROCATING PUMPS 123 
 
 where 
 
 represents the sum of all the hydraulic coefficients of resistance. 
 During the down stroke of the piston the suction valve is 
 closed and the piston valve open, consequently the water 
 presses against the top and bottom of the piston with the 
 same force Y(b + h 2 )y, and therefore the pump load proper is 
 equal to zero. If the piston packing is perfectly elastic the 
 piston friction is also equal to zero, for the water then flows 
 up past the outer surface of the piston, pushing the packing 
 away from the sides of the cylinder. The only friction which 
 the piston has to overcome on the down stroke is due to 
 generating the velocity v n of the water through the piston 
 valve. The quantity which flows through the valve opening 
 F u during the down stroke is equal to that displaced by the 
 piston head which has the area F ~F n ; consequently we have 
 
 F n t; w = (F-F n )f> 2 , 
 and therefore 
 
 where v 2 is the velocity of the descending piston. The corre- 
 sponding head due to this velocity is found, after multi- 
 plying F n by a coefficient of contraction a n determined 
 experimentally, to be 
 
 2? 
 and therefore the force needed to push down the piston is 
 
 or 
 
 where /c 2 represents the coefficient 
 
 In order to reduce this force as much as possible the valve 
 
124 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 openings must be made as large as practicable. Moreover, 
 the force needed to lift the piston is increased by the weight 
 G of the latter and its rod, while that required to produce the 
 downward motion is diminished by the same amount. The 
 buoyant action of the water has the reverse effect. If Y is the 
 volume of the piston, and that part of the piston rod which, 
 on an average, remains immersed during a double stroke, then 
 the diminution of the lifting force, as well as the increase of 
 the force pushing the piston downwards, due to the buoyant 
 effort, is V^ Accordingly neither the weight of the piston 
 nor the buoyant effort exerted by the water on the latter 
 involves any increase in the expenditure of work. 
 
 The work absorbed during a double stroke of the piston can 
 now be determined by means of the well-known expression 
 
 A = PjS + P 2 s = (P l + P 2 )s 
 
 where s is the piston stroke, and Y the theoretical discharge 
 (Fs) per stroke. Now, if the pump makes n double strokes 
 per minute, the work expended per second must be 
 
 L 
 
 or if the theoretical discharge per second be placed equal to 
 ^0 =Q ' 
 
 Letting v represent the average piston speed during a double 
 stroke, we get 
 
 2ns 
 The duration of a double stroke is t = -^r , the duration of 
 
m THEORY OF RECIPROCA 
 
 the up stroke is ti = -^> and W& of Ow clown s 
 
 Vl "4% 
 
 , 2 = - , consequently, "N^ 
 
 2 
 
 2ns ns ns .211 
 
 = - t- , i.e. = h , 
 60y 60^ ol)i' 9 v v^ v z 
 
 2v^v 2 
 and therefore the average piston speed is v = ; when the 
 
 values v l 'and v 9 differ but slightly we may employ the 
 approximation 
 
 Placing the actual discharge Q = yu,Q = 0'S5Q , we have 
 
 and therefore the expenditure of work expressed in terms of 
 actual discharge is 
 
 If greater exactness is desired we must (according to 
 Weisbach's Mechanics, vol. ii.) substitute for v 2 not the square 
 of the average piston speed but the average of the square of 
 the piston speed, hence for the up stroke 
 
 and for the down stroke 
 
 Finally, for the efficiency of a pump we obtain 
 
 r? = 
 
 
126 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 In well-designed pumps, working under favourable con- 
 ditions, we can assume ?; = 0"80, in pumps of average per- 
 fection ?7 = 0-75, and in ordinary pumps 77 = 0*70, and some- 
 times 0"65 only. 
 
 EXAMPLE. In a suction and lift pump the diameter of piston is 
 d = 0'3 m. [0'98 ft.], the stroke s = 1 m. [3'28 ft.], the diameter of 
 the suction pipe ^ = 0-15 m. [0'49 ft.], and its length ^ = 8 m. 
 [26'25 ft.], the diameter of the delivery pipe t/ 2 = 0'3 m. [0'98 ft.], 
 and the length of the latter together with the pump barrel 1 2 = 4 m. 
 [13 '12 ft.]; further, the width of the piston packing is 5 = 50 mm. 
 [1-97 ins.], and the two axes of the elliptic hole through the piston 
 are 2^ = 0*20 m. [0'66 ft.] and 26 1 = (H5 m. [0'49 ft.], the orifice 
 being rounded at each end. If the up stroke of the piston requires 
 six and the down stroke four seconds, what is the power required 
 to drive the pump 1 
 
 The area of the piston is 
 
 irft 2 tr 
 F = =^0-09 = 0-0707 sq. m. [0761 sq. ft.], 
 
 and that of the hole passing through it 
 
 F n = 71-^ = ^0-2x0-15 = | = 0-0236 sq. m. [0'254 sq. ft.] ; 
 further, the average velocity of the plunger on its up stroke is 
 
 ^==^=0-167 in. [0-548 ft.], 
 h 
 
 and on its down stroke 
 
 v 2 = ^ = i=0 -25 m. [0-82 ft], 
 t 2 
 
 and consequently the average of the square of the velocity is, for 
 the ascent and descent respectively, 
 
 ^ = 1-645 f f Y = 1-645 x -^=0-0457 [0'4917], 
 
 \ Ci / 
 
 % 2 = 1 -645 r = 1-645x^=0 '1028 [1-1061]. 
 \*i/ 
 
 The net load of the pump is 
 
 Fhy = Y(h 1 + h 2 )y = 0'0707(8 + 4)1000 = 848 '4 kg. [1870-5 Ibs.], 
 
 whereas the load, including the friction at the piston, is 
 
 '4 = .frx 848*4 = 990 kg. [2182 Ibs.] 
 
 Taking the coefficient of resistance at the entrance to the 
 
in THEORY OF RECIPROCATING PUMPS 127 
 
 suction pipe equal to f = 0'5, and for the passage through the 
 suction valve equal to f m =16, also assuming the coefficients of 
 friction for the motion of the water in the suction pipe to be 
 f,_ = 0'026, and in the pump barrel and delivery pipe f=f 2 = 0'03S, 
 \ve obtain the total head corresponding to the resistances on the 
 up stroke 
 
 or, since d 9 = d, 
 
 = (l7-5 + 30'18)0-00233 = 0-lll m. [0'364 ft.], 
 and hence the correspondiug increase in the load on the piston 
 
 ^-^7 = 111 xO-0707 = 7'8 kg. [17-2 Ibs.], 
 
 which is very slight in comparison with the friction at the piston 
 packing. The total force required for lifting the piston is now 
 found to be 
 
 Pi = 990 + 7-8 = -^ 1000 kg. (2205 Ibs.] 
 
 Assuming a coefficient of contraction a n = -f, the effort needed to 
 push down the piston will be 
 
 = 4-5 kg. [9-92 Ibs.] 
 We now obtain for the work expended per double stroke 
 A = (P! + P 2 )s= (1000 + 4-5)1 = 1004-5 m. kg. [7266 ft. Ibs.], 
 and consequently per second 
 
 L = j = ~-^ = 100-5 in. kg. [726-6 ft. Ibs.] 
 
 Taking the volume of water raised per double stroke equal to 
 V=/4Fs=0-85x 0-0707x1 = 0-060 cub. m. [212 cub. ft], 
 
 we have as the effect delivered per second 
 
 = Jc x 60 x 12 = 72 m. kg. [522-11 ft. Ibs.], 
 
 and consequently for the efficiency of the pump 
 
128 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 This small value of 77 is essentially to be attributed to the friction 
 at the piston packing, which, however, as a rule falls short of the 
 value assumed above. (For further information on the resistance 
 due to the piston packing see the volume on Hoisting Machinery, 
 19-) 
 
 31. Wasteful Resistances (continued). In discussing 
 the pumps provided with solid pistons or plungers, we must dis- 
 tinguish the case where the open end of the barrel is at the 
 top, as in Figs. 34 and 35, from that in which the open end 
 points downward, as represented by Figs. 36 and 37. In the 
 former case water is sucked in on the up stroke and forced up 
 the delivery pipe during the down stroke, while in the second 
 arrangement the reverse takes place. In the following discus- 
 sion we will assume a pump of the former kind (Fig. 78). 
 
 Let A X be the average height of suction estimated from low 
 water-level to the average position of the piston, let d denote 
 the diameter of the piston, I the width of the packing, v^ the 
 average of the square of the piston velocity, ^ the sum of all 
 the coefficients of the hydraulic resistances, and F the area of 
 the piston, then the force needed to lift the piston will be 
 
 On the other hand, let A be the average height of delivery 
 estimated from the average piston position to the point of dis- 
 charge, ^ 2 2 the average of the square of the velocity of the 
 descending piston, and K. Z the sum of the coefficients of the 
 hydraulic resistances on the down stroke of the piston, then 
 the force needed to push down the piston will be 
 
 Now, if we multiply each of these forces by the piston 
 stroke s and add the products we shall find the work required 
 per double stroke to be 
 
 A = P S + P, = 
 
Ill 
 
 THEORY OF RECIPROCATING PUMPS 
 
 129 
 
 where li = h l + /<-., is the total lift and V = Fs the volume swept 
 through by the piston in one stroke. 
 
 This formula agrees with that found for pumps with valved 
 pistons, but differs from the latter in that the coefficients K I 
 and K 2 have somewhat different values. 
 
 Let / represent the length of the pump barrel, / x the 
 length and d l the diameter of the suction pipe, 1 2 and d 2 the 
 length and diameter respectively of the delivery pipe, f, \, 2 
 the coefficients of friction of the water in the pump barrel and 
 
 the two pipes, f the coefficient of resistance to the entrance 
 of water into the suction pipe, f m and f n the coefficients of re- 
 sistance for the passage of the water through the valves, and 
 ti 5fc2 ^ ne coefficients of resistance due to changes in cross - 
 section and direction of the communicating pipe ; we accord- 
 ingly have 
 
 and 
 
 K 
 
130 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 As a rule the term f- can be neglected owing to its small 
 
 CL 
 
 / dy f dy 
 
 value. The coefficients of resistance f w ( -= ) and f J ) for 
 
 \ a i/ \ a 2/ 
 
 the passage through the valves, on the other hand, depend on 
 the areas F m and F w of the valve orifices, on the coefficients of 
 contraction a m and a nf and on the sectional areas F 3 and F 4 of 
 the valve chambers. If v z and ^ 4 represent the velocities of the 
 water in these chambers, then the heads due to the resistances 
 in the valve passages are 
 
 F Q 
 
 / 
 
 \tt m i? m 
 and 
 
 hence 
 
 /dy ( F \ 2 /FV 2 
 
 Stn- \ ~7~ / I TH\ ~~ / \ TT^ / J 
 
 \cii/ \a m r m / \r Q / 
 
 i //t/ "*' O 
 
 and 
 
 The work required per second to drive the pump is, again, 
 
 v v~h Fs 
 
 + Kl f + K2 -f\ 7 
 
 In pumps with inverted cylinders the force needed to lift 
 the piston is equal to that determined above for the down 
 stroke, and the force necessary to depress the piston the same 
 as that absorbed in lifting it in the case just discussed. 
 Consequently the above formulas for the expenditure of work 
 are applicable to both types of pumps. 
 
 Likewise for the double-acting pumps and combinations of 
 two single-acting pumps, of the kinds illustrated in Figs. 38 
 and 39, the forces needed and the power absorbed can be 
 found from the above formulae, the only difference being that 
 
 we must here substitute - = Fv for Q , and consequently 
 
 60 
 
 obtain double the above value for L. 
 
in THEORY OF RECIPROCATING PUMPS 131 
 
 EXAMPLE. A single-acting suction and force pump has a piston 
 stroke s = 0'75 m. [29'53 ins.], and is to lift 300 litres [10'6 cub. 
 ft.] of water per minute to a height of 20 m. [65*6 ft] What 
 dimensions must be given to the pump, and what force must be 
 exerted to drive it? With an average piston speed v = 0'2 m. 
 
 [0*656 ft.] per second, the number of double -strokes is n = -^ 
 = 8, and since the actual discharge per second is 
 
 x \J " i 
 
 Q = - = 5 litres [0*177 cub. ft.], and the theoretical discharge 
 Q = = 5'88 litres [0'208 cub. ft.], the requisite area of the 
 
 O'oO 
 
 piston will be 
 
 v 0-2 
 
 which corresponds to a diameter of 
 
 = 0-274 m. [1079 ins.] 
 
 As suitable diameters of the suction, 'delivery, and communi- 
 cating pipes, we may now take ^ = ^ = 0*140 m. [5*51 ins.], and for 
 the valve chambers d 3 = 0'22 m. [8'66 ins.] If the length of the 
 suction pipe is ^ = 8 m. [26*24 ft.], that of the delivery pipe 
 
 L= 12 m. [39 '36 ft.], and we assume 4<-^ = 4x x- = - , then, 
 
 a o 10 15 
 
 neglecting the hydraulic resistances, we find for the force needed to 
 lift the piston 
 
 P 1= l + 40FA 1 7=(l+A)x 58'8 x 8 = 533 kg. [1175 Ibs.], 
 
 and for depressing it 
 
 |)FA 2 7=^P 1 = 1 |p 1 = 800kg. [1764 Ibs.] 
 
 As the water moves in the pump barrel with a velocity 
 
 the corresponding coefficient of resistance will be 
 
 and the head representing the frictional resistance in the suction 
 
 pipe 
 
 4 = - 25 - Vo51 x 0>22= - 043 m - [0 ' 14 ft] > 
 
132 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 while for the delivery pipe it will be 
 
 ^0-043 = 0-065 m. [0'21 ft.] 
 
 o 
 
 Moreover, if the diameter of the two valve orifices is d m = d n 
 = 0'140 m. [5*5 ins.], and the coefficient of contraction be a m = a n 
 0*6, the heads representing the resistances in these passages 
 will be 
 
 V 1 /220\ 2 ~l 2 /974A 4 
 = [o6(lTo) - (Is) 0-051 x 0-2-0-047 m. [0-154 ft.] 
 
 Now, if we assume the coefficient of resistance for entrance of 
 the water into the suction pipe to be = 0*25, and the coefficient 
 of resistance for the passage through the communicating pipes 
 between the suction and delivery pipes and the pump barrel to be 
 f ]fcl = J fc2 =l'5, then the corresponding heads measuring these resist- 
 ances will be 
 
 iVaO'tt x 0-051 x 0-765 2 = 0'007 m. [0'023 ft.] 
 and 
 
 1 ' 5 x ' 051 x ' 7652 = ' 042 m - [o ' 138 ft -i' 
 
 and consequently the total hydraulic resistances 
 
 + 0-047 + 0-042 = 0-139 m. [0'456 ft.] 
 and 
 
 2 = 0-183 m. [0-6 ft.] 
 
 If the piston velocity were three times as great, that is, equal to 
 0'6 m. [1'97 ft.] per second, the heads due to these hydraulic- 
 resistances would be increased nine-fold, and if in addition the 
 suction and delivery pipes, valve openings, etc., had only three- 
 fourths of the diameters assumed above, the resistances would 
 become 
 
 times as large, and consequently we should have 
 
 /q^- =0-139x28-5 = 3-96 m. [12-99 ft] 
 and 
 
 1-5 = 5-21 m. [17-09 ft.] 
 
o. 
 
 in THEORY OF RECIPROCATING l?pMs Dp' 133 \ {^\ 
 
 If in place of the square of the average velocit$N^ use the average ^ 
 
 of the square of the velocity, we should have N^//ty/ r 
 
 _:i FRANCA 
 ^ = 1-645 x 0-139 = 0-229 m. [075 ft.], 
 
 and 
 
 K 2 ^=l-645x 0-183 = 0-301 m. [0'99 ft.] 
 
 The force needed to lift the piston under the first supposition is 
 
 x 58-8 = 546-5 kg. [1205 Ibs.], 
 and that necessary to push down the piston is 
 
 P 2 =f('l+4^^ 2 + Ac 2 ^lF7=800 + 0-301x58-8 = 8l7-7kg. [1803 Ibs.] 
 
 Hence we have for the work absorbed during a double stroke 
 
 A = (P 1 + P 2 )s=(546-5 + 8l7-7)0-75 = 1023m. kg. [7399 ft. Ibs.], 
 and therefore the expenditure of work per second is 
 L=^ A = ^1023 = 136-4 m. kg. [986-6 ft. Ibs.] 
 
 Theoretically the work necessary is 
 
 Qhy=5x 20 = 100 m. kg. [723'3 ft. Ibs.], 
 and consequently we have for the efficiency of the pump 
 
 Under the second supposition, that the piston velocity is three 
 times as great, we should have 
 
 )l-645 x 58 -8] 
 = 0-1(533 + 800 + 886) = 222 m. kg. [1606 ft. Ibs.], 
 which would correspond to an efficiency of 
 
 , = = 0,50. 
 
CHAPTEE IV 
 
 TYPES OF KECIPKOCATING PUMPS 
 
 32. Hand Pumps. Small pumps are frequently operated 
 by hand, either directly by means of a handle attached to the 
 piston rod or by the aid of a lever or crank. The first men- 
 tioned arrangement has but limited application, since in this 
 case the load must not exceed the force corresponding to the 
 direct application of muscular power, or about 12 kilos [26 
 Ibs.] With the lever pumps the case is different, since the 
 lever arm of the effort may be made from three to six times 
 the length of that of the load, thus admitting of a correspond- 
 ingly increased load, and besides several operators may be 
 more readily engaged at the pump at the same time. Denot- 
 ing by s the path travelled by the point of application of the 
 effort, by a the lever arm of the effort, and by b that of the 
 load, the corresponding stroke of the piston will be 
 
 and consequently for a path of the effort of s= 0*9 m. [3 ft.], 
 which corresponds to the sweep of a man's arm, we have 
 
 .JWm.rv=-3i 
 
 a L a 
 
 For the ratio - = ^ we should have a stroke of s 1 = 0*3 m. 
 a 
 
 [1 ft], and for - = J the stroke would be only 0'15 m. [6 ins.] 
 
 Cv 
 
 The lift of lever pumps is therefore always small, mostly 
 between the limits 0'15 and 0'3 m. [6 ins. to 1 ft.] As 
 
CHAP. IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 135 
 
 muscular effort can be employed to better advantage in 
 pressing down than in pulling up a lever, it is customary to 
 arrange the pump lever in such a manner that it will require 
 essentially a downward pressure or pull. In suction pumps 
 it is therefore as a rule made 
 with two arms, while force pumps 
 usually have a one-armed lever. 
 
 The simplest form of a suction 
 and lift pump is that shown in 
 Fig. 79. It is used for disposing 
 
 of smaller accu- 
 mulations of 
 
 water in build- 
 ing excavations, 
 
 and consists of 
 
 four planed 
 
 boards which are 
 
 joined tightly 
 
 and thus form 
 
 the prismatic 
 
 pump barrel 
 
 A; the latter is 
 
 closed at the 
 
 lower end by a 
 
 hollow block B 
 
 provided with a 
 
 leather clack C 
 
 forming a very 
 
 simple suction 
 
 valve. The piston K, which is 
 moved by means of a rod S 
 having a handle H, is likewise 
 made of a square block of wood 
 having a hole through the centre 
 and provided with a leather clack D, the tight fit at the sides 
 of the barrel being obtained by strips of leather nailed on the 
 sides of the block. Impurities are kept out by the perforated 
 boards E at the lower end ; the discharge spout is also formed 
 in a simple manner by boards G. 
 
 In Fig. 80 is illustrated a well-designed and very common 
 
 Fig. 79. 
 
 Fig. 80. 
 
136 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 type of suction and lift pump. Here the piston E is of brass 
 and packed by leather ; the piston rod S is guided by a stuffing 
 box and is reciprocated by means of a bell-crank lever ABC 
 having its fulcrum at B and provided with a handle at A. The 
 end C is connected to the piston rod by the forked rod CD, which 
 passes through a stuffing box held by a bracket at N. Water 
 is discharged either through the cock K or, when this is 
 closed, through the pipe L leading to a more elevated point. 
 A delivery valve G serves to retain the water in the delivery 
 
 Fig. 81. 
 
 Fig. 82. 
 
 pipe when the pump remains at rest for some time ; this valve 
 is frequently omitted, since it is not needed for the working of 
 the pump. The handle A usually serves as a counterweight, 
 being raised to a certain height by the operator during the 
 down stroke of the unloaded piston and assisting the upward 
 movement of the latter. It is evident that for very deep 
 wells it is necessary to place the pump at a sufficient depth to 
 make suction possible. 
 
 Norton's so-called tube wells are also nothing but single- 
 acting lever pumps, the peculiarity of which consists in that 
 they require no special well to be built, the suction pipe being 
 simply driven into the ground. For this purpose it is pointed 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 137 
 
 at the lower end and, for the admission of water, it is provided 
 with a number of small perforations near this end. The pump, 
 coupled to the upper end of the pipe, is shown in Fig. 81. 
 
 In Fig. 82 is seen the arrangement of a double-acting hand 
 pump. It is readily understood that of the valves either a 
 and b or a! and b' simultaneously open or shut. 
 
 It is a matter of special practical importance in all pumps 
 that the valves should be easily accessible, so that they may be 
 readily examined whenever occasion demands. As a model con- 
 struction with reference to this point may be considered the 
 so-called California pump first introduced by Hansbrmv, an 
 
 Fig. S3. 
 
 Fig. 84. 
 
 improved design of which, as made by Werner} is shown in 
 Figs. 83 and 84. 
 
 Also in this pump the valves a and b or a! and b' always 
 open or shut at the same time when the piston moves back 
 and forth horizontally. Water enters through the pipe c and 
 is discharged through d, and all the valves are made accessible 
 by unscrewing the eye bolts s and removing the air chamber W. 
 
 33. Fire Engines (and garden pumps) are portable pumps 
 which discharge the water, not into pipes, but by throwing it 
 up in streams. For the purpose of obtaining a uniform jet of 
 water, they are always provided with an air chamber, and for 
 easy transportation they are commonly mounted on wheels. In 
 factories stationary fire engines driven by water or steam power 
 are usually employed, while in cities and towns portable steam 
 fire engines are nowadays largely in use. 
 
 1 See Zeitschr. deutsch. Ing. 1870, p. 196. 
 
138 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 A fire engine consists essentially of one or two pump 
 cylinders made of brass and provided with the requisite suction 
 and delivery valves, the water being forced from the latter 
 through one or two short pipes into the air chamber of copper. 
 
 H 
 
 Fig. 85. 
 
 Water is conducted to the suction valve through a suction or 
 supply pipe, and discharged from the air chamber through an 
 eduction or discharge pipe to which is coupled a hose with 
 nozzle. In hand engines the piston is reciprocated simply by a 
 
 Fig. 
 
 lever, while in steam fire engines the pump piston is usually 
 attached to the piston rod of the steam engine and thus driven 
 directly by the latter. The pump is generally placed in a 
 box-shaped reservoir or cistern from which it takes its water, 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 139 
 
 and which is supplied either by buckets or from the suction 
 pipe, or in some cases by a special feed pump. 
 
 The general arrangement of a two-cylinder hand fire engine 
 is shown in Figs. 85 to 87. Fig. 85 represents a half eleva- 
 tion and a half longitudinal section, Fig. 86 the plan, and 
 Fig. 87 a vertical cross-section through the air chamber. At 
 B, B the cylinders are seen, at A the suction pipe, at C, C the 
 communicating pipes, at B the air chamber, and at D the dis- 
 charge pipe. The suction pipe has 
 two inlets E and F, the former 
 from the cistern and the latter 
 from without. When the water is 
 to be taken from the cistern, the 
 inlet F is closed by a cap, and E 
 is provided with a strainer for the 
 exclusion of impurities. On the 
 other hand, when the supply is to 
 be derived from some other source, 
 E is closed and a hose is screwed 
 on to F and carried to the supply 
 reservoir, the strainer then being 
 attached to the end of the hose. 
 Below the air chamber is a cylin- 
 drical casting which is divided into Fig - 87< 
 three chambers by vertical partitions ; two of these chambers 
 communicate with the pump barrels and are covered by sector- 
 shaped valves, while the third, which connects with the discharge 
 pipe, is open at the top. A board GG- placed on the top of the 
 cistern along its entire length, and firmly secured to the latter 
 and to the woodwork below it by eight bolts, serves as support 
 not only for the pump lever bracket K but also for the two 
 guides LL which prevent side motion of the lever, and for the 
 spring buffers which limit the motion of the latter. 
 
 Many other constructions of fire engines have been brought 
 into practical use. For instance, the plungers have been replaced 
 by valved lifting pistons, and the lever arrangement for their 
 working by a crank mechanism. 
 
 In Fig. 8 8 is illustrated the pumping arrangement of a fire 
 engine with valved piston, designed by Levesque. The air 
 chamber W is here placed directly above the pump barrel, 
 
140 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 and the piston rod is surrounded by the lower end of the 
 outlet pipe and guided by a stuffing box. A complete fire 
 engine of this kind consists of two such pumping apparatus, 
 and is operated by a double crank. In order to obtain a uni- 
 form motion of the crank shaft, the latter is provided with two 
 fly wheels which, during the transportation of 
 the machine, serve as waggon wheels. 
 
 Letestu's fire engine also belongs to this class. 
 The characteristic features of this apparatus are 
 a valved piston of peculiar construction, and 
 that the water enters the cylinder from the top 
 and is forced downward into the air chamber. 
 As, first, regards Letestiis piston, it consists of 
 a perforated funnel (Fig. 89, I.), made of iron 
 plate, and a leather funnel (Fig. 89, II.), cover- 
 ing the former on the inside and projecting 
 some 10 mm. [-^ in.] below it, thus serving at 
 the same time as valve and packing. The 
 leather cone is not sewn up, consisting simply 
 of a sector with the radial edges somewhat 
 bevelled and lapping over each other. The pumping mechanism 
 is shown in Fig. 90, which represents a section through the rear 
 end of the engine. When the piston is moving upward, the 
 water entering the cylinder C from the cistern W above it 
 forces the leather covering away from the iron funnel K, and 
 flows through the perforations in the i. n. 
 
 latter. On the other hand, during 
 the clown stroke the water below the 
 piston forces the leather against the 
 iron cone, and upon lifting the de- 
 livery valve V enters the air chamber 
 above it. In ABC is seen one half of Fi s- 89 - 
 
 the pump lever, which oscillates about C and is provided with 
 wooden handles or lra~k.es at A. 
 
 Another departure in fire-engine construction consists in 
 the use of a diaphragm pump, AKA, Fig. 9 1. 1 In place of a 
 
 1 Diaphragm pumps of various types are nowadays frequently employed, also 
 on vessels and railways, in draining excavations for buildings, and for other ser- 
 vice involving the pumping of water containing sand, gravel, or gritty matter, 
 these impurities not affecting the action of the diaphragm. TRANSLATOR'S 
 REMARK. 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 141 
 
 piston a leather (or rubber) cone AA is here employed, which is 
 clamped to the pump casting by means of an iron ring, and at 
 
 c 
 
 B 
 
 Fig. 90. 
 
 the upper end is fastened to the piston rod KL. The further 
 details of the arrangement are evident from the figure. When 
 
 D 
 
 Fig. 91. 
 
 the diaphragm AA (Fig. 92) is depressed to the bottom 
 BB of the barrel, the whole space enclosed between the two 
 conical frusta AD and DB is emptied. Denoting by r^ and r^ 
 the radii of the upper and lower bases AA and DD, and by h 
 the height CK = EK of each frustum, consequently the stroke 
 
142 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 s=2h, then the theoretical quantity of water delivered by the 
 pump per minute will be 
 
 As a rule the stroke s is smaller, however, and were it to 
 be made equal to OK = k only, we should have for the corre- 
 sponding volume AONA 
 
 Horizontal pump cylinders have also been employed in 
 
 fire engines, especially for 
 feed pumps. As examples of 
 this type may be mentioned 
 the designs made by Mter, 
 Kronauer, and others (see 
 Kronauer's Zeitschrift fur 
 Technologic, vol. i.) 
 "" Also the so-called rotary 
 
 pumps have been largely used in fire engines. The 
 arrangement of these pumps will be described in 
 another chapter. 
 
 In ships the system of pipes is generally so 
 arranged that by simply turning a four-way cock 
 they may be made either to draw water from the 
 sea and force it into the ship or to free the ship's 
 hold from water. 
 
 The details peculiar to fire engines are essen- 
 tially the supply and outlet or discharge pipes, hose 
 and nozzle, the air chamber, the pump lever, and 
 the vehicle or means of transportation. The suc- 
 tion pipes are from 5 to 8 mm. [2 to 3 ins.] in 
 diameter, and are made either of leather or vul- 
 canised rubber, or of copper. Suction hose of 
 leather is either sewn or riveted, and, in order to 
 furnish the necessary resistance to the external 
 pressure of the atmosphere, has a lining on the 
 Fig. 93 inside either made of wire 4 to 5 mm. [^ in.] 
 (i. and ii.) thick, and wound in a spiral, or of copper rings 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 143 
 
 Fig. 94. 
 
 3 to 5 cm. [1^ to 2 ins.] wide and 6 to 15 mm. [J to -| in.] 
 
 apart. Suction pipes of copper are provided 
 
 at the middle with a joint as at AB (Fig. 93) 
 
 made tight by a leather ring ab, the object of 
 
 this joint being to admit of a change in the 
 
 direction of the pipe when necessary. The 
 
 inlet of the pipe should be provided with a 
 
 strainer. 
 
 The air chamber is either cast of brass or 
 
 made of sheet copper or brass, and is usually 
 
 cylindrical with a segment-shaped top. Its 
 
 capacity should be at least eight times that 
 
 of the pump cylinder, and the thickness of 
 
 metal is to be calculated in the same manner as for steam 
 
 boilers. The communicating pipes are given a diameter equal 
 
 to half that of the cylinder, 
 and lead to the bottom of 
 the air chamber, while the 
 outlet or stand pipe is either 
 located directly above the 
 bottom or carried through the top 
 of the chamber. Closely above the 
 cistern an elbow is coupled to the 
 stand pipe by means of a joint A 
 (Fig. 94), and to this elbow the hose 
 with its nozzle is screwed. In large 
 engines a swivelling pipe placed 
 directly on the top of the air cham- 
 ber is instead made use of. Such a 
 pipe has several joints, as shown in 
 Fig. 95, also two elbows at the top, 
 and a branch pipe and cocks at the 
 central portion. A suitable joint is 
 shown in Fig. 96. The split coupling 
 AB connecting the pipe ends C and 
 D is screwed on to the flange of D, 
 and grasps the flange of the other 
 pipe C ; after swinging the pipe 
 round, it is clamped in the desired 
 
 position by means of the screw S. 
 
144 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 The hose for conducting the water from the fire engine to 
 distant points is either of leather or of hemp ; it has a diameter 
 of from 3 to 5 cm. [1^ to 2 ins.], and is made in sections from 
 
 Fig. 96. 
 
 Fig. 97. 
 
 6 to 10 metres [20 to 33 ft.] in length. Leathern hose 
 
 is either sewn with waxed thread or riveted by means of 
 
 copper rivets about 1 mm. [0*04 in.] in diameter, while hempen 
 
 ^ hose is woven without a seam. The manner of 
 
 ! joining the sections by screw couplings is evident 
 
 from Fig. 97, 1. and II. Both the nut A (Fig. I.) 
 and the nipple BB (Fig. II.) form the termina- 
 tions of short brass pipes C, over which the hose 
 ends DD are slipped, being secured by cord or 
 wire. 
 
 The short pipe through which the water is 
 finally discharged is usually given an inside dia- 
 meter of from 2 - 5 to 4 cm. [1 to 1^- in.] only, 
 and a length of at least 0'3 m. [1 ft.] ; at one 
 end it is provided with a nut for coupling to the 
 stand pipe or hose, and at the other it is threaded 
 for reception of the nozzle. The latter is a conical 
 brass pipe AB (Fig. 98) 15 to 20 cm. [6 to 8 
 ins.] long, having at the inlet end a diameter of 
 2*5 to 4 cm. [1 to 1^- ins.], while at the outlet 
 it is contracted to 10 or 15 mm. [0*4 to 0*6 in.] 
 (the opening being frequently made adjustable). 
 The sides may suitably be made to converge at an 
 angle BOB of 5 degrees. According to numerous experiments 
 made by the author, the coefficient of resistance of such a nozzle 
 has been found not to exceed 0'03, that is, the reduction in the 
 
 Fig. 98. 
 
iv TYPES OF RECIPROCATING PU 
 
 height of stream due to friction of the water 
 be only 3 per cent. 
 
 The lever for operating the pistons of large 
 
 hand 
 
 is composed of two bars rigidly connected by means of cross 
 stays and located on each side of the swivel pipe and the plat- 
 form for an attendant. The ends of the lever receive the 
 wooden handle bars or brakes, which are from 5 to 7 cm. [2 to 
 2J- ins.] in diameter, and about 3 metres [10 ft.] long, thus 
 providing room for ten operators at the most. Evidently the 
 lever is to be given sufficient length and such curvature that 
 the framework of the waggon will offer no hindrance to the 
 firemen. 
 
 To obtain easy access to the valves for cleaning, which is a 
 matter of great importance in all pumps, and especially in fire 
 engines, various plans have been adopted. A common con- 
 struction is to make the valve seat conical on the outside and 
 grind it to an accurate fit in a taper hole, as in cocks ; by 
 this method the seat, together with its valve, may be easily 
 removed, but at the same time the valve is apt to become 
 rather small or the seat casting inconveniently large. This 
 objection has been overcome in a satisfactory manner by the 
 arrangement introduced in the fire engines built by /. Beduwe 
 of Aachen, and illustrated in Figs. 99 to 
 101. Here the four valve clacks, two for 
 suction s and two for delivery d, are hinged 
 on a peculiarly-shaped piece C (Fig. 99), 
 which can be slid in and out like a drawer 
 through a side opening below the air chamber 
 W (Fig. 100). This clack slide is made to 
 fit tightly against the wall of the air chamber V by means of a 
 wedge-shaped piece K, held in place by a screw s, and easily 
 removable after unscrewing the nut or hand wheel M. The 
 further details of the construction are readily understood from 
 the vertical section in Fig. 100 and the plan in Fig. 101, where 
 AA are the cylinders, S is the suction, and D the discharge pipe. 
 
 The complete arrangement of a hand fire engine mounted on 
 wheels is shown in Fig. 102. The cistern E, internally lined 
 with sheet-metal, is supported by the hind wheels A and the 
 fore wheels B, and, besides containing the whole pumping 
 apparatus, receives the bearings C for the lever D. Further, 
 
 L 
 
146 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 G is the communicating pipe, CM the stand pipe terminating 
 in the nozzle M, etc. 
 
 Fig. 100. 
 
 As, owing to lack of space, the number of firemen that can be 
 engaged at the brakes is in most cases limited to about twenty, 
 
 M 
 
 Fig. 101. 
 
 it is obvious that for the usual height of stream of from 20 to 
 30 metres [65 to 100 ft.] the size of plungers and the volume 
 
iv TYPES OF RECIPROCATING PUMPS 147 
 
 of water that can be thrown are also limited. The plungers 
 are rarely made over 0'18 m. [7 ins.] in diameter, usually only 
 0'15 m. [6 ins.], the corresponding volume thrown being about 
 0*3 cub. m. [10'6 cub. ft] per minute. With a view to throwing 
 greater volumes, 1 to 1*5 cub. m. [35 to 53 cub. ft.] per minute 
 to heights ranging from 40 to 50 metres [130 to 160 ft.], 
 steam fire engines have been introduced, first in America and 
 England and afterward all over the continent of Europe. In 
 order to enable a steam fire engine to be worked to advantage, 
 it is evidently necessary that an adequate supply of water 
 should be available, and as this can be obtained only with 
 
 Fig. 102. 
 
 difficulty by hand supply from buckets or hand engines, the 
 use of steam fire engines is principally limited to cities or 
 towns, where the water may be taken from hydrants. In some 
 cases they are also utilised as supply engines furnishing water 
 through long lines of hose from a river or pond to a greater 
 number of hand engines. 
 
 A steam fire engine must combine lightness of construction 
 with capacity to generate steam of sufficiently high pressure in 
 the shortest time possible, and therefore the heating surface of 
 the boiler must be large and the water space small. By the 
 use of fuel that ignites easily and generates intense heat it has 
 been made possible to raise steam of 8 or 10 atmospheres 
 
148 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 pressure in less than 1 minutes. Horses are always employed 
 for the transportation of steam fire engines, experiments to use 
 steam power for this purpose, as in road locomotives, having 
 proved of little consequence. 
 
 In Fig. 103 is shown a section of a steam fire engine built 
 by Egestorff of Hanover. 1 The vertical boiler A has a cylindri- 
 cal fire box B, and contains 199 tubes of 35 mm. [1-| ins.] 
 diameter, the total surface exposed to the fire or gases being 
 about 28 sq. metres [300 sq. ft.] The steam pump D is 
 
 Fig. 103. 
 
 located on the top of the cylindrical suction air chamber 
 C, from which the water is sucked through the pipe c and 
 forced into the delivery air chamber W. Steam is furnished 
 to the engine through the pipe a, and exhausted through 
 d into the smoke stack S with a view to increasing the 
 draught. The pump is double acting, and has four valves V, 
 the arrangement of which is shown in the section (Fig. 104). 
 The steam piston is directly connected to the pump plunger by 
 
 1 Mittheil. des Hannov. Gewerbe- Vereiiis, 1864, and Riihlmann's Allgem. 
 Maschinenlehre, vol. iv. 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 149 
 
 means of the piston rod, which, by the aid of a slider crank F 
 
 drives an auxiliary shaft provided with a fly wheel E in the 
 
 manner explained below 
 
 in the article on steam 
 
 pumps. The diameter 
 
 of the steam piston is 
 
 0-215 m.[8'46 ins.], that 
 
 of the pump plunger 
 
 0-178 m. [7 ins.], and 
 
 thestrokeofbothisO'228 
 
 m. [9 ins.] ; the steam 
 
 pressure is about 7 kg. 
 
 per sq. cm. [100 pounds 
 
 above the atmosphere]. 
 
 At a maximum speed of 
 
 161 revolutions of the 
 
 fly wheel, or about Ij 
 
 metre [4'1 ft.] piston 
 
 velocity, the engine threw 1*5 cub. m. [53 cub. ft.] of water 
 
 per minute to a height of 47'5 m. [156 ft.], the thickness of 
 
 stream being 30 mm. [1*18 in.] 
 
 Modern portable steam fire engines are frequently made of a 
 capacity of 5 cub. m. [176 cub. ft.] per minute, and are able to 
 throw a 50 mm. [2-inch] stream to a height of 60 metres or more. 
 The general outline of their design often differs from that shown 
 in the cut in that the pumps are placed vertically and together, 
 with the air chambers grouped more closely about the boiler. Minor 
 steam fire engines are sometimes mounted on two wheels only, and 
 arranged to be drawn by a single horse ; a notable fire engine of 
 this type has been designed InyGranell of Stockholm. TRANSLATOR'S 
 REMARK. 
 
 Fig. 104. 
 
 34. Calculations for Fire Engines. Among the data 
 given for the design of a fire engine is the desired height of 
 stream li, and hence the velocity of efflux at the nozzle is 
 determined. This height ranges in hand engines from 15 to 
 30 metres [50 to 100 ft.], while in steam fire engines, as 
 mentioned, it may reach 60 metres [176 ft.] or more. In case 
 no resistance were offered by the air to the motion of the water 
 the velocity of efflux w from the nozzle would correspond to a 
 
150 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 height of stream 7i = , but in consequence of the existing 
 resistance the actual height will be only 
 
 m. [0-01 2w* ft.] , 
 
 as has been proved by experiments. In order to obtain an 
 actual height of stream h it is therefore necessary to generate 
 a velocity of efflux 
 
 w= \/ o2flr&=5'll vh m. [9'26 VA ft.l 
 
 V o 
 
 that is, the pressure to be exerted on the water must be equal 
 
 w 2 
 to that produced by a water column having a height = ^li. 
 
 In other words, the machine is to be proportioned as a pump 
 which is required to force the water to a height of -jA. 
 
 To determine the force needed for this purpose, let Q de- 
 note the water discharged per second, and let F designate the 
 area, and d the diameter of each piston or plunger. The 
 resistance in the suction pipe may be neglected, since the 
 cylinders take their water directly from the cistern. Now, 
 assuming the common arrangement of two single-acting pump 
 cylinders with plungers reciprocated by a lever, and denoting 
 further by d l the diameter of the discharge pipe or hose, by 
 /! the length of the latter, by d 2 the diameter of the delivery 
 valve, and by d m that of the nozzle, then (according to the 
 rules explained in "Weisbach's Mechanics, vol. i.) we have for 
 the head corresponding to the hydraulic resistances of the 
 water on its way from the delivery valve to the nozzle 
 
 where f = 0'05 is the coefficient of resistance at the entrance 
 to the fireman's pipe, f x that due to the friction in the hose, 
 and 2 the coefficient for the delivery valve. Assuming as 
 suitable values the diameter of the hose ^ = 0*05 metre 
 [0-164 ft.], the length ^ = 20 m. [65'6 ft.], the diameter of the 
 
TV TYPES OF RECIPROCATING PUMPS 151 
 
 nozzle orifice d m =0'016 m. [0'052 ft.], i = (V03 or about 1 
 greater than is usual for pipes, and placing 
 
 = T\ = 0-067, 
 
 we obtain 
 
 K = 1 + 0-05 + 0'12 + 0-067 = 1-24, 
 
 while for the case that no hose is used, the water being thrown 
 directly from the stand pipe, we can place 
 
 KI = ! + 0-05 + 0-067 = 1-12. 
 
 The pressure which must be exerted on the water by the 
 plunger in its descent is now determined to be 
 
 and hence taking into account the friction at the plunger we 
 obtain for the force which must be communicated to the 
 latter 
 
 Assuming in this formula 
 
 and introducing the values found above K = 1'24 and K I = 1/12, 
 we accordingly have 
 
 P = 1/90FA7, when the water is forced through hose, and 
 P = 1'72FA7, when it escapes directly from the stand pipe. 
 
 In hand fire engines the available force P is, as a rule, 
 given by the maximum number of men in each working shift, 
 and hence for a given height of stream h, the volume thrown 
 Q and the size of the pump are already determined. As the 
 men engaged at the engine remain at work only a short time, 
 we can assume the effect produced by them much greater, em- 
 pirically about three times greater, than when a working day 
 of eight hours is taken as the basis (6m. kg. or 4 3 '4 ft. Ibs.) 
 If we therefore fix the effect of each workman per second at 
 
152 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 18 m. kg. [130*2 ft. Ibs.], and suppose the brakes to move at a 
 velocity of 1*6 m. [5^ ft.], it is obvious that, since each man 
 exerts a downward pressure only or through an average distance 
 of 0'8 m. [2 '6 2 ft.], the force derived from each individual 
 will be 
 
 K = ^| = 22-5 kg. [49-6 Ibs.] 
 
 If in all 2z men are at work, or z men on each side of the 
 fire engine, and if further a denotes the distance of the brakes, 
 and I that of the pumps from the fulcrum of the lever, then, 
 neglecting the trifling journal friction, we have 
 
 and with K = 22'5 kg. [49*6 Ibs.], when pumping through 
 hose, 
 
 or 
 
 za za 
 
 = 7-r sq. m. F== _ A17 sq. ft. , 
 S5bh H L 2-396A H J 
 
 while, for the case that the water escapes directly from the 
 stand pipe, we obtain 
 
 3? = 0-076Ffcy = 76FA p^ = 0-035FA 7 = 2-16FA~| 
 and 
 
 The area of plunger must be taken twice as great when 
 there is only one single-acting pump cylinder, and only half as 
 great when two double-acting pump cylinders are used. 
 
 From the velocity v=l'Q m. [5j ft.] of the brakes follows 
 
 the average velocity of the plungers V Q = -V, and hence, placing 
 
 a 
 
 the actual volume Q delivered equal to 85 per cent of the 
 theoretical, we obtain for the quantity thrown by both pumps 
 per second 
 
 Q = 0'85F-v=l-36-F cub. m. |Q = 4-46-F cub. ft.] 
 a a a J 
 
iv TYPES OF RECIPROCATING PUMPS 153 
 
 After this value has been computed, we can determine the 
 diameter of the nozzle from 
 
 = Q., giving ^=1-1 
 
 Denoting by s the distance passed through by each brake per 
 stroke, which distance in larger engines varies from 1 to 1'2 
 metre [3'28 to 3'94 ft.], the number of single strokes n of 
 each plunger will be given by 
 
 600 96 T 315, "I 
 n = = m. = ft. , 
 
 s s s 
 
 or, in other words, it may be assumed at from 80 to 90. As 
 two plungers are used, n cylinder volumes are also forced into 
 the air chamber, and hence we have the volume Q= Q'85nFs Q , 
 
 where s = -s is the stroke of plunger, which varies from 0'16 
 a 
 
 to 0-25 metre [6 to 10 ins.] 
 
 The size of the air chamber is determined according to the 
 rules laid down in 29, from the fluctuations in volume of the 
 water per stroke, and the variations allowed in the height of 
 stream. In the latter paragraph we found for the pressures 
 w l and w 2 in the air chamber, which pressures are to be 
 assumed proportional to the corresponding heights of stream, 
 the relation 
 
 derived from Mariottes law, when z/V is the fluctuating volume 
 of the water, and W 2 the minimum volume of the air in the 
 chamber. Giving this equation the form 
 
 W 2 
 
 
 
 and denoting by S the value ? - \ which may serve as a 
 
 w 2 
 
 measure of the variations in the height of stream, we can deter- 
 mine the volume W 2 of the air in the chamber at the moment 
 when it contains the most water from 
 
154 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 where the fluctuating volume z/V is dependent on the move- 
 ment of the plungers. Assuming the movement of the latter, 
 as produced by the brakes, to be subjected to the same 
 variations as characterise the crank motion, we shall have 
 for z/V the value found in 29 for a double-acting pump, or 
 
 0'210V=0-210F-s, and consequently obtain for W 2 the 
 a 
 
 expression 
 
 For instance, if the value 
 
 were chosen, the inequality in the height of stream would be 
 
 or about 4 per cent. 
 
 As already explained, W 2 does not signify the total volume 
 of the air chamber, but the volume which the original quantity 
 of air of atmospheric pressure assumes when compressed so as to 
 
 IV 
 
 exert a pressure ^ = h Q = j^h. If therefore b is the height of 
 
 a water column corresponding to the pressure of the atmo- 
 sphere, the total volume W of the air chamber down to the 
 inlet of the discharge pipe must be made equal to 
 
 REMARK. For ordinary fire engines with two single-acting pump 
 cylinders, and worked by a crew of from eight to thirty-two men, 
 the diameter of plungers is from 0*12 to 0'18 metres [4f to 7 ins.], 
 the volume of water thrown per minute to a height of 25 to 30 
 metres [80 to 100 ft.] being 0'30 to 0'60 cub. m. [10'6 to 21'2 cub. 
 ft.], with a nozzle ranging from 12 to 20 mm. [0*47 to 0'79 ins.] 
 in diameter. The number of single strokes of each plunger per 
 minute varies from 80 to 120, being usually about 90. 
 
iv TYPES OF RECIPROCATING PUMPS 155 
 
 EXAMPLE. If by a single-acting, double-cylinder fire engine with 
 a crew of 2z = 1 6 men and a lever ratio of 7 = 5, water is to be 
 
 thrown from the stand pipe to a height of 30 metres [9 8 '4 ft.], the 
 area of each plunger will be 
 
 which corresponds to a diameter d= 0'150 m. [5 '9 ins.] 
 
 Assuming the distance travelled by each brake on the down 
 stroke to be 1 metre [3*28 ft.], the stroke of plunger will be 
 
 s- = 0*2 m. [7-9 ins.] and the capacity of each pump cylinder 
 
 Ci 
 
 V = Fs ^=0-0175 x 0-2 = 0-0035 cub. m. [0'1236 cub. ft.] 
 The number of single strokes of each plunger per minute is 
 
 and the actual volume of water thrown per second will be 
 Q = 0-85F-v=l-36xx 0-0175 = 0-00476 cub. m.= 4 '76 litres [0-1681 cub. ft.] 
 
 Hence we now obtain for the diameter of the nozzle 
 
 d m =l-lS fj ^. = 1-13 / " " =Q.QU7 metres = about 15 mm. [0-59 ins.] 
 
 2^30 
 
 If the volume W 2 of the air in the chamber is to be equal to 
 four times the capacity of each pump cylinder, or if 
 
 W 2 =4F$!=4x 0-0035 = 0-014 cub. m., 
 we shall have for the total volume of the air chamber 
 
 )14 = 0-068 cub. m. =68 litres [2-4 cub. ft], 
 
 i/ j. \j citt 
 
 which volume may be furnished by a cylinder 0*38 metre [15 ins.] 
 in diameter and 0'6 metre [2 ft.] high. 
 
 More detailed information on fire engines may be obtained from 
 Frick's work : Die Feuerspritze, Anleitung zu deren Ban, JBerechnung, 
 Behandlung und Prii/ung, Braunschweig, Fr. Vieweg und Sohn. 
 
 35. Driving Gear for Pumps. Mine pumps deriving 
 their power from a water-wheel are usually driven by cranks. 
 If an ordinary vertical water-wheel is used, no gears are needed, 
 
156 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 since the number of revolutions (four to eight per minute) of 
 such a wheel corresponds to the usual number of double strokes 
 of the pump. On the other hand, when turbines are employed, 
 the number of revolutions is so great that one or more pairs of 
 gears are always required in order to give the crank shaft the 
 desired speed. 
 
 The pumps may be driven with or without the aid of levers. 
 In the latter case the pump rod is suspended directly from the 
 crank, which is either in one piece with the water-wheel shaft, 
 or on a shaft coupled to the latter, while in the former case it 
 is suspended from a lever which is reciprocated by the crank by 
 means of a special connecting rod. When one pair of gears is 
 employed, the smaller is placed on the water-wheel or turbine 
 shaft, and the larger on the crank shaft ; when two pairs of gears 
 are made use of, a third shaft is interposed between the turbine 
 and crank shafts, receiving the power from the former by means 
 of a large gear, and provided with a smaller gear for driving 
 the crank shaft. If, for instance, the turbine makes sixty 
 revolutions per minute, and only five are required for the crank 
 shaft, that is, for a velocity ratio of ty = ^ = - r ^-, two pairs of 
 gears may be employed, having the ratios ^ = ^ and ^ 2 ~ i 
 Owing to these necessary reductions in speed, turbines are less 
 suited for driving mine pumps than the slow-running vertical 
 water-wheels. 
 
 Smaller pumps that are intermittently in use, and then only 
 for a short period, are occasionally driven from a vertical shaft 
 rotated by horse power. The arrangement is then practically 
 the same as when a water-wheel is the source of power, only, 
 a pair of gears is always needed on account of the slow speed 
 of the vertical shaft, which, with the usual length of sweep, 
 makes only two revolutions per minute. 
 
 Pumps used for feeding boilers and for various other purposes 
 in mills, factories, etc., are often driven from a horizontal line of 
 shafting. Such pumps are for this purpose usually provided with 
 a fast and a loose belt pulley mounted on a shaft, which, by a 
 crank, either directly or indirectly through gears, connects with 
 the piston rod. Various types of power pumps of this class are 
 met with in practice. A novel form of power pump is the electric 
 pump, which is at the present time coming into the field, especially 
 for pumping in mines. The power is derived from an electric 
 motor which, in some instances, by means of double inclined tooth 
 
TYPES OF RECIPROCATING 
 
 157 
 
 PROF LI, 
 
 s to each other, 
 number of 
 
 gearing and a crank shaft with cranks at 
 
 drives three pump pistons working in a cor 
 
 cylinders. The multi-cylinder type is 
 
 the variations in resistance to the very regular drrong force as 
 
 slight as possible. In this manner the maximum variation, as stated 
 
 by some builders, may be brought down to about 5 or 6 per cent 
 
 of the mean resistance. TRANSLATOR'S REMARK. 
 
 Finally, pumps are frequently operated by windmills. The 
 simplest arrangement is then obtained by making a bend in the 
 windmill shaft and attaching the pump rod to the crank thus 
 formed. As, however, by this method a very large number of 
 revolutions is obtained, and hence a very short stroke must be 
 W 
 
 D 
 
 Fig. 105. 
 
 given to the pump, which materially reduces the useful effect 
 of the latter, the better plan is to make use of a pair of gears 
 reducing the motion of the crank shaft to one revolution for 
 every three revolutions of the windmill shaft. Since the 
 wind- wheel must always be pointed against the wind, and 
 therefore must be made movable about the vertical axis of the 
 mill building, it is necessary, when no gears are employed, to 
 attach the pump rod to the connecting rod by means of a 
 swivel joint, while in windmills with gears an upright gear 
 shaft must be introduced in the centre of the building in order 
 that the proper contact of the gears shall not be interfered 
 with as the direction of the wind-wheel shaft changes. 
 
 The sketches shown in Figs. 105 to 110 indicate some of 
 the arrangements above referred to. 
 
158 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 Fig. 105 represents a simple method of driving a pump by 
 a water-wheel "W ; CA is the crank, AB the connecting rod, 
 BD the pump rod, and EF the piston rod connected to BD by 
 means of the arm E. Figs. 106 and 107 show two lever 
 
 J~ 
 
 i 
 
 Fig. 107. 
 
 Fig. 108. 
 
 motions ; in the former a bell crank or so-called lob BDE is 
 used, while in the latter a straight lever DBE is acted on by 
 the connecting rod AB with the short arm DB, and receives 
 the load at the end of the long arm DE. In Fig. 108 the 
 pump is driven by a turbine through the medium of two pairs 
 
 Fig. 109. 
 
 Fig. 110 
 
 of gears. W is the turbine wheel, GH the shaft belonging to 
 the latter, DE the gear shaft, CO the crank shaft with the 
 cranks CA, which reciprocate the pump rods AK. Fig. 109 
 illustrates a pump driven by horse power, DE representing the 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 159 
 
 upright shaft with the sweep EF and the driving gear DB 
 engaging the gear B on the crank shaft C. Finally, in Fig. 
 110 is shown a windmill pump with two pairs of gears. By 
 means of the bevels F and E the wind-wheel shaft GH drives 
 the vertical shaft DE, which in turn rotates the 
 crank shaft C by the aid of the bevels D and B. 
 
 The piston rods of mine pumps are attached to 
 long rods or systems of rods or beams working up 
 and down in the so-called engine shaft. The axes of 
 these rods as well as those of the pump cylinders 
 will therefore fall in the line of direction of this 
 shaft, being vertical when the shaft is vertical, and 
 inclined when the latter inclines to the horizon ; the 
 connection to the piston rods is usually one-sided, 
 rarely central, being accomplished by means of 
 cross bars. Evidently a central connection would 
 be mechanically more perfect, as it would bring a 
 uniform tensile stress on the main pump rod, which 
 is otherwise subjected to a bending action ; but, on 
 the other hand, such an arrangement would involve 
 greater complication, since the rods would have to 
 be made forked, and bends must be introduced in 
 the suction and in some cases also in the delivery 
 pipe. One method of applying a central connection 
 is shown in Fig. Ill, where AB is the suction pipe with a 
 bend at B, C the pump barrel, K the piston 
 rod attached to the arm FF, and FFGG the 
 forked portion of the pump rod. 
 
 Both inclined and vertical pump rods with 
 eccentric connections require to be guided 
 by rollers. When the rod is inclined at an 
 angle a to the horizon, as DE, Fig. 112, the 
 roller B sustains the component N = G cos 
 a of its weight G. If < is the coefficient of 
 friction, r the radius of the roller, and p the 
 radius of its journal, then the journal friction reduced to the 
 axis of the rod will be 
 
 Fig. 111. 
 
160 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 or, if the total weight Gj of the rollers is taken into account, 
 approximately 
 
 F = < (G + GJ cos a. 
 
 Combining this resistance with the remaining lateral force 
 S = G sin a, we obtain 
 
 (1) the force required for pulling up the rod alone, 
 
 P = S + F = G sin a + <j> " (G + G x ) cos a, 
 and (2) the force which assists the rod in its descent, 
 P x = S - F = G sin a - </> (G + G x ) cos a. 
 
 When the rod is vertical and the connection is eccentric, 
 guide rollers, D and E, Fig 113, are introduced to keep the 
 rod from bending. For this case, if Q is the load of the pump, 
 a the eccentricity or the distance AB from the axis of the 
 piston rod to that of the pump rod, and I the distance apart 
 DE of the two rollers D and E, then each of the latter will 
 be acted on by a force 
 
 -*$" 
 
 since the couple ( Q, Q) of moment Q& must be in equili- 
 brium with the couple ( N, N) of moment N7. 
 
 If there are several pumps attached to the same side of the 
 rod, we must substitute for Qa the sum Q 1 a 1 + Q 2 2 + > 
 where Q 1 , Q 2 . . . represent the respective loads of the pumps 
 and % , a . . . the corresponding lever arms ; we then obtain 
 
 I 
 
 On the other hand, when Q x and Q 2 act on opposite sides of 
 the rod, we have 
 
 x = 
 
 
 
 In the latter instance, if Qj^ Q 9 + . . . were equal to 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 161 
 
 zero, we should also have N = 0, that is, guide rollers would be 
 unnecessary. 
 
 If, when the pump rod is inclined, the load is attached to 
 the upper or lower side of it, the pressure on the rollers will 
 be dependent both on the load on the pumps and the weight of 
 the rod. Supposing the centre of gravity S of the rod DE 
 (Fig. 114) to be located midway between the two rollers, then, 
 owing to its weight, the rod will in D and E exert a normal 
 
 + Q 
 
 -Q 
 
 Gcoso 
 
 Fig. 113. 
 
 Fig. 114. 
 
 downward pressure of -J-G cos a, while, in consequence of the 
 
 load Q on the pump, it will press downward with a force 
 
 I 
 
 at D, and upward with the same force at E. The total pres- 
 sures on the rollers will therefore be, at D, 
 
 and at E 
 
 The journal friction of the rollers due to both of these pres 
 sures, and reduced to the axis of the pump rod, will be 
 
 M 
 
162 MECHANICS OF PUMPING MACHINERY CHAP, iv 
 
 which becomes either 
 
 or 
 
 = <- G COS a, 
 
 according as is greater or smaller than -JG cos a. 
 I 
 
 When the pumps in a mine are operated by one pump rod 
 only, the latter must be balanced. This can be done either by 
 means of counterweights or by a hydraulic balancing arrange- 
 ment (see Weisbach's Mechanics, vol. iii. 1, chap. 9), or by 
 using both suction and force pumps and making the load due 
 to the forcing action equal to that due to suction together with 
 the weight of the rod. 
 
 Two rods are frequently employed, so connected to the driv- 
 ing motor or to each other that one ascends while the other 
 descends, the two being therefore always in balance. For 
 further details of the latter mode of connection we refer to 
 the volume of Weisbach's Mechanics just cited. 
 
 36. Mine Pumps operated by a Water-Wheel. The 
 general features of a pumping arrangement of this kind are 
 illustrated in Fig. 115. The motive power is taken from an 
 overshot water-wheel ECO, the driving water W being intro- 
 duced to the wheel through the sluice gate S. The water- 
 wheel shaft C has two cranks, one at each end, and set at 180 
 angle to each other. By means of connecting rods and bell 
 cranks or bobs these cranks cause two equally loaded pump 
 rods to move alternately up and down. In the figure only 
 one crank CA is shown, together with its connecting rod AB, 
 bob BDE, and pump rod EF. Of the suction pumps attached 
 to the latter only the upper one KL is completely visible, 
 while the next lower pump Hj, which supplies water to that 
 above it, is but partly shown. The arms G and G 1? to which 
 the piston rods are attached, are secured to opposite sides of 
 the pump rod, and consequently the couples due to the 
 eccentric connection neutralise each other, so that the Trending 
 stress in the rod is very slight. The lifted water is discharged 
 at L, and flows away through the adit or tunnel M, while 
 the driving water after being utilised is carried off by the day 
 
Fig. 115. 
 
164 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 level P. Usually in a plant of this kind there is a second fall 
 between the day level and the tunnel ; this fall is available for 
 other purposes, the water after having been used being also 
 carried away by the tunnel. 
 
 In making the calculations for a pumping arrangement of 
 above description, it is evidently necessary, besides computing 
 the load on the pistons in accordance with the rules already 
 given, to take into consideration the friction at the bearings 
 and pins of the bell cranks as well as of the driving cranks. 
 The efficiency 77 of the whole arrangement is a product rj l ?; 2 77 
 of the efficiencies ^ of the water-wheel, ^ of the cranks, 
 pump bobs, connecting rods, and pump rods, and rj s of the 
 pumps ; when these three efficiencies are known, the efficiency 
 of the whole machine will therefore be known, and we can 
 determine the ratio of the net load on the pumps to the 
 driving force required. 
 
 Denoting by Q the quantity of driving water used per 
 second, by h the fall, and letting Q 1} Q 2 . . . represent the 
 quantities to be raised per second by the pumps to the heights 
 h lf h 2 . . ., we have the following general formula 
 
 or simpler, 
 
 From the given volumes Qi, Q 2 . . . and the corresponding lifts 
 A! , A 2 . . . we can now compute the necessary water power, and 
 from the known fall we can determine the driving water re- 
 quired 
 
 = Q 1 /i 1 + Q 2 fr 2 + . . . . 
 
 rjh 
 
 If s is the stroke of the pistons, n the number of double 
 strokes per minute, p the coefficient of discharge (see 25), 
 and F 1? F 2 . . . the areas of the pistons, then we have 
 
 and consequently 
 
iv TYPES OF RECIPROCATING PUMPS 165 
 
 The number of revolutions of the water-wheel is the same 
 as the number of double strokes n made by the pumps ; conse- 
 quently, if a is the radius of the wheel, its circumferential 
 velocity will be 
 
 From the well-known formula Q = edev, where d is the width 
 of shrouding, e the width of the wheel, and e the coefficient of 
 fill, the wheel must have a width 
 
 = Q = 30Q = 9-55Q 3 
 enda 
 
 in order to receive the requisite volume of driving water Q. 
 
 EXAMPLE. A pumping plant driven by a water-wheel is to be 
 designed for a mine; O'l cub. m. [3 '53 cub. ft.] of water per 
 minute are to be raised from the bottom to a height of 48 metres 
 [157-48 ft.], then from the latter level 0'15 cub. m. [5'29 cub. ft.] 
 to a height of 60 metres [196*85 ft], and finally from this point 
 0'25 cub. m. [8 '8 3 cub. ft.] are to be lifted per minute to the tunnel 
 80 metres [2 6 2 '4 7 ft.] above it. The available water power has a 
 fall of 10 metres [32-81 ft.] 
 
 Assuming the efficiency of the whole arrangement to be 77 = 0'50, 
 we obtain in the first place the driving water required per second, 
 
 n 1 0-lx48 + 0'15x60 + 0-25x80 
 
 Q = gQ - 0-6xTo =0-113 cub. m. [3 '99 cub. ft.] 
 
 Giving the wheel a radius = 4'5 m. [14'76 ft.], and a speed 
 of five revolutions per minute, we have for the circumferential 
 velocity 
 
 r = -14 x 4-5 *5 = 2 . 85 . m , [7 . 72fu 
 
 and thus for a radial depth of the shrouding d = 0'3 m. [0'98 ft.], 
 and a coefficient of fill e = \, we obtain the width of the rim 
 
 g = -S- = . A ' n ;L e , = 0-64m. [2-1 ft] 
 edv x 0'3x2'355 
 
 If we desire to overcome the respective delivery heights by 
 using bucket pumps having lifts not exceeding 8 metres [2 6 '2 5 
 ft.], we shall require for the lowest section 6 pumps of 8 metres 
 [2 6 '2 5 ft.] lift, in the middle section 8 pumps of 7 '5 metres [24*6 
 ft.] lift, and in the upper section 10 pumps of 8 metres [26 '25 ft.] 
 lift ; of these respectively 3, 4, and 5 pumps will be attached to 
 
166 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 each rod. Giving to all the pumps a stroke of 1 m. [3 '2 8 ft.], 
 and assuming the coefficient of efflux to be /z = 0'85, we obtain for 
 the piston areas the following values 
 
 o-i 
 
 F 2 = 
 
 row X y X 
 0-15 
 
 r = 0-023o sq. m. [0'2528 sq. ft.] for the lowest pumps, 
 
 J. 
 
 0-85x5 
 0-25 
 
 = 0*0353 sq. m. [0'3798 sq. ft.] for the middle ones, and 
 = 0-0588 sq. m. [0'6327 sq. ft.] for the upper pumps. 
 
 ' 0-85x5 
 Hence the corresponding diameters will be 
 
 ^ = 0-173 m. [6'81 ins.], <Z 2 = 0'212 m. [8'35 ins.], 
 
 ^3= 0-274 m. [10-79 ins.] 
 
 and 
 
 37. Water-Pressure Pumps. The water-pressure engines 
 are specially adapted to serve as prime movers for pumping 
 plants, inasmuch as they move in the same manner and at the 
 same velocity as pumps. Water-pressure pumps are, therefore, 
 always direct acting. The methods of connecting the pump 
 rods to the piston rods of the water -pressure engines are 
 illustrated in Figs. 116 to 120. 
 
 In the arrangement shown in Fig. 116 the pump piston L 
 is attached to the same rod KL as the driving 
 piston K, and while the latter ascends water is dis- 
 charged by the pump into the delivery pipe BC, 
 whereas during the descent, which is caused by 
 the weight of the rod, water is sucked in through 
 the suction pipe AB. The rod KL must be guided 
 by a stuffing box both at the driving and at the 
 pump cylinder. The arrangement indicated in 
 Fig. 117 is quite different, the driving rod KL 
 being carried upward and the pump rod DS being 
 attached to one side of it. Owing to the eccentric 
 application of the load a couple is formed, which 
 necessitates guiding the joint of the two rods be- 
 tween rollers. The weight of the rods is balanced 
 by a counterpoise attached to a lever ACB. A 
 more perfect joint is that shown in Fig. 118, where 
 the pump rod BS is united to the piston rod KL by 
 means of a forked or two-sided connection CD, and therefore the 
 application of the load is perfectly central. In order to balance 
 
 Fig. 116. 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 167 
 
 the weight of the rod in its descent, a so-called hydraulic 
 balance HA is made use of, through which the driving water is 
 discharged upward ; the rod will be completely balanced by 
 giving the water column in the hydraulic balance a height 
 G 
 
 When a water -pressure pump is to be employed for an 
 inclined shaft, the driving cylinder may either, together with 
 
 Fig. 117. Fig. 118. 
 
 the pumps, be made to work in the direction of the shaft, or 
 it may be placed vertically, the pump rods BS (Fig 119) being, 
 in this case, by means of a bell crank or sweep ABC, attached 
 to the piston rod KL, whose upper end is provided with a 
 friction roller L travelling between vertical guides DE. 
 
 Some older constructions consist of two water -pressure 
 engines having the same supply pipe EH (Fig. 120). Their 
 pistons move alternately up and down, and the two engines 
 
168 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. IV 
 
 are connected by means of an equal armed balance beam 
 in such a manner that the rods keep each other in equilibrium, 
 no further counterpoising being necessary. 
 In the apparatus illustrated there are two 
 
 force pumps LL X with a 
 
 common suction pipe D, 
 
 and a common delivery 
 
 pipe S. 
 
 The general arrange- 
 ment of a pumping plant 
 
 operated by water-pressure 
 
 engines is evident from 
 
 Figs. 121 to 124, which 
 
 represent such a plant de- 
 signed by Brawnsdorft and 
 
 in actual operation in a 
 
 mine near Freiburg. In 
 
 Figs. 121 and 122 the 
 
 water -pressure engine is 
 
 shown ; EE is the supply 
 
 pipe, D is a branch pipe 
 leading to the valve cylinder and containing 
 a stop valve, TT is the driving cylinder, CC 
 a pipe which connects the latter and the valve cylinder, and AA 
 is the discharge pipe with the necessary regulating valve. The 
 pump rod PQ is attached to the piston rod K (as in Fig. 118) 
 by means of a forked connection on each side of the driving 
 cylinder, consisting of the coupling rods MN, etc. The main 
 valve consists of the distribution piston S and the counter 
 valve G ; an auxiliary piston valve H is also used, attached to a 
 rod suspended from a lever L, which is moved alternately up 
 and down by lugs on the piston rod K. At c is a branch 
 pipe leading from the supply pipe EE, and at a the discharge 
 pipe for the water used in the valve cylinder. The cuts 
 represent the driving piston on its down stroke, during which 
 period both the main valve SG and the auxiliary piston valve 
 H are in their highest positions. Towards the end of the 
 down stroke of the driving piston the auxiliary valve H 
 reaches its lowest position, and now the space above the 
 counter piston G is brought in communication with the driving 
 
sVX 
 
 Fig. 121. 
 
 Fig. 122. 
 
170 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 water through the pipe c, the double piston valve SG- in conse- 
 quence being forced downward. When the distribution valve S 
 has arrived to its lowest position, the pipe CC, and accordingly 
 the space below the driving piston, will be in communication 
 with the driving water column EED, and the driving piston 
 will therefore begin to ascend, etc. 
 
 Figs. 123 and 124 illustrate the arrangement of the force 
 pumps driven by the above-described water engine. Also at 
 this point the pump rod PQ forms a fork MN", which straddles 
 the pump barrel C, and is united to the piston rod K by the 
 scarf M. The suction and delivery pipe DS contains the 
 suction valve V and delivery valve W, and communicates 
 with the lower end of the barrel by means of a short pipe. 
 During the down stroke of the pump piston K, which is 
 shown in the figure, V is closed and W open, and consequently 
 the water is forced upward through the delivery pipe WD ; 
 on the other hand, when the piston K ascends, V is opened 
 and W closed, and a fresh supply of water is sucked in 
 through the suction pipe SV from the cistern S, which obtains 
 its water from the delivery pipe AB of the next lower pump. 
 
 The mechanical relations of a water-pressure pump of the 
 common construction just described are to be calculated as 
 follows. 
 
 The efficiency 77 = rj^ of the whole machine is here a pro- 
 duct of the efficiencies ^ of the water-pressure engine and fj 2 
 of the pumping apparatus. Hence, denoting by Q the volume 
 of driving water, by h the fall for driving the water-pressure 
 engine, and finally by Q r Q 2 . . . the volumes which are to be 
 raised by the pumps to the heights h v 1\ . . . , we can 
 write 
 
 Now, if s is the stroke of piston, ft the coefficient of dis- 
 charge for the pumps, and n the number of double strokes per 
 minute, we also have 
 
 and consequently 
 
iv TYPES OF RECIPROCATING PUMPS 
 
 from which we obtain the formula 
 
 171 
 
 tj h 
 
 for determination of the necessary area of driving piston. This 
 
 Fig. 123. 
 
 Fig. 124. 
 
 area is, as a rule, made larger in a new plant in order that 
 sufficient power may be available in case it should be necessary 
 
172 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 to attach additional pumps ; the surplus of power must evi- 
 dently be disposed of by adjusting the regulating valve. 
 
 In the water-pressure pump above described the water is 
 forced upward by the weight G of the descending rod, while 
 the driving piston of the water engine merely sucks in water 
 and lifts the rod. 
 
 If we place 
 
 h = -z 
 
 h 2 = y 2 + z z , etc., 
 
 where y and z are the heads corresponding to the ascent and 
 descent respectively of the driving piston, y v y 2 the heights of 
 suction, and z l9 2 9 the delivery heights of the individual pumps, 
 then we have 
 
 - G) = 
 and 
 
 - Fzy) = X*>! + I> 2 + . . .)y ; . (2) 
 
 hence we obtain by addition 
 
 p 
 
 or, as above, 
 
 After the piston area F has been determined from this 
 formula, we can now, from equations (1) and (2), compute 
 either the necessary weight G of the rod or the head z of the 
 hydraulic balance. 
 
 EXAMPLE. If, as in the example, 36, the volumes 0*10, 0'15, 
 and 0-25 cub. m. [3 '5 3, 5 '2 9, and 8 '8 3 cub. ft.] are to be raised per 
 minute to the respective heights of 48, 60, and 80 metres [157*48, 
 196-85, and 2 62 '4 7 ft.], for which purpose a fall of 75 metres 
 [2 46 '07 ft.] is available, the proportions of a water-pressure engine 
 suitable for the conditions mentioned may be computed in the 
 following manner. 
 
 Assuming again for the total efficiency of the plant 77 = '50, we 
 obtain, as the necessary volume of driving water per second, 
 
 Q = ^ O-lx 48 + 0-^15 x 60 + 0-25 x80 
 
iv TYPES OF RECIPROCATING PUMPS 173 
 
 Making use of three fvrce pumps of the kinds shown in Figs. 123 
 and 124, and placing the stroke s = 2 metres, the number of double 
 strokes per minute at 4, and assuming the coefficient of discharge 
 /x= 0'S5, we have for the piston areas and diameters of the three 
 pumps 
 
 ' 5 ^i = ' 137 m - [F, = 0-158 sq. ft., ^ = 5'39 ins.] 
 F 2 = =0-0221 sq. m., d 2 = 0'168 m. [F 2 = 0'238 sq. ft., d> = 6'61 ins.] 
 
 U oO X 4 X ^ 
 
 F 3 =. ,?' 2 ^ = 0-0368 sq. m., d 3 = 0'2!7 m. [F 3 = 0'396 sq. ft., d 3 = 8'54 ins.] 
 
 U oO X 4 X 
 
 For the driving piston we get 
 
 ^ rf = . 379 m< [F = 1 . 210 sq> ft>> ^ = 14.92 ins.] 
 
 4 x 2i 
 
 According to equation (1) the necessary pressure column is 
 
 G 
 
 Assuming the weight of the trussed rod to be 9000 kilos [19,840 
 Ibs.] and the height of suction of each pump to be 5 metres [16'4 
 ft.], we obtain 
 
 0-85 0-0147 + 0-0221 +0-0368 g , 9000 ...-_,_ an 
 y = ^5 ~ 0-1125 -5 + n 2T5 = 5-56 + 80 = 85-56m. [2807ft.] 
 
 As, however, the available fall is only 75 metres [246*07 ft.], the 
 machine must be placed at a distance 
 
 2 = 85 -56- 75 = 10-56 m. [44 -63 ft.] 
 
 below the level of the tunnel. By deducting the suction of 5 
 metres from the total heads of the pumps we obtain the heights 
 43 m., 55 m., 75 m. [141-08, 180-45, 246'07 ft.] to which the 
 water is forced. 
 
 38. Water-Pressure Pumps (continued). On the pipe 
 line between Berchtesgaden, Keichenhall, Traunstein, and 
 Kosenheim, in Upper Bavaria, nine water-pressure pumps con- 
 structed by the celebrated Eeichenbach are used for pumping 
 brine over the mountain. In these machines three different 
 systems may be distinguished, the most modern and preferable 
 being that employed at Berchtesgaden and illustrated in Fig. 
 125. This machine differs from the ordinary water-pressure 
 pumps essentially in that it has two driving pistons secured to 
 the same piston rod ; the smaller of the two is pushed upward 
 
Fig. 125. 
 
CHAP, iv TYPES OF RECIPROCATING PUMPS 175 
 
 by the driving water and creates the suction necessary to cause 
 the brine to rise, while the larger, which is moved downward 
 by the driving water, forces the brine into the delivery pipe. 
 The fall utilised for this machine is 116 metres [380'58 ft.] r 
 and the height to which it raises the brine is 378 metres- 
 [1240-18 ft] 
 
 The water-pressure engine proper consists of the driving 
 cylinders C and D, with the driving pistons K and L, the 
 supply pipe E, the discharge pipe A, the valve rods with the 
 three piston valves S, T, and U all enclosed in one valve 
 cylinder, and an auxiliary valve composed of the two pistons 
 m and p and operated by means of a lever srq from the driving, 
 piston rod KP. The pump is composed of the cylinder with 
 the plunger P attached to the end of the driving piston rod,, 
 further, the valve chamber in which the suction valve V and 
 delivery valve W are located, and the suction pipe connected 
 at Q as well as the delivery pipe attached at K. In the piston 
 position shown in the figure the driving water is admitted 
 through EF above the larger piston K, and forces the combina- 
 tion of pistons LKP downward, causing the water contained 
 below the smaller piston L to flow back through the pipe G- 
 into the valve cylinder and to discharge through the orifice M ; 
 at the same time the brine contained in the pump below the 
 plunger P is forced through the delivery valve W into the 
 delivery pipe E. Towards the end of the down stroke the 
 piston valve mp is pushed upward by the lever srq, thus expos- 
 ing the lower side of the reversing piston U to the driving 
 water entering from the small pipe L As a result, the valve 
 combination UST ascends, the main valve S shutting off the 
 water from the driving piston K, while the piston valve T 
 places the smaller driving cylinder DD in communication with 
 the supply pipe E. 
 
 The pressure of the water on the small driving piston L- 
 now causes the trussed driving rod PKL to ascend, together 
 with the pump plunger P, which sucks in the brine through 
 the suction pipe at Q and suction valve V, while the water 
 above the large piston K is discharged through FA. At the 
 latter portion of this up stroke the double piston valve mp is 
 pulled down by the lever srq, thus removing the pressure from 
 the piston U ; as the pressure on the larger piston S is greater 
 
176 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 than that on the smaller T, the valve combination will now 
 descend and a new stroke will commence. 
 
 Denoting by li the fall of the water engine, by 7^ the height 
 of suction, h. 2 the delivery height, and by e the specific gravity 
 of the brine ; further, letting F designate the area of the large 
 piston K, Fj that of the smaller driving piston L, and F 2 that 
 of the pump plunger P, then, neglecting all wasteful resist- 
 ances, we can place 
 
 F a /l = eF^, 
 
 and 
 
 (F-F^eF^; 
 
 we consequently have 
 
 J\ __ h 
 
 F-FrV 
 and the ratio 
 
 A pipe located above the supply pipe, and provided with a 
 cock N, serves to let in air when it is desired to draw off the 
 water after the machine has been stopped. In other respects 
 the water engine does not differ from the machines describee! 
 in the volume on Hydraulics. The apparatus just described 
 has a stroke of nearly 1 metre [3 '2 8 ft.], the diameter of the 
 large piston is d 0'738 m. [2'42 ft], and that of the smaller 
 driving piston as well as of the pump plunger is d^ 0*292 m. 
 [0'96 ft.]; consequently the driving water absorbed per stroke 
 is 
 
 V = ?[(^O = . 495 cub m |- 17 . 48 cub ft j 
 
 Adding the water needed for operating the valves, or 0'015 
 cub. m. [0'53 cub. ft.], we obtain for the theoretical effect of 
 the motor per double stroke 
 
 A = Vh 7 = (0-495 + 0-015)116 x 1000 = 59160 m. kg. [427917 
 
 ft. Ibs.] 
 
 The theoretical volume of brine raised per double stroke is 
 V 1 = ^s = 0-067 cub. m. [2-37 cub. ft.], 
 
iv TYPES OF RECIPROCATING 
 
 and therefore, if the specific gravity o 
 we have for the theoretical effect 
 stroke 
 
 A l = y i (h l + h f) )y = 0'OQ7 x 378 x 1200 = 30391 m. kg. [219828 
 
 ft. Ibs.], 
 
 which corresponds to an efficiency for the whole machine of 
 
 A 30391 . 
 = 
 
 Some very interesting water -pressure engines have been 
 placed in the " Konigin-Marien-Schachte " at Clausthal. They 
 were designed by Jordan 1 after the manner of the two-cylinder 
 steam engines, having two horizontal driving cylinders A 
 (Fig. 126), the piston rods by means of the connecting rods B 
 rotating a fly-wheel shaft C having two cranks D at right 
 angles to each other. The pumps K are in a line with the 
 driving cylinders, each piston rod k transmitting the motion of 
 the driving pistons a directly to the pump plungers p, while 
 the fly-wheel shaft C merely serves to make the motion more 
 uniform, and to operate the valve pistons S by means of the 
 eccentrics E. Both driving cylinders and pumps are double 
 acting, thus producing great uniformity in the discharge of the 
 water. 
 
 The column of driving water has a height of 368*4 metres 
 [1208'7 ft.], and the water is raised by the pumps to a height 
 of 228-8*7 metres [750'7 ft.], of which 4 metres [13'1 ft.] is 
 overcome by suction. On account of the arrangement chosen 
 the use of a pump rod is entirely avoided, inasmuch as the 
 machines are located at M (Eig. 127), or about 225 metres 
 [7 3 8 '2 ft.] below the level of the adit or tunnel A, the pumps 
 sucking in water from B and forcing it up to A, while the 
 driving water is admitted at C and conducted to the machine 
 through the pipe D ; the latter water, after being utilised in 
 the cylinders, rises together with the water delivered by the 
 pumps through the discharge pipe E to the tunnel. Accord- 
 ingly the driving column is given by the height between A 
 
 1 See Zeitschr. f. Berg-, Hiitten- u. Salinenwesen, Jahrg. 1878, pp. 233 and 
 240. 
 
CHAP. IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 179 
 
 and C. As already mentioned, the necessity of using a pump 
 rod is hereby avoided, an advantage in comparison with which 
 the accompanying disadvantages are trifling ; the latter are due 
 to the facts that the driving water must pass through an extra 
 
 length of 2 x 224'8 in. = 449'6 m. [1474-7 y 
 
 ft.] from A to M and again back to A, and 
 that the driving cylinders are subjected to 
 a correspondingly increased pressure. In 
 modern practice the use of pump rods in 
 mines is also avoided by the employment 
 of steam pumps placed underground, as will 
 be further referred to below. 
 
 The double -cylinder water -pressure 
 pumps at Clausthalhave given satisfactory 
 results ever since they were started, being 
 characterised by smoothness of running with 
 no signs of shocks, such as are easily apt 
 to occur in water -pressure engines, even 
 when the regular speed of 12 revolutions 
 per minute was increased to 1 6 revolutions. 
 The driving pistons are 0'3 1 metres [11*81 
 ins.] in diameter, the pump cylinders 0*328 
 metres [12 '92 ins.], and the stroke common 
 to both is 0'625 metres [2'05 ft.], and con- 
 sequently for 12 revolutions per minute 
 the mean piston velocity is 0'25 m. [0'82 
 ft.], and the water raised per minute 1'878 
 cub. m. [6 6 '3 2 cub. ft.] ; all pipes are made 
 of such proportions that for this effect the 
 velocity of the water never exceeds 1 metre 
 [3*28 ft.] 
 
 Special calculations and data regarding the exact results 
 obtained may be found in the interesting articles by Hoppe 
 in Zeitsclir. /. Berg-, Hutten- und Salinenwesen, Jahrg. 1878 
 and 1879. According to these articles, the efficiency of 
 the pumps increased with the velocity, amounting to 0'35 at 
 12 revolutions per minute. Nearly the same result was 
 obtained by a calculation which took into account the various 
 
 losses. By efficiency is here understood the ratio 77 = -~~ , 
 
 -X- 
 
 A 
 
 Fig. 127. 
 
180 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 where li is the fall of the driving water Q, and 7^ the height 
 to which the volume Q x is pumped. 
 
 39. Steam Pumps. Analogous to the use of the terms 
 steam hammer, steam pile-driver, etc., the name steam pump 
 is applied to pumps in which the plunger is reciprocated 
 directly by a steam piston and rod, in distinction from pump- 
 ing engines where the motion is transmitted in a less direct 
 manner, as by the use of walking beams, pump rods, etc. 
 Smaller steam pumps are largely employed as boiler feed- 
 pumps, also in procuring water for factories or public build- 
 ings, and for steam fire engines ( 33). The modern pumping 
 engines located in the shafts of mines are usually of the direct- 
 acting type. In nearly all the cases cited the pumps are 
 double-acting suction and force pumps, only the boiler feed- 
 pumps, owing to their comparatively small capacity, being 
 often made single-acting, with plungers of the kind shown in 
 Fig. 64. Even in the latter instance, however, the steam 
 cylinders are always double acting, only that the effective 
 piston areas, by the use of a large piston rod, are made to 
 differ materially in size, so as to conform to the great differ- 
 ence in the resistances offered to the plunger on forward and 
 return stroke. With a view to obtaining a still more uniform 
 motion a fly-wheel is sometimes employed, 
 being placed on a revolving shaft which 
 may also be used to operate the valve by 
 means of an eccentric. The double-acting 
 pumps are likewise frequently provided 
 with a fly-wheel shaft, though in modern 
 practice the latter is occasionally dispensed 
 with. 
 
 The arrangement of a single-acting 
 steam pump can be seen in Fig. 128. 
 Here the steam piston A is connected to 
 the plunger D by a rod which at the 
 middle is expanded into a slide E with a 
 slot in which the block C receiving the 
 crank pin of the auxiliary shaft H is guided. 
 This movement, which has been termed 
 the slider crank (see Weisbach's Mechanics, vol. iii. 1), offers 
 greater resistance to motion than the ordinary crank, but where 
 
iv TYPES OF RECIPROCATING PUMPS 181 
 
 simplicity of construction is of prime importance, as is the 
 case with small pumps, it may be used to advantage, more 
 especially as the forces transmitted to the fly-wheel shaft, 
 which are due only to the inequalities of pressure on the pistons, 
 are there quite insignificant ; for larger pumps this arrange- 
 ment is not to be recommended. 
 
 As the height of delivery for a pump of the above descrip- 
 tion feeding a boiler against a pressure of n atmospheres when 
 the water-level is at the height k 2 above the pump cylinder, 
 we must introduce Ii 2 + n~b = h^+ 10 '3 4% metres [7t 2 + 33'9% 
 ft.], and consequently, if friction is neglected, the resistances 
 opposing the plunger on the up and down strokes are to each 
 other as \ : h 2 + rib, when the height of suction is denoted by 
 /ij. In order that steam pressure and pump resistance may 
 correspond as nearly as possible, it would be necessary to pro- 
 portion the surfaces exposed to the steam in the same ratio, 
 i.e. we should make 
 
 hnb~W~ D 2 ' 
 
 where F is the area and D the diameter of the steam piston 
 A, while / is the sectional area and d the diameter of the 
 piston rod C. But, owing to the insignificance of the resist- 
 ance due to suction as compared with that due to the forcing 
 action, disproportionately large piston rods would then be 
 needed in boiler feed-pumps, and therefore the above rule is 
 usually disregarded, smaller rods being used and the fly-wheel 
 being depended on for uniformity of motion. Besides, it 
 should be borne in mind that the pump must be capable of 
 feeding the boiler also when the steam pressure has fallen 
 considerably below the average, and also on this account the 
 rod must not exceed a certain size if the annular surface of 
 the piston is to be sufficient for producing the suction. 
 
 Such steam pumps are generally quick running (making 
 100 double strokes per minute and more), and therefore, 
 according to 26, they require an air chamber on the suction 
 pipe, except when the height of suction is very slight. In 
 boiler feed-pumps this height is usually but trifling, often 
 being equal to zero or negative, in which case the water flows 
 into the pump of its own accord. 
 
CHAP. IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 183 
 
 In Fig. 1 2 9 is shown a section of a vertical steam pump of 
 this kind, 1 which can be easily understood from what has been 
 said above. The plunger D is joined to the piston rod C by 
 the slide E (sometimes termed " Scotch yoke "), which in its 
 slot receives the block G- for 
 the crank pin of the fly-wheel 
 shaft H, which is provided 
 with an eccentric pin L for 
 moving the valve S. In the 
 machine referred to the dia- 
 meter of steam piston is 105 
 mm. [4*13 ins.], that of the 
 piston rod 65 mm. [2*56 ins.], 
 and of the plunger 59 mm. 
 [2'32 ins.], the stroke being 
 144 mm. [5*67 ins.] ; the ratio 
 
 of piston areas is therefore 
 
 Y f 
 
 !i = 0-62, and the volume 
 
 F 
 
 passed through by the plunger 
 
 7r ' 592 1-44 = 0-394 litres 
 4 
 
 [0-014 cub. ft.] 
 
 In the pump illustrated in 
 Fig. 130, which was constructed 
 by Weise and Monski in Halle, 
 and is designed to be fastened 
 to a wall, the slide is replaced 
 by the forked connecting rod 
 EF attached by means of the 
 pin E and rotating the auxiliary 
 crank shaft H with the fly- 
 wheel E. The manner of operat- 
 ing the valve rod S by the 
 eccentric L is evident from the figure, as is also the mode of 
 attaching the suction pipe J and delivery pipe K to the valve 
 chamber with the air chamber W. 
 
 The arrangement of a double-acting steam pump is obvious 
 
 Fig. 130. 
 
 1 Wiebe's Skizzeribuch, Heft 1. 
 
184 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 from the diagram shown in Fig. 131, where A is the steam 
 cylinder and B the pump barrel provided with four valves. 
 The piston rod CD between the two cylinders carries a cross 
 bar E, from which the crank shaft H is rotated by means of 
 the forked connecting rod EG. Also, in this case, this shaft is 
 a mere auxiliary shaft which receives the fly-wheel E and the 
 eccentric L for operating the slide valve S. 
 
 Such double-acting pumps have, of late, been largely con- 
 structed, without an auxiliary shaft, for use in the shafts of 
 mines, being placed near the bottom only a few metres above 
 the sump, 1 and made to force the water directly to the surface. 
 For moving the steam distribution valve various methods may 
 then be employed. Either a small double piston- valve is made 
 use of, operated by leading steam through suitably arranged 
 passages alternately to each side of it, and which moves the 
 main valve, 2 or the valve is moved by an arm on the piston 
 
 
 f JT=^ p 
 
 CJ 
 
 1 El " LQ - D 
 
 11 
 
 Fig. 131. 
 
 rod which strikes against collars (tappets) secured to the 
 valve rod. The latter arrangement is used in the pump 
 shown in Fig. 132, which was designed to overcome a differ- 
 ence of level amounting to 100 metres [328 ft.] at a mine 
 in Silesia. 3 Here also the steam piston at A and the double- 
 acting plunger are connected by a piston rod in common to 
 both, and provided with an arm C which in its reciprocating 
 motion strikes against the collars D and E alternately. By 
 this means the valve rod G moves the valve contained in the 
 
 1 In sinking or recovering a shaft vertical, direct-acting pumps are often used, 
 which are kept suspended in the shaft, and are gradually lowered (see, for 
 instance, Deane's sinking pump, illustrated in Engineering, London, May 1, 
 1885) ; large bodies of water may also be removed from old mines by means of 
 horizontal pumps located on a platform floating on the surface and descending 
 with it. TRANSLATOR'S REMARK. 
 
 2 See Maxwell's pumps, Zeitschr. deutsch. Ing. 1870, p. 196, also the pumps 
 constructed by Taugye Brothers, and described in Riihlmann's Allg. Maschinen- 
 lehre, vol. iv. p. 693. 
 
 3 See Zeitschr. deutsch. Ing. 1872, p. 545. 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 185 
 
 steam chest S in such a manner that the steam admitted at a x 
 acts on the side of the piston exposed to it, and, after being 
 utilised, escapes through a 2 . The stroke of the pistons can be 
 regulated by adjusting the tappets D and E. In order to pre- 
 vent a flooding of the machine, the latter is placed at a height 
 of 5*65 metres [1S'53 ft.] above the sump, from which water 
 
 Fig. 132. 
 
 is sucked through the pipe b lt and then forced through & 2 to 
 the day level 100 metres [328 ft.] above. 
 
 The diameter of the pump cylinder is 0'275 m. [10'83 
 ins.], and that of the steam piston 0'550 m. [21*65 ins.], the 
 stroke being 0*435 m. [17*13 ins.] The average speed is 
 from 40 to 50 single strokes per minute, and, according to 
 tests made, the actual capacity is from 0'89 to 0'91, or, on an 
 average, 0'9 of the theoretical. The duty of the pump work- 
 
186 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 ing under a boiler pressure of 62 Ibs. [4'2 atm.] above the 
 atmosphere was 1,306,995 m. kg. [9,453,495 ft. Ibs.] per 1 cwt. 
 of coal. Steam is conducted to the machine through pipes 
 leading from the boilers above ground, and exhausted from the 
 shaft through a special pipe, though the exhaust steam may be 
 used for the ventilation of the air shaft. More recently a 
 simple means of condensation has been introduced in pumps of 
 this kind by conducting the exhaust steam from 2 directly to 
 the suction pipe \ of the pump, the condensing water being 
 thus carried off together with the lifted water by the delivery 
 pipe 1 2 . Besides the gain in power effected by the condensa- 
 tion, an advantage of this arrangement consists in that it is 
 possible to dispense with the elaborate system of piping for 
 discharge of the steam. 
 
 Such underground pumping engines, both with and without 
 an auxiliary shaft, have gained extensive application in modern 
 mining practice, owing to the fact that by their use the heavy 
 pump rods which greatly encroach on the space in the shafts 
 are entirely dispensed with, although a disadvantage results 
 from the cooling of the steam caused by the great length of the 
 steam pipes. To avoid this objection, it has been proposed to 
 place the boilers also below ground, but this arrangement seems 
 to have met with but little favour. 
 
 An arrangement for operating the main valve by means of an 
 auxiliary piston, as used in the direct-acting steam pumps built 
 by the Knowles Steam Pump Works at Warren, Massachusetts, is 
 shown in Fig. 133. Here a roller on a tappet-arm T, attached 
 to the piston rod A of the pump, near the end of each stroke 
 depresses a rocking bar E which is fulcrumed on the central frame- 
 work, and by means of a connecting link L and a short arm on 
 the valve rod V gives a slight rotary motion to the auxiliary 
 piston P. By this rotation small steam ports at the under-side of 
 this piston are brought into proper relation to corresponding ports 
 in the steam chest C. In the position shown in the cut, the space 
 at the left of the auxiliary piston connects with the exhaust, while 
 steam enters behind it at the right, causing it to move towards the 
 left-hand side, and push the slide valve S with it over to the left, 
 thereby reversing the motion of the pump piston B. When the 
 auxiliary piston P has moved a short distance, it closes its steam 
 port at the right and exhaust port at the left, and subsequently 
 uncovers a port at the left through which steam enters and pro- 
 vides a cushion which prevents its further progress in this direction. 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 187 
 
 When the pump piston arrives near the opposite end of its stroke 
 the roller on the tappet arm gives the auxiliary piston a rotary 
 movement in the reverse direction, thereby bringing this piston into 
 such a position that it will take steam at the left- and exhaust at 
 the right-hand end through the corresponding ports in the steam 
 chest, and enabling it to repeat the same action as on the preceding 
 stroke. 
 
 Direct -acting pumps are frequently made of the "twin" or 
 " duplex " type, i.e. in the form of two complete single steam pumps 
 placed together side by side. In this case the steam valves are 
 usually operated in substantially the same manner as in the example 
 shown in Fig. 132, with the difference that the piston rod of each 
 single pump operates, not its own slide valve, but that of the other 
 
 Fig. 133. 
 
 pump, by means of long vibrating arms. With this arrangement 
 one pump takes up the motion when the other is about to leave it 
 off, thus effecting a more uniform delivery than when a single pump 
 is used. One half of a pump of this class, as built by Henry R. 
 WvriHngton, New York, is shown in Fig. 134, where A is the 
 steam piston, B the double-acting plunger working through a deep 
 metallic packing ring, which can be easily taken out together with 
 the plunger, C is the suction chamber and D the delivery chamber, 
 with their respective rubber lift valves, and E is the plain slide 
 valve, operated by a vibrating arm connecting with the piston rod 
 of the other pump, and corresponding to the arm F shown, which 
 moves the steam valve of the opposite engine. Pumps of this and 
 similar types are often made to use steam expansively by "com- 
 pounding" (compare 41 and following), a high- and a low-pressure 
 
188 
 
 MECHANICS OF PUMPING MACHINERY 
 
 cylinder placed in line or " tandem " being used for each division of 
 the pump. In another form of duplex pump, built by the Hall 
 Steam Pump Company of New York, the engine piston of one division 
 is made to operate the slide valve of the other division by letting 
 in steam from the cylinder at the proper moment to an auxiliary 
 piston ; by this arrangement the use of valve rods, tappets, and 
 vibrating arms are entirely dispensed with. 
 
 In double-acting mining pumps it is of importance that the 
 plunger packing should be easily accessible for inspection and 
 repairs ; such pumps of the duplex class are therefore often made 
 with four water cylinders placed in pairs, with a space between the 
 ends, and the plungers that are visible between the latter working 
 in exterior stuffing boxes (see Engineering, London, 1889, vol. i. 
 p. 798, and American Machinist, New York, August 13, 1891). 
 Duplex pumps for high-pressure hydraulic service are, for the same 
 
 Fig. 134. 
 
 purpose, provided with four single-acting plungers, working in pairs, 
 through exterior stuffing boxes in two water cylinders, each divided 
 by a partition in the middle, and each pair of plungers being coupled 
 by yokes and exterior rods in such a manner that they will move 
 together, so that while one is drawing the other is forcing the liquid, 
 thus making the pump double-acting. TRANSLATOR'S EEMARKS. 
 
 EXAMPLE. A double-acting steam pump is to suck 1 cub. m. 
 [35-316 cub. ft] of water per minute from a well 6 metres [19 '6 9 
 ft] deep, and force it into a reservoir located 20 metres [65'62 ft.] 
 above the pump. It is required to determine the proportions of 
 the latter under the assumption that the average piston velocity of 
 the latter is 0'6 m. [1'97 ft] 
 
 Placing the actual capacity equal to 0'80 of the theoretical, we 
 obtain, in accordance with the above requirements, the area F of 
 the plunger from 
 
 0-SFx 60x0 -6 = 1 to be F = 0-0347 sq. m. [0*3734 sq. ft.], 
 
iv TYPES OF RECIPROCATING 
 
 which corresponds to a diameter of D = '2 1 m. [8*2f "4*^ fLfcttuig \ ^ j" 
 the pump make 36 double strokes per minute, we obtain for the 
 length of stroke 
 
 3sSSp*S 
 
 If the velocity of the water in the pipes is not to exceed 1 m. [3*28 
 ft.] the sectional area of the latter will be 
 
 /=0-6F = 0-0208 sq. m. [0'2238 sq. ft.], 
 
 and their diameter d = 0*163 m. [6*42 ins.] 
 
 For an absolute boiler pressure of 5 atmospheres [73*65 Ibs.], 
 
 and a pressure in the steam cylinder of f of the former, or = 3*75 
 
 atmospheres [55*24 Ibs.], and assuming the back pressure (no con- 
 denser being used) to be. 1*15 atm. [16*94 Ibs.] ; further, placing the 
 efficiency of the pump at 0*75, and that of the steam engine at f , 
 then the area F x of the steam piston will be obtained from 
 
 F.Q-75- ! -15)14-73 x 144 x 
 
 
 which gives F x = 0*0538 sq. m. [0'578 sq. ft.], corresponding to a 
 diameter D x = 0*262 m. [10*31 ins.] 
 
 EXAMPLE 2. A single-acting steam pump is to feed 50 litres 
 [1*7658 cub. ft.] of water per minute into a boiler from a well 
 5 metres [16*4 ft.] deep. What must be the area of plunger when 
 the velocity of the latter is not to exceed 0*4 metres [1*31 ft.], and 
 what size must be given to the steam piston if feeding is to be 
 possible even when the boiler pressure has fallen to one atmosphere 
 (14*73 Ibs.) above the outside atmosphere? 
 
 Assuming the capacity to be 0*80 of the theoretical, we obtain 
 the area of plunger from 
 
 corresponding to a diameter of D = 0*081 m. [3*19 ins.] Further, 
 giving the pump a stroke s= 0*150 m. [5*91 ins.], we have for the 
 number of revolutions of the fly-wheel per minute 
 
 60 x 0-4 
 
 The resistance of the water in pipes and valves, together with 
 the friction of the pump plunger, may be estimated at 25 per cent 
 of the useful effect, and consequently the work absorbed per double 
 
190 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 stroke of plunger will, for a boiler pressure of one atmosphere, or 
 10*334 m. [3 3 '9 ft.] water column, be given by 
 
 A = 1-25F(5 + 10-334)1000 x 0*150 = 2875F = 14-95 = ~~ 15 m. kg. 
 [~A = l-25F(16-4 + 33-9)62-5x^:=1935F = 108-36:=: ~~ 108-5 ft. lbs.1 
 
 Now assuming that the piston rod has the same sectional area 
 as the plunger, or 0*0052 sq. m. [0*056 sq. ft.], and denoting the 
 area of steam piston by F 1 , the steam pressure behind the piston by p t 
 and the back pressure by p Q , then the work done, theoretically, by 
 the steam piston per double stroke will evidently be expressed by 
 
 - F)p - F^ > = (2F X - F)(p -p )s. 
 
 If, on account of the small size of the engine, we place the 
 efficiency equal to O60 only, we shall have for the determination 
 of Fj the equation 
 
 Placing here the back pressure p Q = I'l x 10334 kg. [p = 1*1 
 
 x 33-9 x 62*5 Ibs.], and p equal to 80 per cent of the boiler 
 
 pressure, or 0*80 x 2 x 10334 kg. [0*80 x 2 x 33'9 x 62*5 Ibs.], and 
 
 after substituting the values found above, F = 0*0052 [F = 0*056], 
 
 A -15 [A = 108-5], and s = 0*15 ^ we obtain 
 
 0-60(2F 1 -0'0052)(1 -6- 1-1)10334 x 0-15 = 15 
 [~0-60(2F 1 - 0-056)(1 -6- 1-1)33-9 x 62'5 x ^ = 10 
 
 or 
 
 which gives F 1 = 0'0187 sq. m. [0*2012 sq. ft.], and thus a piston 
 diameter of D x = 0*154 m. [6*06 ins.] 
 
 It is evident that feeding can be done also for higher steam 
 pressures. For instance, if the boiler pressure is five atmospheres 
 in excess of the barometric pressure, the work required per double 
 stroke will be given by 
 
 A = l-25 x 0-0052(5 + 5 x 10-334)1000 x 0'150 = 55'3 m. kg. 
 f"A = l-25 x 0-056(16-4 + 5 x 33'9)62'5 x ^r=400 ft. Ibs. T 
 
 of which the fraction 
 
 A = 4-7 m. kg. [34 ft. Ibs.] 
 
 is absorbed for the suction on the up stroke, while 
 A = 50 -6 m. kg. [366 ft. Ibs.] 
 
iv TYPES OF RECIPROCATING PUMPS 191 
 
 is expended during the down stroke. The pressure p now required 
 in the steam cylinder will be obtained from the equation 
 
 55 3 = 0-6(2F 1 -F)(p- I'l x 10334)0-150 = 0-09(2 x 0-0187 - 0'0052)(^- 11367) 
 [~400 = 0-6(2x0 -2012 -0-056)0* -1-1x33 -9x62 -5)^1, 
 
 from which we deduce 
 
 kg ' ^= 43 * 3 lbs - P er S( l- in -l> 
 
 or less than three atmospheres. On the up stroke the steam per- 
 forms an amount of work 
 
 0-6[(0-018- 0-052)30436- 0-0187 xl!367]0-15 = 17-85 m. kg. [129 ft. lbs.], 
 and on the down stroke an amount 
 
 A"= -6[F^ - (Fj - F)p ]0-15 = 
 0-6[0 -0187 x 30436- (0-0187 -0-0052)11367]0 -15 = 37 -45 m. kg. [271 ft. lbs.] 
 
 Consequently during each up stroke an amount of energy 
 A'- A x = 17-85 -4-7 = 13-15 m. kg. [95-11 ft. lbs.] 
 
 is expended in accelerating the fly-wheel, and during each down 
 stroke the same amount 
 
 A 2 -A"= 50-6 -37 -45 = 13-15 m. kg. [95'11 ft. lbs.] 
 
 must be given out by the fly-wheel. From this condition the size 
 of the wheel may easily be computed (see Weisbach's Mechanics, 
 vol. iii. 1, chap. 9) for any maximum variation in speed desired. 
 
 40. Cornish Pumping Engines. The characteristic 
 feature of all pumping arrangements for mines, except when 
 the pump is located near the bottom of the shaft, consists in 
 the presence of a pump rod or a system of rods set in motion. 
 by the steam piston either directly or indirectly by the use of 
 a walking beam ; the mode of attaching the piston rods of the 
 individual pump cylinders has already been explained in 3 5 
 and following. 
 
 The direct method of driving the pump rod is evidently the 
 simpler and least expensive, besides allowing of greater speed 
 than when a walking beam is used, but the latter cannot very 
 well be dispensed with when it is desired to leave a clear 
 space directly above the shaft. For this reason the older 
 pumping engines were always constructed as beam engines. 
 
192 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 A special advantage of the latter type lies in the possibility of 
 giving the steam piston a greater velocity than the pump 
 plungers by the use of a beam of unequal arms ; a common 
 proportioning, with this object in view, being to make the arm 
 to which the pump rod is attached about -J or | of that acted 
 on by the steam piston. 
 
 In single-acting pumping engines the steam acts on one 
 side of the piston only, lifting the heavy rod, while the weight 
 of the latter is utilised on the return stroke to force water 
 into the delivery pipe. As a consequence the steam pressure 
 must evidently act on the lower side of the piston in direct- 
 acting engines, while in beam engines the upper surface is 
 exposed to its force. When the pump rods are very heavy, 
 which is the case in deep shafts, their weight frequently 
 exceeds the force required for overcoming the resistances in 
 the pumps, and it is then necessary to balance the excess of 
 weight by means of counterpoises (compare Weisbach's Mechanics, 
 vol. iii. 1, chap. 9). 
 
 Beam engines are either of Watt's or of the Cornish type. 
 The essential difference between the two is that, while the 
 former works with the low pressure of 1*1 atmospheres 
 (16*2 Ibs.), the latter makes use of a pressure of 5 atmo- 
 spheres (73*7 Ibs.) Otherwise, both constructions are con- 
 densing and use the steam expansively, in the Cornish engine 
 from eight to twelve times, while in Watt's the expansion is 
 only threefold. The latter circumstance explains the vast 
 difference in coal consumption of the two engines. The 
 maximum duty of Watt's engine was 27,500,000 foot pounds 1 
 per 1 bushel of Newcastle coal a 42*638 kg. [94 Ibs.], or 
 89,167 m. kg. per kilogram of coal, 2 whereas in the best 
 Cornish engines an average duty of 60,000,000 foot pounds 
 was obtained with the same quantity (94 Ibs.) of coal, corre- 
 sponding to a duty of 194,547 m. kg. per kilogram of coal, 
 and an hourly coal consumption of only 1'39 kg. [3'06 Ibs.] 
 per horse -power. According to later accounts of Cornish 
 engines of the ordinary proportions, i.e. from 2*5 to 3 metres 
 
 1 See Kley, Die Woolfschen Wasserhaltungsmaschinen, where data are given 
 in great detail regarding the duty of Cornish engines. 
 
 2 One million English foot pounds per 1 bushel of coal is equal to 3242 '45 
 m. kg. per 1 kg. 
 
TYPES OF RECIPROCATING PUMPS 193 
 
 to 10 ft.] stroke, 1'5 to 2'5 m. [5 to 8^ ft.] cylinder 
 diameter, and making from 6 to 10 strokes per minute, the 
 coal consumption may be placed at 2 kg. [4*4 Ibs.] per horse- 
 power per hour. 
 
 Two large Cornish pumping engines, built by the cele- 
 brated machine works in Seraing, are in operation at Bleiberg 
 near Aix-la-Chapelle. 1 Each of these engines have steam 
 cylinders of 2'67 m. [8f ft.] diameter and 3'66 m. [12 ft.] 
 stroke, and pump cylinders of 1 m. [3'28 ft.] diameter and 
 2 '8 6 in. [9 '3 8 ft.] stroke. When running at seven double 
 strokes per minute, and without expansion, each engine 
 develops from 700 to 800 h.p., while with five expansions 
 234 h.p. are developed with an economy of only 1*45 kg. 
 [3*19 Ibs.] of coal per h.p. per hour, as compared with 4 or 5 
 kg. for the ordinary Belgian engines. 
 
 With reference to the condensing action in these single- 
 acting engines, which are provided with cataracts for producing 
 the periodical working of the valves (see Weisbach's Mechanics, 
 vol. ii., on Steam Engines), it may here only be noted that the 
 steam, after pushing the piston ahead, is not conducted directly 
 to the condenser, but is allowed to enter to the other side of 
 the. piston by the opening of an equalising valve introduced for 
 this purpose. The same pressure is thus obtained on both 
 sides of the piston, which completes its return stroke under 
 influence of the weight of the pump rod, in the meantime 
 forcing the steam from one side to the other. If, now, at the 
 proper moment the equalising valve is closed, the admission 
 valve opened, and on the exhaust side the cylinder is placed 
 in communication with the condenser, then the steam will 
 again force the piston ahead with its total pressure in excess 
 of that of the condenser. Double-acting engines, having com- 
 munication between cylinder and condenser at the end of each 
 stroke, were early abandoned on account of the necessity of 
 applying excessively large counterweights to balance the great 
 weight of the pump rod. 
 
 In Fig. 135 an elevation of a Cornish pumping engine is 
 shown. At A is the steam cylinder, at B the piston rod, at 
 CE the walking beam with its gudgeons D, and at F the pump 
 
 1 Armengaud, Publication industrielle, vol. iv., and John Cockerill's Porte- 
 feuitte. 
 
 
 
194 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 rod attached to the short arm of the beam. With the ex- 
 ception of the lowest one, all the pumps are mere force pumps. 
 During the down stroke of the steam piston the resistance to 
 
 Fig. 135. 
 
 be overcome is therefore practically the weight of the pump 
 rod only, and by the action of this weight the water is lifted 
 on the next stroke, when, as already mentioned, the steam 
 which was previously acting on the upper side of the piston 
 is admitted to the lower side also. In order to limit the 
 
\\ 
 
 TYPES OF RECIPROCATING PUMPS 
 
 ! Ll 
 
 stroke iii case of breakage of the pump rod, a N nd>prevent the 
 piston from striking the cylinder heads, a stronj^Sg ra catch 
 pin X is secured to the driving arm of the bea 
 stops are attached at intervals to the pump rod. In case the 
 rod should break, the catch pin would strike against the elastic 
 block Y, and the disconnected portion of the rod would drop 
 on heavy timber supports. From the walking beam are also 
 suspended the valve rod G-, the piston rods of the boiler feed- 
 pump M and of the air and hot-water pump L. 
 
 We further distinguish at K the condenser, and at P the 
 cataract. The steam distribution is governed by four double- 
 
 rig. 136. 
 
 seated valves, whose position, with reference to the steam 
 cylinder A, may be better understood from the plan in Fig. 136. 
 These valves are 
 
 1. The throttle valve Q. 
 
 2. The admission valve R 
 
 3. The equalising valve S, and 
 
 4. The release or condenser valve T. 
 
 The throttle valve Q, to which steam is admitted from 
 below, is suspended from the lever qq lf and may be adjusted 
 according to the demand for steam by means of the rod q ?i , 
 which at one end is provided with a screw mechanism. By 
 
 
196 MECHANICS OF PUMPING MACHINERY CHAP, iv 
 
 way of this valve steam reaches the admission valve B, which 
 is suspended from another lever m\, and, after being opened by 
 the fall of a weight, allows the steam to enter at the top of the 
 cylinder and force the piston downwards. When the latter 
 has passed through a portion of its stroke this valve is closed, 
 and the remainder of the stroke is completed under influence 
 of the expanding steam. The equalising valve S now opens, 
 placing the upper and lower ends of the cylinder in com- 
 munication with each other through the vertical pipe H, and 
 allowing the piston to ascend under the action of the weight of 
 the pump rod, the steam above the piston being at the same 
 time forced into the space below it. Finally, by the dropping of 
 a weight the release valve T is opened, discharging the steam 
 through the exhaust pipe JJ to the condenser K. The 
 admission valve is now again opened and a new stroke begins. 
 
 The general arrangement of the outside valve motion and 
 cataract, and the method of operating the valves by means of 
 levers, rods, tappets, weights, etc., will be explained below for 
 a few special constructions. 
 
 In Beam engines it is quite necessary that the cylinder 
 should be firmly secured to the foundation, owing to the 
 tendency of the steam pressure to lift it ; and besides, on 
 account of the great oscillating mass, this type does not allow 
 of the same velocity of running as the direct-acting pumping 
 engines. For these reasons, and because of their simpler con- 
 struction, the latter are employed to advantage when local 
 conditions admit of placing the cylinder directly above the 
 shaft. A good idea of the arrangement and working of a 
 direct - acting pumping engine may be obtained from the 
 annexed illustrations of a machine erected at the coal mine 
 " Laumonier " near Liege. 1 
 
 Fig. 137 represents a side elevation showing the steam 
 cylinder A resting on cast-iron girders, between which the 
 piston rod B passes. The latter is connected to the upper 
 end of the pump rod CDC by means of a joint block provided 
 with gudgeons CC, and a balance beam EFG supported at F is 
 attached to the rod by the link DE. The balance beam is 
 weighted with a sufficient number of cast-iron discs G, and 
 
 1 See Bulletin tic, la Societe de V Industrie minfrale, Tome i., St. Etienne, 1855 
 et 1856. 
 
198 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 through the connecting rod HL gives motion to the valve rod 
 KL, to which the piston of the feed-pump M is also attached. 
 In Fig. 138 a vertical section through the valve chest may be 
 seen, showing the two double-seated valves U and V. Steam 
 is supplied from the boiler through the pipe N, and, when the 
 admission valve U is opened, enters the valve chest UY, and 
 
 thence the cylinder 
 through the inlet pipe 
 0, forcing up the piston 
 together with the pump 
 rod. During the ascent 
 of the piston the valve 
 U is pressed down, and 
 at the end of the stroke 
 the release and equalis- 
 ing valve V is opened, 
 allowing the previously 
 active steam to return 
 through 0, and through 
 V reach the space W, 
 which, by means of the 
 pipe Q, communicates 
 with the upper end of 
 the steam cylinder, and 
 by the regulating valve 
 X and the. pipe E with 
 the outside atmosphere. 
 In consequence of this 
 arrangement the exhausting steam is partly utilised to keep 
 the cylinder at a somewhat higher temperature, and thus 
 further the action of the live steam. 
 
 The proper opening and closing of the valves U and V is 
 accomplished by weights, and is governed by tappets S and T 
 attached to the valve rod LK (Fig. 139), the mechanism and 
 mode of action being as follows. The admission valve U is 
 connected to the arm dk of the valve shaft d by means of the 
 rods u and u^ and the two-armed lever u l} and similarly the 
 release valve V is connected to the arm el of the valve shaft e 
 by the rods v and v 2 and the one-armed lever i\. Further, the 
 shaft d carries a rocker arm s which is pressed upward by the 
 
 Fig. 138. 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 199 
 
 tappet S, and the shaft e an arm t which is depressed by the 
 tappet T, the former shaft being thus revolved through a 
 
 Fig. 139. 
 
 certain angle to the left, and the latter through an angle to 
 the right. Two weights p and r, the former acting on the 
 arm dm of the shaft d, and the latter on the arm en of the 
 
200 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 shaft g, serve to give opposite rotations to the shafts. Finally, 
 there are attached to the shafts the two stops d and e lt which 
 engage the pawls wx and yz (Fig. 140), and thus counteract 
 the tendency of the weights to rotate the shafts. The release 
 of the pawls is effected by the cataract Y (Fig. 137), which 
 essentially consists of a force pump. During the ascent of the 
 pump rod the weighted lever aog, having its fulcrum at o, and 
 being connected to pump k of the cataract, is pushed upward 
 at the right by the balance beam EFG through the slotted 
 connection/, while at the end of the up stroke it is pressed 
 downward by the weight g ; the rod ac, which is attached to 
 the lever aog, is thus first pulled downward and subsequently 
 pushed upward, which causes the pawls yz and xw to be alter- 
 nately disengaged from the stops ^ and d 1 by the action of the 
 studs I and c (Fig. 140) secured to the rod. 
 
 The valve motion operates as follows. Suppose the steam 
 piston, and consequently also the pump rod, to be in their 
 lowest position and both valves to be closed. The weight g 
 
 of the cataract now descends, and, 
 pushing the rod ac upward, releases 
 w the pawl xw from the stop d v allow- 
 ing the weight p suspended from the 
 valve shaft d to turn the latter to 
 y the right and open the admission 
 valve U by means of the arm dk, etc. 
 When the ascending steam piston 
 has completed a certain portion of 
 its stroke, the rocker arm s is raised 
 by the tappet S, which causes the 
 admission valve U to close and the 
 
 Fig- 140. . 111. 
 
 pawl ivx to drop back against the 
 
 stop d lf During the remainder of the stroke the steam acts 
 expansively, and the balance beam raises the right arm og of the 
 lever ag together with the weight g and the plunger h, thus 
 evidently pulling the rod ac downward. At the end of the up 
 stroke, therefore, the stud I disengages the pawl yz from the 
 stop e l} releasing the shaft e and causing the latter to be turned 
 to the left by the weight r\ the release valve V, which is con- 
 nected to the arm d of the shaft is thus opened, and conse- 
 quently the piston descends together with the pump rod and 
 
 Id, 
 
iv TYPES OF RECIPROCATING PUMPS 201 
 
 valve rod LK. When, finally, the rocker arm t is depressed 
 by the tappet T, the valve V will close, the pawl yz will again 
 drop against the stop e v and a double stroke will be completed. 
 The pause which now occurs is evidently dependent on the 
 time required by the plunger h to descend, and this time may 
 be regulated by varying the discharge orifice of the , plunger 
 cylinder by the aid of a cock. 
 
 The above pumping engine has a steam cylinder of 1'88 
 metre [6 '17 ft.] and pump cylinders of 0'5 m. [1'64 ft.] 
 diameter, the stroke is 3 m. [9 '8 4 ft.], and the machine makes 
 from 6 to 8 double strokes per minute. 
 
 41. Compound Pumping Engines. Since a high degree 
 of expansion is favourable to the action of steam in steam 
 engines, pumping engines ever since the days of Watt have 
 been designed to use the steam expansively, and it is essentially 
 to the high ratio of expansion (sometimes twelve-fold) em- 
 ployed in the Cornish engines that we must attribute the 
 economical performance of this type. This was made possible by 
 the use of high-pressure steam (of 4- to 5 atm.) and by the em- 
 ployment of a condenser. It must be borne in mind, however, 
 that serious disadvantages accompany the use of great expan- 
 sion in pumping engines, capable at times not only of disturb- 
 ing the proper action of the machine but also of causing its 
 entire destruction, as has been the case in some instances. 
 These disadvantages are due to the great variation of steam 
 pressure on the piston, which evidently increases with increased 
 expansion. The following may serve to illustrate this point. 
 Let F denote the sectional area of the piston, p the pressure 
 of steam per unit of area, and consequently ~p = P the driving 
 force, then, in a non-expansive engine the total resistance W, 
 including friction, opposing the motion of the pump rod may 
 be placed at the same amount. The pump rod in this case 
 ascends with a practically uniform velocity, the rate of which 
 may be easily governed by means of the throttle valve. 
 
 On the other hand, when admission of steam is cut off 
 
 when the piston has completed a certain fraction - 1 of its total 
 
 6 
 
 stroke I, that is, when the expansion is e-fold, then the pre- 
 viously constant pressure ~Fp will gradually decrease until at 
 the end of the stroke, according to Mariotte's law, it will 
 
202 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 f o 
 become P a = Fpj = F , The resistance W of the pump rod can 
 
 therefore no longer be taken at the maximum value P of the 
 original steam pressure, but will be expressed by a mean value 
 between the initial pressure P and the final P 1; being obtained 
 by placing the work Wl performed by this resistance equal to 
 work done by the steam. Basing our calculation on Mariotte's 
 
 law, it is well known that the latter, for the volume V = F 
 
 e 
 
 and the pressure p of the steam and the ratio of expansion 
 
 _ = ) w ill be given by 
 Pi 
 
 + hyp log ^J = F (1 + hyp log e). 
 After placing the two expressions equal, or 
 
 we therefore obtain for the uniform resistance W 
 
 W = F^ (1 + hyp log e) - Fjp x (l + hyp log e). 
 
 A clear picture of the above is obtained from the well- 
 known diagram, Fig. 141, in which above the base line AB = I 
 the pressures on the piston at different points are drawn as 
 ordinates. While the pressure is constant from A to D l 
 
 through the distance /, and here equals AC = D X D = Fp, it 
 e 
 
 has at B dropped to the value BE = F p = ~Fp lf the area 
 
 
 
 ACDEBA furnishing a measure of the work done by the steam 
 during one stroke of the piston. If we further set off AK 
 = Fp to represent the pressure in the condenser, or, for non- 
 condensing engines, the pressure of the atmosphere on the back 
 of the piston, and if we make KF equal to the constant resist- 
 ance Q of the rod, we evidently obtain in the rectangle AG 
 the amount of work consumed by the back pressure and resist- 
 ance. The point of intersection H determines the piston 
 position in which the driving force is exactly equal to the 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 203 
 
 resistances (including back pressure), and we see therefore that 
 while the work A represented by the four-sided figure FCDH 
 is spent in accele- c j> t 
 
 the masses, 
 equal amount 
 
 rating 
 
 an 
 
 |Q F P 
 
 .JB 
 
 of energy, given by 
 the area HGE, must 
 be derived from 
 their retardation 
 during the re- 
 mainder of the 
 stroke in order that 1>l 
 
 the rod may con- 
 tinue to ascend. From the above it is apparent that the 
 pump rod which begins its motion at A and concludes it at B 
 with no velocity will reach its maximum velocity v at H. 
 Since this velocity is produced by the work A = FCDH which 
 has been expended on the rod, we can calculate it from the 
 relation 
 
 where G is the weight of the rod including counterpoises, 
 balance lever, etc., which take part in the motion, the latter 
 parts being reduced to the axis of the rod. 
 
 This equation shows that the maximum velocity v becomes 
 greater as the weight G decreases and as the quantity A in- 
 creases ; the latter quantity evidently increases with the ratio 
 of expansion, and becomes zero when the steam is used non- 
 expansively. It is therefore apparent that when the weight G 
 of the rod is very great, the value of A may be taken corre- 
 spondingly large without danger of excessively increasing the 
 velocity v. 
 
 This explains why such a high degree of expansion was 
 possible in the deep mines of Cornwall, where the weight of 
 the pump rods is very considerable. When, however, it 
 was desired to use great expansion also with lighter pump 
 rods, the velocity v of the latter increased considerably, and 
 serious accidents have been caused by such arrangements, as, 
 for instance, that the piston has been thrown with great force 
 
204 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 against the cylinder head, shattering it into fragments. Ex- 
 perience has proved that it is inadvisable to allow the 
 velocity of the rod to exceed 2 metres [6*56 ft.] By thus 
 limiting the maximum velocity v and deducing a value for the 
 energy A spent in accelerating the masses with a certain ratio 
 of expansion e, the required weight G of the masses may be 
 
 v 2 
 calculated from the equation G = A ; in case the pump rod 
 
 has a smaller weight G lt the deficiency G G x may be made 
 
 p p 
 
 up by adding one-half of it, or - -, directly to the rod, and 
 
 allowing the other half to act on a balance lever so as to 
 retain the excess of weight G x of the rod. It is evident that 
 this arrangement subjects the rod to a greater pull and adds to 
 the expense of the whole construction, and this is the reason 
 why pumping engines which operate with pump rods are often 
 allowed to work without or with but little expansion, a greater 
 expenditure of fuel being preferred to the above objections. 
 
 There is another disadvantage connected with the expansive 
 use of steam in the pumping engines referred to, resulting from 
 the variation of the steam pressure on the piston. This is 
 owing to the fact that at the beginning of the stroke the steam 
 pressure Fp, which in the figure is represented by AC, exceeds 
 the back pressure, together with the resistance of the rod AF, 
 by an amount FC = F(p p ) Q, which causes the rod to begin 
 
 F(p -p ) - Q 
 its motion with the corresponding acceleration - ~- ff- 
 
 As a result a separation of the water will occur in the lowest 
 pump, which is alwa'ys arranged for suction, and consequently 
 a shock or water-blow will take place unless the water in the 
 suction pipe is correspondingly accelerated by the pressure of 
 the atmosphere, as was further explained for pumps driven by 
 cranks in 26. Denoting by 7^ the height of suction and 
 length of suction pipe, and by 5 the height of the water 
 barometer, we have for the maximum acceleration of the 
 water in the suction pipe the expression 
 
 b-h, 
 
 T* 
 
 and consequently, under the assumption that the pump barrel 
 
iv TYPES OF RECIPROCATING PUMPS 205 
 
 and suction pipe have the same sectional area, the following 
 condition must be satisfied : 
 
 l-h 
 
 As from practical considerations the height of suction 7^ is 
 as a rule considerable, amounting to between 5 and 8 metres 
 [16 to 26 ft.], it will be seen that a water-blow may easily 
 occur for high degrees of expansion when the rod is consider- 
 ably accelerated through the excess of pressure during the 
 period of admission. 
 
 To avoid the above objections to a certain extent, and yet 
 gain economy by the use of a high degree of expansion, two 
 cylinders have been employed in the same manner as in Woolfs 
 steam engine (Weisbach's Mechanics, vol. ii., on Steam Engines), 
 with simultaneous expansion in both cylinders, the results 
 obtained being very favourable. Already in the last century two 
 cylinders were employed by Hornllower l for the same purpose in 
 Cornish pumping engines, using low-pressure steam, but the plan 
 was abandoned and was not again introduced until in modem 
 times Kley applied it to high-pressure steam, and demonstrated 
 the value of the principle. This may be explained by Fig. 142, 
 which represents the essential features of one of the two single- 
 acting pumping engines erected by Kley in 1861 and 1862 at 
 the mine " Altenberg " near Aachen. The two steam cylinders 
 A and B are placed side by side above the shaft in such a 
 manner that the pump rod G is attached directly to the piston 
 rod & 2 of the larger cylinder B. As usual, the weight of the 
 pump rod while the latter descends presses up the water 
 from the force pumps, the excess of weight being balanced by 
 means of the counterpoise lever C attached to the pump rod 
 by the connecting rod c^. The piston rod & x of the smaller 
 cylinder A is likewise connected to the balance lever by c 3 c 4 , 
 and the pump rod is therefore raised by the combined action 
 of both pistons in their ascent, together with the force exerted 
 by the counterweight. The steam distribution is effected by the 
 five valves a^ a 2 , /3j, /3 2 , and 7, of which a^ and ^ are admission 
 valves letting in steam under the pistons A and B, while a 
 
 1 See Kley, Die einfach- und direct wirkenden Woolf'schen Wasserlialtungs- 
 maschinen der Grube " Altenberg" bci Aachen, 1865. 
 
206 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 and /3 2 are the corresponding release valves. The valve 7 
 finally allows the escaping steam to reach the condenser 
 through the pipe E, the air pump L being driven from c 4 . 
 
 Fig. 142. 
 
 From the figure it is, in the first place, evident that if, 
 during the descent of the rod, only the release valves a 2 and 
 /3 2 are open, the steam contained below each piston will 
 simply escape through the communicating pipes a 3 and /3 3 to 
 
iv TYPES OF RECIPROCATING 
 
 the spaces above the pistons, thus establishing the same 
 pressure on both sides of the latter and aJb^^the punrp 
 rod to sink under influence of its net weight. But when t 1 
 ascent is to commence the valves a 2 and @ 2 are closed, w'Hereas 
 the other three valves a l} /3 l} and 7 are opened, and conse- 
 quently fresh steam from the boiler will be supplied through 
 the pipe d and valve a^ to the under side of the smaller 
 piston ; moreover, the steam contained above the latter escapes 
 through /9i to the lower side of the larger piston B, and at the 
 same time the space above this piston will be in communica- 
 tion with the condenser. From the theory of compound 
 engines it is now apparent that the work obtained from the 
 steam which acts on the upper side of the smaller piston and 
 on the lower side of the larger one will equal the expansive 
 action of the steam which originally fills the small cylinder 
 and finally occupies the volume of the large one. Since in the 
 engines at Altenberg the ratio of piston areas / and F are as 
 1:2, and the same ratio obtains for the length of strokes, we 
 perceive that the steam expands four times, or in general the 
 
 FL 
 
 ratio of expansion will be 6, if d> = denotes the ratio of 
 
 /* 
 
 cylinder volumes. If the admission valve a x is closed before 
 the end of the up stroke so as to give a ratio of expansion v 
 already in the small cylinder, the total expansion will be given 
 by e = v<f>. In the Altenberg engines there is no expansion in 
 the small cylinder, and consequently, since v = 1 , we have 
 e = <f) = 4. 
 
 The valves are operated in the same manner as in the 
 single -cylinder Cornish engines (by pawls, tappets, and 
 cataracts), this being easily accomplished owing to the fact 
 that the opening of the admission valve a^ always coincides 
 with that of &, and that <z 2 and /5 2 likewise always move 
 together. It is only for the case that a z^-fold expansion is 
 desired in the smaller cylinder that the valves a^ and /^ do 
 not close simultaneously. The arrangement of the valve 
 motion is therefore practically no more complicated than for 
 single cylinder engines. From the diagram we can readily see 
 that there is much less irregularity in the action of the 
 driving force when compounding is adopted than for the same 
 degree of expansion in one cylinder. 
 
208 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 To make this clear, let us assume the action of the small 
 piston A to be transferred to the point of the balance lever 
 where the large piston B acts. This can be done by assuming 
 
 fl 
 
 at this point a piston of the area/ x = working in a cylinder 
 
 L 
 
 having a volume / X L equal to that of the smaller cylinder, or 
 
 F FL 
 
 fl', we then have = = </>. By this assumption the action 
 
 of the steam will be unaltered, provided that the expansion in 
 this cylinder is retained the same as before, or y-fold, that is, 
 
 that the admitted volume of steam V=/ 1 L=/ I remains 
 
 v v 
 
 unaltered. We can now construct the diagrams for both pistons 
 on the same base line 00 1 = L, Fig. 143. 
 
 Let p be the initial steam pressure, and p =-p the pres- 
 
 v 
 
 sure below the smaller piston at the end of the stroke, then 
 the line A will give a representation of the work done by 
 the steam acting on the under-side of the smaller piston, pro- 
 vided that 
 
 /i- 
 
 and 
 
 and that the curve A 2 A 1 is constructed according to Mariottes 
 law. During this stroke the steam which was exhausted 
 from the small cylinder during the previous stroke exerts a 
 driving action on the large piston and a resisting effort on the 
 upper side of the smaller one. Since the pressure of this 
 steam is p l in the beginning, the initial driving force on the 
 large piston will be OB = F/^, and the force resisting the small 
 piston will be Oa=f 1 pi. At the end of the stroke this steam 
 
 F 
 
 has expanded from the volume /JL to FL, or in the ratio = <, 
 
 /i 
 
 the pressure therefore having dropped to p. 2 = -p 1 = p = -p. 
 
 9 z^9 e 
 
 The pressure on the piston at the end of the stroke will there- 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 209 
 
 fore be Fp 2 =fi2h = C^Aj, so that the work done by the ex- 
 panding steam on the large piston will be obtained from, the 
 line BA 1? and that done on the upper side of the small piston 
 from the line aa lt if we make 0^ =J\p f> . These lines BA X and 
 
 Fig. 143. 
 
 aa l may be easily constructed by the aid of Mariotte's law, as 
 the pressure of the steam p x for any piston position X, at the 
 distance x from the beginning of the stroke, may be found from 
 the equation 
 
210 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 and the ordinates 
 
 XN = Fpa- and Xn=f 1 p x 
 
 drawn accordingly. If, finally, p denotes the pressure in the 
 condenser, the straight line bb at a distance Ob = Fp from the 
 base line will represent the back pressures on the large 
 piston. By combining all these lines in such a manner that 
 the lines C will represent the sum of A and B, and c the 
 sum of a and b, and by subtracting the ordinates of the result- 
 ing back-pressure curve c from those of the resulting driving- 
 pressure curve C, we finally obtain in the area ODD^Oj, 
 determined by the curve D, the total work done during one 
 stroke of the pistons. If we now draw, parallel to the base 
 line, the straight line QQj representing the average pump 
 resistance, we find at the point of intersection M the position 
 where the pistons have their maximum velocity, and in the 
 cross-hatched surface QDD 2 M we have a measure of the work 
 expended in accelerating the masses. While the average resist- 
 ance of the pump rod is given by OQ, there will be a maximum 
 driving force OD applied to it at the beginning of the stroke, 
 so that the accelerating force is given by QD. It is now easily 
 seen that both this excess of force and the work expended in 
 accelerating the rod will, in the case under consideration, be" 
 considerably smaller than in a single-cylinder engine of equal 
 power, that is, one in which the same volume of steam 
 
 is allowed to expand in the same ratio e = vty. Such an engine 
 must evidently have a cylinder volume 
 
 that is, equal to the large cylinder, and the steam must be cut 
 off when the piston has passed through the distance - L. The 
 initial pressure, therefore, would be given by OE = Yp, and 
 would remain constant throughout the distance OF = L. The 
 diameter corresponding to such an engine is represented by the 
 
iv TYPES OF RECIPROCATING PUMPS 211 
 
 dotted line EEjAgAj in the figure, and it clearly shows not 
 only that the initial pressure to a higher degree exceeds the 
 average resistance, but also that a greater amount of work, or 
 that represented by the area QGGjMj, is expended in accelerat- 
 ing the rod than is the case in an engine constructed on Woolfs 
 compound principle. 
 
 Owing to this fact, and also on account of their great economy 
 of fuel, the compound types of pumping engines have been largely 
 introduced in recent times, both as single and double-acting. 1 
 In regard to Kley's pumping engines at Altenberg, it may be 
 mentioned that their steam cylinders are 1/70 m. and 1*20 m. 
 [5-58 and 3'94 ft] in diameter, and the stroke of the larger 
 cylinder is 2'8 m. [9'19 ft.], and that of the smaller one half of 
 the former. The plungers are 0'55 m. [1*80 ft.] in diameter, 
 and their maximum velocity is 0*84 m. [2 '7 6 ft.] when making 
 nine double strokes per minute. Their coal consumption is 
 2 '4 kilograms [5 '3 pounds] per horse-power per hour. 
 
 42. Double- Acting Pumping Engines. All of the older 
 pumping engines with pump rods were single-acting, that is to 
 say, the steam power was utilised merely to raise the rods, 
 which latter forced the water upward on their down stroke by 
 the action of their weight. 
 
 In order, however, to reduce the dimensions of the steam 
 cylinders, double-acting engines have been constructed in 
 recent times using steam power on both strokes. .There are 
 chiefly two distinct arrangements adopted with this object 
 in view. One is to balance the weight of the pump rod to 
 such an extent by means of a counterpoise G (Figs. 144 and 
 145), that the excess of weight will be equal to one-half only 
 of the total resistance, or -|-Q. The steam pressure required 
 on the piston for raising the rod will therefore also be equal 
 to JQ = D, and since the piston on the return stroke likewise 
 acts with the same force to lift the counterpoise, the total force 
 acting on the pump rod will equal the resistance Q. This 
 arrangement was only possible with heavy wooden rods, owing 
 to the compression to which the rod is subjected on the down 
 stroke by the action of its weight, wrought-iron rods made of 
 
 1 Concerning the Woolf engines erected by Klcy at Saarbriicken (single-acting) 
 and at Riidersdorf (double-acting), see Hermann's pamphlet, entitled Die neuen 
 IVasserhaltungsmaschincn, etc. 
 
212 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 round iron being generally of so small diameter that bending 
 would result were they to be exposed to compression. For 
 
 Fig. 144. 
 
 Fig. 145. 
 
 this reason Ehrhardt attempted, by the use of a cross-section, 
 as shown in Fig. 146, to make wrought-iron rods of sufficient 
 stiffness to permit of their being subjected to compression not 
 only by the action of their weight, but also by the steam pres- 
 sure from above. By this method the rod obtains a weight 
 equal to one-half of the pump resistance only, or JQ, and is 
 forced down by the equally great steam pressure. Pump rods 
 have also been constructed in the shape of 
 wrought-iron pipes (Rittinger's system), serv- 
 ing at the same time as delivery pipes for the 
 discharging water. 
 
 Besides dispensing with the counterpoise, 
 the above arrangement offers a special advan- 
 tage due to the slight weight of the pump 
 rod. If, for instance, the rod should break by accident, it 
 will be supported by the water column in the delivery pipe, 
 since the latter exerts an upward pressure on the plunger equal 
 to twice the weight of the rod. On the other hand, when a 
 pump rod is used which is heavier than the water column, a 
 break below the balance lever would cause the rod to fall with 
 an acceleration, which might be detrimental to the pumps. 
 The continual change from tension to compression in the rod 
 has caused a number of breakages in spite of the greatest care 
 exercised in the construction, and for this reason the plan of 
 
 140. 
 
iv TYPES OF RECIPROCATING PUMPS 213 
 
 allowing the steam to act on the rod from above has been 
 abandoned in modern practice, the use of a counterweight being 
 preferred. 
 
 The pumping engines described above, both the direct and 
 indirect acting, belong to the reciprocating class, no rotary 
 motion whatever being employed. As a result, these engines 
 are objectionable in some respects. In the first place, the 
 reversal of the piston does not take place smoothly with a 
 gradually decreasing and increasing velocity, as in the machines 
 driven by a crank, the action being instead sudden and jerky, 
 thus causing severe stresses in the parts. Neither is the stroke 
 constant, but varying with the fluctuations in steam pressure, 
 especially when expansion is employed. It was shown above 
 that, as the steam expands a certain fixed mass must be 
 accelerated in order that too great a velocity of the rod may 
 be prevented. It is therefore evident that when the steam 
 pressure is somewhat low the stroke easily falls short of the 
 intended length, and that an increase of pressure above a cer- 
 tain limit may cause the piston to strike against and blow out a 
 cylinder head. Such accidents have often occurred, and could 
 not possibly have been avoided in some instances, when the 
 pump rods have broken, causing the unloaded piston to be 
 sent forward by the mighty force of steam at a velocity against 
 which even the most powerful catch pins would offer no pro- 
 tection. Also in starting, when the delivery pipes are not yet 
 filled with water, or when the pumps " snift," that is, draw in 
 air in place of water, which happens from lack of water in the 
 pump well, similar accidents may occur owing to the reduced 
 load. As a safeguard, the clearance between piston and 
 cylinder heads is made large, which naturally interferes with 
 economy of steam ; moreover, from considerations given above, 
 the expansion in most cases cannot be carried very far, and 
 for this reason the coal consumption is considerable. 
 
 Fly-wheel shafts have therefore been largely introduced in 
 pumping engines, connection to the walking beam being brought 
 about by the usual crank and connecting rod. With this 
 arrangement the changes of direction at the dead centres evi- 
 dently take place gradually and without shocks, and besides, 
 the stroke being fixed once for all, danger of the piston striking 
 against the cylinder heads is prevented. In consequence, these 
 
214 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 rotative, or so-called crank and fly-wlicel engines may be run 
 at a greater velocity, and the energy stored up in the fly-wheel, 
 admitting as it does of the use of a higher degree of expansion, 
 materially increases the efficiency of these machines. Their 
 construction, however, is not so simple as that of the recipro- 
 cating type, their first cost is greater, and they are not possessed 
 of one advantage peculiar to the latter type, namely, to admit 
 of reducing the speed at will when the water supply is scant, 
 the cataract furnishing a means of varying the intervals between 
 the strokes. 
 
 On the other hand, in crank and fly-wheel engines a certain 
 velocity of rotation depending on the mass of the wheel is re- 
 quired to pass the dead centres, and experience has proved 
 that even if the lower limit of speed is placed at four revolu- 
 tions per minute, the fly-wheel required will be very large. 
 This is of the greatest importance in pumping plants for mines, 
 where, as a rule, the water supply is variable, and where, in 
 case of failing supply, when a crank and fly-wheel engine 
 is used, it would be necessary to run it periodically and to 
 construct large and expensive sumps for the water to collect 
 in during the periods of rest. 
 
 It is owing to the above facts that these engines, in spite 
 of their great advantages, have met with considerable opposi- 
 tion, and they are principally employed only in cases where 
 the water supply is abundant and steady. The results obtained 
 in such cases have been very satisfactory. The arrangement 
 of a compound crank and fly-wheel pumping engine of 700 
 h.p.. constructed at Hoppe's machine works in Berlin for the 
 coal mine " Ferdinand " near Kattowitz x is indicated by Fig. 
 147. A and B are the steam cylinders of diameters 1*491 
 m. [4-89 ft.] and 2*040 m. [6*69 ft] respectively, the piston 
 rods being connected to the walking beam FED by means of 
 a parallel motion ; the fulcrum of the beam is at C, and the 
 pump rod is attached at the end D. The connecting rod JK 
 and crank HK rotate the fly-wheel shaft H, which, besides 
 the fly-wheel S, carries the eccentric for operating the valves 
 of the steam cylinders. The air pump for the condenser is 
 driven by a separate steam engine. By the aid of two sets of 
 suction pumps [of 36*1 metres or 118*44 ft. lift] and three sets 
 
 1 See Hermann, Die neuen WasserhaltungsmascJiinen ait f den, etc. 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 215 
 
 of force pumps [2 7 2 '9 m. or 895'3 ft.] the water is raised to 
 a total height of 309 metres [1013'8 ft.] The stroke of the 
 large cylinder B is 3-452 m. [1T33 ft.], that of the small 
 cylinder 2'432 m. [7'97 ft.], and that of the pump 1'726 m. 
 [5*66 ft.], or exactly one -half of that of the large cylinder. 
 From these figures we obtain a ratio of cylinder volumes of 
 1 : 2 - 6 6 ; the steam pressure is three atmospheres by gauge 
 and the total expansion is six-fold. To prevent the upper 
 pumps from drawing in air, the plunger diameters are made 
 to increase slightly downward, those of the upper pumps being 
 
 Fig. 147. 
 
 0-628 m. [2-06 ft.], and those of the lowest 0'642 m. [2'11 
 ft.], so that at a speed of 15 revolutions per minute a delivery 
 of 7-420 cub. m. [262 cub. ft.] may be counted on. The 
 pump rod is made cylindrical, of wrought-iron, its weight being 
 balanced by the beam in such a manner that the force required 
 to raise it is the same as that needed to depress it ; the rod is 
 therefore subjected alternately to tension and compression. 
 
 With a view to combining the above-mentioned advantages 
 of both the reciprocating and crank and fly-wheel engines, 
 and at the same time avoid their objectionable features, Kley 
 has invented an arrangement which has been extensively 
 introduced, and must be considered one of the most import- 
 
216 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 ant advances in this field. The engine is provided with a 
 walking heam DCE (Fig. 148) and a fly-wheel shaft H ; the 
 
 valve motion is independent of this shaft, however, being 
 operated from the rod s by means of cataracts, as in the Cornish 
 
iv TYPES OF RECIPROCATING PUMPS 217 
 
 engines. The steam piston A acts on the walking beam at B, 
 the pump rod being attached at D and the necessary counter- 
 poise at G. For operating the valve rod a lever CK is secured 
 to the beam shaft C and acts on the auxiliary lever kct. In 
 consequence of this arrangement it is possible to limit the 
 number of strokes at will down to one per minute by lengthen- 
 ing the intervals between strokes by means of the cataract, 
 while by dispensing with the intervals the engine may be 
 run at as quick a rate as is consistent with its proper working. 
 In the latter case the fly-wheel revolves continuously in the 
 same direction, while in slow running the valve motion is so 
 adjusted that the interval occurs when the crank stands either 
 a little in front of or a little beyond the dead centre. The two 
 cases differ in that in the former instance the fly-wheel on 
 
 the next stroke will move in a direction opposite to its previous 
 motion, while in the latter it will move in the same direction. 
 For instance, if the crank on its up stroke proceeds from the 
 position A near the lower dead centre (Fig. 149) in the direc- 
 tion of the arrow a, and reaches the point B' only, in front of 
 the upper dead centre, then the motion during the down stroke 
 succeeding the pause will be in the direction of the arrow of. 
 On the other hand, when the crank is not brought to rest 
 until it reaches the point B" (Fig. 150), on the other side of the 
 centre, the motion a' on the down stroke will be in the same 
 direction as a. By adjusting the valve tappets, either one or 
 the other of these two conditions may be brought about. 
 
 In addition, these engines are especially safe in case of a 
 breakage in the pump rod, or when the greater portion of the 
 load is suddenly thrown off for some other cause. The whole 
 force acting on the piston will then be expended in accelerating 
 
218 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 the fly-wheel, and consequently the latter will be thrown con- 
 siderably beyond the dead centre, causing the plunger of the 
 cataract, which in its descent was to open the admission valve 
 in preparation for the following stroke, to ascend again before 
 it has had time to act, thus throwing the valve motion out of 
 action and bringing the engine to a stand-still. These pump- 
 ing engines are double-acting, have light fly-wheels, are con- 
 densing and work with a high rate of expansion, their perform- 
 ance therefore being very economical. The larger engines, 
 above 200 horse-power, are compounded. 
 
 43. Pumps for Waterworks. The purpose of a pump 
 is not always merely to raise water to a greater elevation, but 
 to force it into some space which is already filled with air, steam, 
 or water under a higher pressure. This is the case not only with 
 boiler feed-pumps but also with the majority of pumps used 
 for supplying cities with water. In order to prevent, in the 
 latter instance, the irregular motion of the pumped water from 
 being transmitted to the water in the pipe conduits, which would 
 interfere with the working of the machine and unduly strain 
 the pipes, 1 it is often necessary to collect the water in the first 
 place in a reservoir located near the pump, and thence distri- 
 bute it to various points according to demand. Such reservoirs 
 must be located at a great height, or be made in the shape of 
 a tower or column in order to supply water to the upper stories 
 of high buildings. At the present day they are often made 
 of iron plates forming so-called stand pipes of 1 to 2 metres 
 [3J to 6^ ft.] diameter, and of a height not infrequently reach- 
 ing 50 or 60 metres [160 to 200 ft.] Occasionally two stand 
 pipes are erected side by side, the water being pumped into 
 one of these, from which it is discharged through a side pipe 
 at the top into the other stand pipe, whence it descends into 
 the main conduit. 
 
 In place of high stand pipes large column -shaped air 
 chambers have been introduced (in France) ; small air pumps 
 are then made use of for replacing the air which leaks through 
 the seams of the vessels or is carried away with the water. 
 
 The arrangement of the pump end of a waterworks pump 
 
 1 Direct pumping into the water mains without the use of a reservoir or stand 
 pipes is frequently resorted to, and will be commented on below. TRANSLATOR'S 
 REMARK. 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 219 
 
 for city supply is shown in Fig. 151, which represents a 
 vertical section through a portion of the Cornish pumping 
 
 Fig. 151. 
 
220 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 engine at East London Waterworks, Old Ford, England. 1 CA 
 is the left half of the walking beam, which is oscillated by a 
 single-acting Cornish steam engine coupled to it at the right 
 by means of a Watt's parallel motion ; further, B is the 
 plunger with the case U for reception of the balance weights. 
 At E the pump barrel is visible, at HK a portion of the stand 
 pipe, at F and G pipes which connect the pump barrel with 
 the stand pipe, at V the suction valve is shown, and at W the 
 delivery valve. The plunger is on its down stroke, and con- 
 sequently V is closed and W open. From the walking beam 
 there are further suspended the piston rods of the air pump 
 N and the boiler feed-pump Q, while that of the cold-water 
 pump ES, which, like the main pump, takes its water from a well 
 built of masonry, is attached to the plunger B, and consequently 
 has the same stroke as the latter. Finally, we see in L the exhaust 
 pipe for the steam, which is condensed in the condenser M. 
 
 The diameter of the steam piston is 2'04 m. [6*72 ft.], that 
 of the plunger 1/04 m. [3 '44 ft.], that of the pump barrel and 
 pipes 1-093 m. [3'59 ft.], and that of the 38-m. [125 ft.] 
 stand pipe is 1-27 m. [4*1 7 ft] The steam piston has a 
 stroke of 3'15 m. [10'33 ft.], and the plunger B one of 2'90 
 m. [9-51 ft.] The high-pressure steam with which the engine 
 works is generated in four cylindrical boilers, as shown in Fig. 
 152, which represents a plan of the whole plant, including 
 boilers and boiler house, only omitting the walking beam and 
 valve motion. As in the preceding illustration, E here 
 represents the pump barrel, FG the communicating pipe, K the 
 stand pipe, L the exhaust pipe, M the condenser, 1ST the air 
 pump, Q the feed pump, and S the cold-water pump. Of the 
 four boilers, Dj, D 2 , D 3 , and D 4 , with inside fire-boxes E, two 
 are shown in longitudinal section. The steam cylinder A has 
 a wooden casing, the space between the latter and the cylinder 
 being filled with ashes. The steam spaces of all four boilers 
 are connected by the steam pipe BBjB^. The feed water is 
 supplied by the feed pump Q through the pipe TTjT 2 to the 
 heater U, whence it is conducted to the boiler by the pipe V. 
 There are further seen in the equalising valve, in W the 
 release valve, in X l5 X 2 the two cataracts, etc. 
 
 1 See the Cornish and Boulton and Watt engines erected at the East London 
 Waterworks, Old Ford, by Th. Wicksteed, London, 1842. 
 
[V 
 
 TYPES OF RECIPROCATING PUMPS 
 
 221 
 
 The object of stand pipes, namely, to produce a nearly 
 uniform pressure in the pipe conduit, can be only partly 
 accomplished by the use of air chambers, owing to the 
 great elasticity of air, but it may be attained in a simpler 
 manner by substituting a loaded plunger for the water column 
 contained in a stand pipe. For, evidently, the same result will 
 be produced whether the water is forced into a reservoir by 
 the pressure of a water column having a height h and a 
 
 Fig. 152. 
 
 sectional area F, or is subjected to the pressure P = FAy of a 
 plunger having a sectional area F. For instance, if in a given 
 time the water supplied to the main reservoir exceeds or falls 
 short of that drawn from it by a volume Y, either the water 
 column or the loaded plunger will rise or fall through a 
 
 Y 
 
 distance s = - ; in both cases the difference in water pressure 
 
 on the area F will be given by the quantity 
 
 AP= F,5= Y 
 
222 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 and the pressure per unit of area by 
 
 AP V 7 ' 
 
 4J-TT F ' 
 
 the variation being therefore smaller the greater the area F of 
 the water column or loaded plunger is chosen. 
 
 The arrangement of these so-called accumulators, which 
 were first introduced by Armstrong for operating hydraulic 
 cranes, etc., is described in the volume on Hoisting Machinery, 
 17, where their advantages in driving machinery which is 
 only intermittently in motion are discussed. 
 
 In modern practice the Cornish steam engine is frequently 
 replaced by a crank and fly-wheel engine for driving water- 
 works pumps, the same remarks applying to this arrangement 
 as to the mine pumps treated above. As was previously 
 mentioned, such engines may be run at a greater velocity than 
 the former type, and a more uniform action is attained, 
 especially when they are constructed of the duplex type with 
 cranks at right angles. 
 
 A horizontal pumping engine of this type, constructed by 
 E. A. Cowper for the Crystal Palace, 1 is shown in Fig. 153. 
 The reciprocating motion of the steam piston K of 0'90 m. 
 [2*95 ft] diameter is transmitted directly to the plunger L of 
 0*548 m. [1'80 ft.] diameter by the piston rod, which is 
 common to both ; from the crosshead C motion is com- 
 municated, through a forked connecting rod, to the crank ED 
 on the fly-wheel shaft D, which is also provided with another 
 crank at right angles to ED at the other end for coupling to 
 the second engine. As in the ordinary double-acting pumps, 
 two suction valves V and two delivery valves W are used, the 
 water lifted from the well U being first forced into the air 
 chamber K of 2'5 m. [8'2 ft.] length and 1-15 m. [3-77 ft] 
 width, and hence to the pipe X, which is common to both 
 pumps, and leads to a height of 37 m. [121 ft] The valves 
 are of bronze and double-seated, of the style shown as applied 
 to a piston in Fig. 55, the clear passage area of each valve, 
 corresponding to a lift of 15 mm. [0'59 ins.], being 0'041 sq. m. 
 [0'441 .sq. ft] The manner of operating the cold-water pump 
 and the air pump P by means of the bell crank MNF, which has 
 1 See The Artisan, August 1858, and Civil Ing., 1859. 
 
TYPES OF RECIPROCATING PU 
 
 223 
 
 its fulcrum at G and is connected to the crosshoad C, is evident 
 from the figure. Since the engine makes 15-, revolutions per 
 minute, the average piston velocity for 0*915 nxf&rft.l stroke is 
 
 2 x 0-915 x 15 
 60 
 
 = 0-457 m. [1-5 ft], 
 
 with which the water is raised to a height of 37 in. [121 ft] ; 
 the steam has a pressure of 1'2 atrn. by gauge, and is allowed 
 to expand to three times its original volume. 
 
 Fig. 153. 
 
 Also the pumps of the waterworks at Berlin are of the 
 rotative type, the arrangement being illustrated by Fig. 154. 
 Each of the four steam engines originally erected side by 
 side is provided with two cylinders A, the piston rods being 
 attached to equal -armed walking beams BCD by means of 
 parallel motions. Also here the two cranks EF on the fly- 
 wheel shaft are placed at right angles to each other. Each 
 walking beam drives two pumps, of the type shown in Fig. 
 59, the piston rods k of which are provided with cylindrical 
 plungers 0, whose sectional area is equal to half that of the 
 valved piston K. Of the water lifted from the supply pipe 
 S during the ascent of the plunger one-half is therefore 
 
224 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 discharged on the up stroke and the other half on the down 
 stroke into the air chamber W, whence it flows through the 
 pipe R, which connects with the air chambers of all the pumps. 
 It may yet be noted that in the branch pipes between the air 
 
 0-. 
 
 Fig. 154. 
 
 chambers and pumps clack-valves U are inserted, which are 
 kept closed by the pressure in the chamber, thus allowing of 
 the pumps being opened for inspection whenever necessary. 
 
 The steam cylinders A have 0'942 m. [3 '09 ft.] diameter, 
 and 1*255 m. [4*12 ft.] stroke, while the stroke of the plungers 
 is only 0'942 m. [3*09 ft.] As the valved pistons K have a 
 
iv TYPES OF RECIPROCATING PUMPS 225 
 
 diameter of 0'555 m. [T82 ft], and consequently the diameter 
 of the plungers is 
 
 0-707 x 0-555 = 0-392 m. [1-29 ft], 
 
 the water sucked in by each pump per double stroke, neglect- 
 ing all losses, will be 
 
 - x 0-555 2 x 0-942 = 0-228 cub. m. [8'052 cub. ft.] 
 
 In Fig. 155 there is shown one division of a double compound 
 .waterworks pump, of a type which has of late years been exten- 
 sively introduced in the United States, especially for direct pump- 
 ing into the water mains, the regulation being then effected by 
 means of an automatic regulator which is influenced by the varying 
 pressure in the mains. This style of pump is the design of Gaskill^ 
 and is manufactured by the Holly Manufacturing Company of Lock- 
 port, New York. 
 
 Each division has one high pressure and one low pressure steam 
 cylinder, and one water cylinder. A (Fig. 155) is the high pres- 
 sure cylinder arranged on the top of the low pressure cylinder B, 
 which is bolted to the bed plate. The piston rods of the pistons 
 P and Q are attached to crossheads C, running on guides D, and 
 connected by links L to the rocking beam R ; the latter is mounted 
 on a shaft S, journalled in heavy supports X, firmly bolted to the 
 bed plate, and rigidly stayed by wrought-iron struts E to the low 
 pressure cylinder B and the water cylinder F. The latter cylinders 
 are in line with each other, the piston rod of the low pressure 
 cylinder B being directly connected to the rod of the pump plunger 
 G. On a level with the centre of the high pressure cylinder A, 
 and directly above the two water cylinders of the pump, a shaft H 
 is arranged, which supports a fly-wheel K, and is connected to the 
 beams E, by means of two cranks placed at right angles and con- 
 necting rods M. The pillow blocks for this shaft are braced to the 
 high pressure cylinders by heavy cast-iron girders N. The air 
 pump of the condenser is driven by a short arm keyed to the inner 
 end of the beam shaft S. The double-acting plunger G works in a 
 gland at the centre of the pump barrel, both being accessible on 
 removing the cover U. The suction valves V, communicating with 
 the suction pipe v, and the delivery valves (not shown), are arranged 
 in horizontal plates below and above the plunger. The gland 
 divides the valves of one end of the water cylinder from those of 
 the other end at the centre of the valve plates. I is the air chamber 
 on the delivery pipe T. 
 
 The valves of the steam cylinders are operated by means of eccen- 
 trics e and c (Figs. 156 and 157) on a shaft m running parallel to the 
 
 Q 
 
226 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 cylinder, and driven by bevel gears from the main shaft H. The 
 admission valves of the high pressure cylinder (Fig. 156) are double- 
 seated (balanced) lift valves which are opened by the eccentrics at the 
 
 proper time, and, by means of the "cut-off" motion shown in Figs. 
 156 and 157, closed at any desired point of the stroke, the cut-off 
 motion being either regulated by hand or, when pumping is done 
 directly into the mains, by the automatic regulator above referred 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 227 
 
 to, which is connected with the water main. As long as the lug b 
 of the eccentric strap / rests on the abutment p, the valves are 
 moved by the eccentric c ; when the lug is released from the abut- 
 ments the straps swing around on the eccentrics, and the valves are 
 closed by the pressure of the springs d. The exhaust valves W 
 from the high pressure and Z from the low pressure cylinder are 
 " grid-iron " slide valves, and remain open somewhat less time than 
 is required to complete a stroke ; the former are also admission 
 valves to the low pressure cylinder B. Owing to the very close 
 connection between the two cylinders the clearance spaces are corn- 
 
 Fig. 156. 
 
 Fig. 157. 
 
 paratively small. Steam jackets k are provided for the steam 
 cylinders. 
 
 The automatic regulator used when pumping directly into the 
 mains consists essentially of a small water cylinder, containing a solid 
 piston acted on by the pressure in the water main, and having a 
 weight attached to it which counterbalances this pressure. This is 
 effected by suspending the weight from a strap passing over a cam 
 that rotates as the pressure changes, thus altering the lever arm of 
 the counterbalance, and keeping it in equilibrium with the water 
 pressure, no matter how much the latter may vary. Whenever the 
 water pressure varies from a given amount, the regulator, by means 
 of a weighted lever, throws into gear a reversible friction clutch 
 which is driven from the engine, and acts to either lengthen or 
 shorten the cut-off of the steam valves by changing the position of 
 the cams or abutments p with reference to the eccentric cams cf 
 (Fig. 157), which are attached to the shaft m, and, by means of 
 
228 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 the link connections n and levers o, govern the motion of the spring- 
 actuated admission valves. The rods g of each of the abutment 
 pieces p are so connected that all four of these pieces will be moved 
 simultaneously. 
 
 The shaft on which the counterbalance cam rotates has an index 
 wheel, and the index can be set at any desired water pressure. As 
 long as the water pressure varies one way or the other from the 
 figure at which the index is set, the friction clutch is kept in gear 
 by the weighted lever, and, operating in one direction or the other, 
 acts to change the "position of the abutments, and to adjust the 
 cut-off until the required pressure is reached. At this point the 
 index engages with the weighted lever and throws the clutch out 
 of gear. In this manner the pressure is kept practically constant 
 in the system of water pipes. Should the pressure in the latter 
 rise very suddenly, a piston in a safety cylinder raises a lever to 
 which the cut-off gear is connected, and throws the cut-off instantly 
 to zero if necessary. 
 
 A horizontal pumping engine of the type just described, erected 
 at the waterworks of South Bethlehem, Pennsylvania, in 1892, for 
 pumping into a reservoir, has a capacity of about 13,150 litres per 
 minute [five million U.S. gallons per twenty -four hours] when 
 operating under a steam pressure at the throttle valve of 5 '6 kg. 
 per sq. cm. [80 Ibs. per sq. in.], and against a head of 84 metres 
 [276 ft.] The diameter of the two high pressure cylinders is 5 3 '3 
 cm. [21 ins.], of the two low pressure cylinders 106*6 cm. [42 ins.], 
 and of the two pump plungers 49*5 cm. [19J ins.]; the stroke of 
 both steam pistons and plungers is 91 '4 cm. [36 ins.], and the 
 piston speed, when the pump works at its rated capacity, about 
 0'58 metres per second [115 ft. per minute]. The duty guaranteed 
 by the builders was 100 million foot pounds per 100 Ibs. of coal, 
 which approximately equals 304,670 m. kg. per 1 kg. of coal. A 
 description of a plant for direct pumping into the mains, with a 
 Gaskill engine of the type described above, may be found in American 
 Machinist, New York, Nov. 14, 1885. 
 
 A most noteworthy departure in recent pumping engineering is 
 the direct-acting "high -duty" pumping engine, designed by Henry 
 R. Worthington of New York with a view to securing a high fuel 
 economy with direct-acting pumps, by using the steam expansively 
 in the respective cylinders without the need of employing a fly- 
 wheel for equalising the force exerted by the steam in each stroke. 
 The general arrangement of this type of engine is substantially the 
 same as that of the "duplex" pump shown in Fig. 134, p. 188, 
 with the difference that compounded steam cylinders are used, and 
 a " high-duty " or compensating attachment is introduced which per- 
 forms the same function as the fly-wheel in the rotative types above 
 described, viz. to store up a portion of the energy given off by the 
 
IV 
 
 TYPES OF RECIPROCATING PUMPS 
 
 229 
 
 steam during the earlier part of the stroke, and restore it to the 
 pistons in the latter half of the stroke. 
 
 A section through one division of a horizontal duplex pumping 
 engine of this description is shown in Fig. 158. Here A is the 
 
230 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 high pressure and B the low pressure cylinder, both being provided 
 with semi-rotating cylindrical steam and cut-off valves I and K 
 arranged one above the other, the steam valves being operated from 
 the piston rod of the other division of the pump, and the cut-off 
 valves being operated by adjustable link connections from the piston 
 rod of the division to which they are attached. The steam exhaust- 
 ing from the high pressure cylinder through the lower rotary 
 valves passes through a reheater H to the valves of the low pres- 
 sure cylinder, and after spending its energy in the latter cylinder 
 it is discharged into the jet condenser C, which is connected to the 
 double-acting air pump L, driven by a vibrating lever M attached 
 to the plunger rod R of the pump. P is the pump cylinder with 
 its double-acting plunger F, suction valves V communicating with 
 the suction pipe 'E, and delivery valves T communicating with the 
 delivery pipe G. 
 
 The compensating attachment is arranged as follows : The 
 plunger rod E is prolonged through the outer end of the pump 
 cylinder, and to the end of this prolongation there is attached a 
 crosshead moving in guides N secured to the pump. This cross- 
 head is provided with two semi -spherical sockets opposite each 
 other, and into these sockets enter the spherical ends of a pair of 
 plungers S, which can move back and forth through stuffing boxes 
 in a pair of short cylinders U, the " compensating cylinders " being 
 journalled on trunnions in bearings arranged in the guide castings N. 
 The cylinders U, which swing back and forth as the plunger F 
 reciprocates, communicate through their hollow trunnions with an 
 accumulator (compare the volume on Hoisting Machinery, 17). 
 This accumulator may be connected with the delivery pipe, deriving 
 its power from the pressure in the latter. 
 
 From the figure it is now evident that at the beginning of each 
 stroke, when the steam pressure on the pistons is at a maximum, 
 and the compensating cylinders U point either as shown in the cut 
 or at the same angle from the opposite end, the plungers S will 
 encounter the greatest resistance from the fluid in the accumulator ; 
 as the steam pistons advance, this resistance will gradually decrease 
 as the angle of the compensating plungers with the guides increases, 
 until at the middle of the stroke the resistance will have fallen to 
 zero, since the compensating plungers at this point form right angles 
 with the guides. During the remaining half of the stroke the reverse 
 condition will maintain, inasmuch as the compensating plungers 
 now, instead of opposing the steam pistons, will push in the same 
 direction as the latter move, and consequently the pressure in the 
 accumulator will assist the steam pistons in their motion instead of 
 resisting them as before. Near the middle of the stroke, where the 
 decrease in steam pressure due to expansion is not so great, this 
 assisting action will be comparatively small, and it will gradually 
 
iv TYPES OF RECIPROCATING PUMPS 231 
 
 increase to a maximum at the end of the stroke, where the expansion 
 has been carried the farthest. By this method the inequalities of 
 driving force due to expansion of the steam in the respective steam 
 cylinders are equalised in a simple, inexpensive, and efficient manner, 
 without the need of cumbersome and heavy fly-wheels with connec- 
 tions. To avoid shocks at the dead centres a throttle valve is intro- 
 duced in the pipe connecting the compensating cylinders with the 
 accumulator, this valve being throttled at the dead centres by means 
 of a lever swinging with the oscillating cylinders. 1 When an engine 
 provided with an attachment of this kind pumps directly into the 
 water main, the compensating cylinders being connected with the 
 latter, the variation in the water pressure increases or diminishes 
 the load on the compensators, and the engine at once responds auto- 
 matically by running slower or faster, until the water pressure has 
 been restored to its normal point. In case of a break in the main, 
 the load on the compensators would be removed, and inasmuch as 
 there will be no stored energy to dispose of, and the steam is cut off 
 early in the stroke, there will be no danger of injury to the engine 
 through " racing," as is liable to be the case .in pumping engines 
 provided with a fly-wheel when the latter is suddenly deprived of 
 its normal resistance. Descriptions and illustrations of a Worth- 
 ington pumping engine of the type just commented on, as erected 
 on Quai d' Or say at Paris in 1889 for the Eiffel Tower hydraulic 
 plant, will be found in Engineering, London, May 3, 1889 ; diagrams 
 and accounts of tests of Worthington high-duty engines by Mair 
 and Unwin are given in the same journal of October 1, 1886, and 
 December 7, 1888. 
 
 In Fig. 159 there is shown a perspective view of three vertical 
 Worthington duplex high-duty pumping engines 2 erected in 1891 
 at the waterworks of the Artesian Water Company in Memphis, 
 Tennessee, each engine having a rated capacity of 26,300 litres per 
 minute [ten millions U.S. gallons of water per twenty-four hours] 
 when working against a pressure of 76 '2 metres [250 ft.], the 
 maximum plunger velocity being 0'76 metres per second [150 ft. 
 per minute]. The diameter of the high pressure cylinders is 76 '2 
 cm. [30 ins.], that of the low pressure cylinders 152*4 cm. [60 ins.], 
 and that of the plungers 68*6 cm. [27 ins.] ; nominal stroke of 
 plungers and steam pistons is 1'219 metres [4 ft.] At the test 
 prescribed in the contract with the builders, one of these engines is 
 reported to have shown a duty of 117,325,000 ft. Ibs. per 1000 Ibs. 
 of feed water consumed, which approximately equals 365,680 m. kg. 
 per 10 kg. of feed water (the boiler pressure during the test was 
 7*7 kg. per sq. cm. = 110 Ibs. per sq. in.) From the cut the arrange- 
 ment of the high and low pressure cylinders A and B and the water 
 
 1 See Zeitschrift des Vereins Deutscher Ingenieure, 1888, p. 736, and following. 
 2 Compare Engineering, London, February 12, 1892. 
 
232 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 cylinders C is evident, as well as the mode of operating the semi- 
 rotary cut-off valves from the crossheads on the plunger rods by 
 means of levers and link connections. These crossheads, which are 
 located between the low pressure and water cylinders, and run in 
 guides in the centre castings D, also serve to receive the ends of the 
 
 Fig. 159. 
 
 plungers of the compensating cylinders U. The latter are filled with 
 water, and communicate with an air tank which is kept filled with 
 air under pressure. 
 
 Further particulars regarding modern pumping plants may be 
 obtained from the following articles in technical journals, describing 
 and illustrating a number of notable pumping engines of English, 
 American, and German design : In Engineering, London, sewage 
 
iv TYPES OF RECIPROCATING PUMPS r , 233 
 
 pumping engine at Boston, Mass., designed by Leavitt, and built at 
 the Quintard Iron Works of New York (Dec. 11, ft&Slso described 
 in American Machinist, New York, May 31, 18 
 engine for East London Waterworks, built by T. 
 Sons, Hartlepool, England (Aug. 8, 1890); Worthington pumps at 
 the Chicago Exhibition 1893, built by Henry R. Worthington, New 
 York (April 21, 1893) ; quadruple expansion pumping engine, built 
 by E. P. A His and Company, Milwaukee (June 15 and 22, 1894); 
 Worthington triple expansion pumping engines at Bombay, India, 
 for pumping sixty million gallons of sewage per twenty-four hours, 
 built by James Simpson and Company, London (May 4, 1894); Glas- 
 gow hydraulic supply pumps (July 13, 1894); Worthington high- 
 duty pumps at Hornsey Sluice, built by James Simpson and Company, 
 London (Nov. 30, 1894); triple expansion pumping engine for 
 Glasgow Docks Hydraulic Installation, built by Fullerton, Hodgart, 
 and Barclay, Paisley, near Glasgow (Oct. 18, 1895). 
 
 In Zeitschrifl des Vereins Deutscher Ingenieure ; Hiilsenberg, Ueber 
 directwirkende Dampfpumpen (1884 and 1885); Eiedler, Pumpen 
 mit gesteuerte F'entilen (1888), Neuere Wasserwerksmaschinen (1890), 
 Amerikanische Pumpwerke (1893), and Das Wasserwerk in Boston 
 (1893); Gutermuth, Direktwirkende Pumpen (1888); Ballauf, Die 
 Worthington Pumpen in den charakteristischen Stellungen (1893). 
 TRANSLATOR'S REMARKS. 
 
CHAPTEK V 
 
 ROTARY PUMPS 
 
 44. Rotary Pumps. This name is applied to pumps in 
 which a revolving piston is made use of, whose rotation may 
 be either continuous or reciprocating, and which in its action 
 somewhat resembles the piston of ordinary reciprocating pumps. 
 Many arrangements of this kind have been devised, but with 
 all their variety they have this principle in common with each 
 other and with the ordinary piston pumps, namely, that by 
 the relative motion of two bodies a certain inclosed space is 
 alternately increased and diminished. If care be taken to 
 connect this space while it is enlarging with the suction pipe, 
 and while it is contracting with the delivery pipe, then suction 
 and forcing of the water will be effected as in the ordinary 
 piston pumps ; for, in fact, the action of the latter is simply 
 due to the alternate increase and decrease of the cylinder space 
 occasioned by the motion of the piston. 
 
 All rotary pumps have a closed casing through which pass 
 one or two shafts surrounded by stuffing boxes to prevent 
 leakage. On these shafts, and within the casing, there are 
 bodies of suitable form which, while turning, are in contact 
 with the inner circumference of the casing. If there is only 
 one shaft, valves of some kind are needed, but they are unneces- 
 sary when the machine has two rotating shafts, as will be seen 
 hereafter. 
 
 We shall first consider the Bramali pump (Fig. 160), in 
 which the piston is formed by a rectangular plate AB, provided 
 with two valves WW 15 and swinging about the shaft C in a 
 cylindrical casing. Here the suction pipe H terminates in 
 a chamber provided with the clack valves Wj, and we see how 
 
CHAP. V 
 
 ROTARY PUMPS 
 
 235 
 
 the oscillations of the piston AB caused 
 
 alternately open and close the pairs 
 
 of valves VW and V^. We 
 
 also see how the water passes from 
 
 the suction pipe through the open 
 
 valve V into the part of the casing 
 
 that is below the piston, while an 
 
 equal volume of water above the 
 
 piston is forced by the closed 
 
 delivery valve W l into the air 
 
 chamber E, and from there into 
 
 the delivery pipe S. This pump 
 
 is principally used in fire and 
 
 garden engines, and, so far as its 
 
 mode of action is concerned, it can 
 
 be regarded as a combination of 
 
 two single-acting suction and lift 
 
 pumps. The quantity delivered at 
 
 each oscillation of the lever of 
 
 course depends, as in all fire engines 
 
 and hand pumps, on the extent of 
 
 the swing of the lever. 
 
 by the lever DE 
 
 Fig. 160. 
 
 Owing to the one-sided pressure on the oscillating piston in the 
 operation of the pump just described, the wear of journal boxes, 
 piston, and casing is quite rapid. This defect is avoided in a 
 Bramah pump, patented by Abrahamson-JRoxendwff, and manufactured 
 by G. Allweiler in Baden, Germany. In this pump 1 two suction 
 and two pressure chambers g, g and h, h are provided, as will 
 be seen from Fig. 161, which represents vertical sections of the 
 pump. Two suction valves n, o, and two delivery valves p, q, 
 are made use of, these valves being attached to the casing, and 
 no valves being needed in the piston m. The latter is provided 
 with two independent passages s, s and I, b, the former effect- 
 ing the communication between the chambers h, h, and the latter 
 between the chambers g, g. As the lever is oscillated, the spaces 
 g, g and h, h will alternately become pressure and suction cham- 
 bers, and as the pressure due to suction and forcing at the upper 
 side of one wing of the piston is always counteracted by an equal 
 and opposite pressure at the lower side of the other wing, it is 
 evident that the wear as well as the power lost in friction will be 
 very slight. On account of their double suction and double forcing 
 1 Zeitschr. d. Ingenieure, 1892, p. 1021. 
 
236 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 action, these pumps may be made about one-half the size for the 
 same capacity as the older types of Bramah pumps. At d is shown 
 a small pocket just below the delivery pipe a', this pocket serving 
 to receive sand and impurities which are drawn in with the water. 
 
 d 
 
 Fig. 161. 
 
 The pocket d is provided with a clean-out hole k, ordinarily closed 
 by a screw r, and through which the water may also be drawn 
 from the delivery pipe to prevent freezing. These improved 
 Bramah pumps, which are in extended use as hand pumps, are to be 
 regarded as very efficient and durable machines for pumping a 
 variety of liquids. TRANSLATOR'S REMARK. 
 
 Another pump with a single shaft but continuous rotation 
 is that originated by Dietz, Fig. 162 ; the shaft W is located 
 in the centre of the cylindrical casing BB, and lias rigidly 
 
 attached to it a rim AA which 
 is rotated by it. In this rim 
 A there are slits in which 
 four floats C can move radially, 
 their motion being effected, as 
 shown in the figure, by a suit- 
 ably curved groove, bounded 
 on the inside by the cam- 
 shaped piece E rigidly secured 
 to the casing, and on the 
 outside by the casing B itself. 
 Opposite the flat portion of the cam plate E is placed a 
 guiding piece FGH of such a form that the radial width of 
 the groove is everywhere equal to the width of the slides C. 
 It is easy to see that as the shaft W turns with the rim A 
 in the direction of the arrow, the slides will be moved inward 
 
 Fig. 162. 
 
ROTARY PUMPS 
 
 237 
 
 by the pressure of the guide L while passing from H to 
 G, and outward by the cam plate E while they are passing 
 from G to F. If the guide is provided with slots L and K, it 
 follows that, owing to the increase of volume at K, water will 
 be sucked in from the pipe J, and in consequence of the con- 
 traction of the space between H and G water will be forced 
 through the pipe M. If the shaft were turned in the opposite 
 direction, water would be drawn from the pipe M and forced 
 into J. 
 
 In another construction (Fig. 163) the shaft A carries an 
 eccentric disc E, which touches the cylindrical casing G at a 
 
 point B ; this disc is always in contact with a slide S, which 
 is pressed against it by a spring, and can move radially in a 
 recess in the casing. The two spaces Oj and 2 , included 
 between the casing and eccentric disc, are therefore subject to 
 continual variation, 1 becoming smaller and 2 larger when 
 rotation takes place in the direction of the arrow. Water 
 must therefore be continually drawn in from the pipe H and 
 forced out through S. 
 
 As a rule, every rotary steam engine or water -pressure 
 engine can act as a rotary pump, as, for instance, the water- 
 pressure wheel (Fig. 164) described in the volume on Hydraulics. 
 
238 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 If in this arrangement the hollow shaft and its pistons AA 
 be revolved in the direction of the arrow, the water in the spaces 
 O l will be forced through the oblong openings C into the cen- 
 tral hole of the shaft, from which it is carried through a 
 stuffing-box into the delivery pipe. On the other hand, the 
 spaces 2 are filled by the side channels B, which communicate 
 with the other end of the shaft. Of course the slides F, which 
 separate the suction pipe from the delivery pipe, must be so 
 moved that they will offer no obstruction to the passage of the 
 pistons. 
 
 The quantity of water which these pumps with one shaft 
 can deliver per revolution is, in every case, determined by the 
 space left free in the casing by the rotating body ; it must be 
 noted, however, that the losses due to leakage are very great. 
 
 In the pumps just discussed valves are needed to separate 
 the suction water from that in the delivery pipe, but when 
 there. are two rotating shafts in the casing such valves can be 
 dispensed with. The separation of suction water and force 
 water is then effected by keeping the two pistons in continual 
 contact, 'suitable shapes being for this purpose given to the 
 latter. A large number of rotary pumps of this kind have 
 been invented, a few examples of which will be given in the 
 following. 
 
 In Fig. 135 Repsold's pump is shown, five different positions 
 of the two rotary pistons C and D being indicated. It is 
 
 I. 
 
 Fig. 165. 
 
 evident that if the shafts are revolved at the same rate in 
 opposite directions, as indicated by the arrows, water is sucked 
 in from the pipe A and forced out through the pipe B. Each 
 of the pistons C and D consist of two half cylinders of different 
 diameters, and joined by the steps c and d. As these steps 
 
ROTARY PUMPS 
 
 239 
 
 are brought into contact with each other they must be profiled 
 according to the rules for shaping the teeth of gears (see Weis- 
 bach's Mechanics, vol. iii. 1, Gearing) ; as shown in the figure, 
 they are consequently given radial flanks and epicycloidal faces. 
 The pistons C and D may therefore be regarded as one-toothed 
 wheels. The shafts receive opposite rotations from two equal 
 spur-wheels on the outside of the casing, which gear with each 
 other and are keyed to the rotating shafts. The figure shows 
 that during one revolution each piston delivers a quantity of 
 water equal to the clear space in the cylindrical portion of 
 the casing which surrounds the piston. This law is generally 
 true for all rotary pumps with two rotating pistons. 
 
 The toothed form of the pistons is still more clearly shown 
 
 Fig. 166. 
 
 Fig. 167. 
 
 in Pappenheim's pump (Fig. 166), where the driving-wheels 
 may be dispensed with, for the rotary motion received by one 
 shaft can be communicated to the other by the pistons C and D 
 themselves. It is evident that when rotation takes place in 
 the direction of the arrow, water is sucked in from A and 
 forced out through B, and with an opposite rotation of the 
 shafts the water must move from B to A. 
 
 Such pumps have also been employed as blowers, for 
 example Root's pump, Fig. 167, where the pistons C and D 
 are to be regarded as two-toothed wheels, two outside spur- 
 wheels being here necessary for the transmission of motion. 
 This also applies to the pump shown in Fig. 168, whose mode 
 of action needs no further explanation, after what has been 
 said. 
 
 A more detailed discussion of the preceding and other 
 
240 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 constructions may be found in Keuleaux's Kinematics, chaps. 9 
 and 10, which treat of chamber -wheel trains. 
 
 The greatest disadvantage connected with all rotary pumps 
 is the difficulty of maintaining water-tight contact between 
 
 the casing and the rotating pistons. 
 This difficulty is most marked at the 
 Hat surfaces or ends of the casing, for 
 here the relative velocity, and conse- 
 quently the wear, differs in amount 
 for different points, according to their 
 distance from the axis of rotation. 
 The consequence is that after these 
 pumps have been in use but a short 
 time, the loss of water from leakage 
 is considerable, especially when the lift is great. This is 
 probably the principal reason why these rotary pumps, not- 
 withstanding their comparative simplicity of construction and 
 mode of action, are but little used. They are chiefly adapted 
 for lifting thick, pasty fluids with which valves cannot readily 
 be used and water-tight contacts are less important. In such 
 cases, however, it is more common to make use of centrifugal 
 pumps, which we will now consider. 
 
 45. Centrifugal Pumps. These water-raising machines, 
 in which, as their name indicates, it is principally the centri- 
 fugal force which is brought into action, generate the energy 
 needed to lift the water by the living force imparted to the 
 latter by a rapidly rotating wheel. For this purpose the 
 wheel is provided with floats like a turbine wheel, and is 
 enclosed in a casing so arranged that the water can be 
 admitted to the wheel at one side and discharged at another. 
 As a matter of fact, these water-raising machines are reversed 
 reaction turbines, and their effect may therefore be estimated 
 in nearly the same manner as that of turbines. Centrifugal 
 pumps may be allowed to exert a suction, though not to the 
 same extent as piston pumps, since experience has shown that 
 their efficiency is reduced thereby. They are likewise little 
 suited for forcing water to great heights, and the lift is there- 
 fore seldom taken greater than, say, 15 m. [50 ft.] This is 
 due not only to the fact that the velocity of the wheel would 
 become very great with greater lifts, but also to the increased 
 
v ROTARY PUMPS 241 
 
 loss of water through the clearance space necessarily existing 
 between the casing and the rapidly rotating wheel. The- 
 efficiency of the best centrifugal pumps is less than that of 
 
 piston pumps, and seldom exceeds the value . 
 
 o 
 
 Experiments made by Morin with an Appolcl pump gave in 
 the most favourable case an efficiency of 0'6S, while other 
 experiments with wheels of unfavourable proportions, for 
 instance with flat floats placed radially, have given much 
 lower efficiencies, down to 20 per cent. Similarly, in the 
 tests made by Rittinger?- the efficiency did not exceed 35 
 per cent. But when the wheels are well designed and well 
 made we may in most cases depend on an efficiency of from 
 60 to 65 per cent. In spite of these low efficiencies, centri- 
 fugal pumps are largely used at the present day for moderate 
 lifts or in cases when, as in draining excavations, it is im- 
 portant to procure an apparatus that can be easily set up and 
 started, and may be readily transported. The absence of 
 valves (for at the most only a clack valve at the bottom of the 
 suction pipe is needed) is another advantage which is of par- 
 ticular value when dirty or sandy water is to be lifted. In 
 fact these pumps have been successfully employed in peat beds 
 for removing thick, pasty masses, and they have taken the 
 place of dredging machines 2 when the bottom was of a slimy 
 character. 
 
 Centrifugal pumps are made with vertical as well as with 
 horizontal shafts. When the former arrangement is chosen, 
 the wheel is often wholly immersed in the water to be lifted, 
 in order to avoid suction, while pumps with horizontal shafts 
 are always placed above the lower water-level, and consequently 
 must be arranged for suction. 
 
 The smaller horizontal pumps are usually driven by belts 
 on account of the great velocity required (up to 2000 revolu- 
 tions per min.), while the large stationary centrifugal pumps, 
 for example, such as are employed to drain low lands, are 
 usually provided with a vertical shaft and driven by toothed 
 wheels, since, owing to the large diameters (up to 1*5 m. [5 
 ft.]) and small lifts, a smaller number of revolutions will suffice. 
 
 1 See Rittinger, Centrifugalventilatoren utid Centrifugalpumpen. 
 
 2 Zeitschrift dcs Vereins deutscher Ingenieurc, 1869. 
 
 R 
 
242 
 
 MECHANICS OF PUMPING MACHINERY 
 
 A small centrifugal pump l with horizontal shaft is shown 
 in Figs. 169 and 170. The wheel B is fastened to the end 
 of the shaft A and consists of two shroudings &&, between 
 which are curved floats c; this wheel turns in the spiral- 
 shaped casing H, making 1500 to 2000 revolutions per 
 minute. The water is supplied from the suction pipe C, 
 enters at the centre of the wheel, and, after being caught by 
 the floats, is driven outward to the circumference of the 
 spiral-shaped casing, which guides it to the delivery pipe D, 
 and up the latter to a height corresponding to the imparted 
 velocity or pressure. The pump is driven by a belt pulley 
 
 Fig. 169. 
 
 Fig. 170. 
 
 keyed to the shaft A. Before starting it is necessary to fill 
 the casing H with water, otherwise the wheel will not 
 generate sufficient vacuum to draw the water up the suction 
 pipe. For this reason the lower part of the suction pipe 
 must be provided with a foot valve, usually a rubber clack, 
 which remains open when the pump is running, but closes 
 when the latter is brought to rest, thus preventing the water 
 from running out. The pump is filled through a hole that is 
 afterwards stopped up with a screw. In the machine shown 
 the wheel has a diameter of 160 mm. [6'3 ins.], and the 
 quantity discharged is claimed to be 0*45 cub. m. [15*89 cub. 
 
 1 Collection of Drawings by the Society Hiitte, 1869, PI. 9. 
 
ROTARY PUMPS 
 
 243 
 
 ft.] per minute. The lift, as we shall see in the following, 
 depends upon the rotary velocity of the wheel. 
 
 A centrifugal pump built by Henschel and Son of Cassel is 
 shown in Figs. 171 and 172; it differs from that just 
 
 Fig. 171. 
 
 described principally in that the wheel B is here composed of 
 a single central plate, with floats on both sides, the casing 
 being made with branch pipes E leading from the suction pipe 
 C for admitting water on each side of the wheel. At the 
 
 Fig. 172. 
 
 same time the cover F is so formed that it can be easily 
 removed and the interior rendered accessible without stirring 
 the casing H from its foundation. 
 
 As an example of a centrifugal pump with a vertical shaft, 
 
244 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 that designed by Sckwcurtikopff is shown in Figs. 173 and 
 174. 1 Here the vertical shaft A carries at its lower end 
 
 Fig. 173. 
 
 the wheel B, which is shaped like a conoid, and on its 
 lower surface is provided with blades of the form shown in 
 
 O 
 
 Fig. 175. 
 
 Fig. 174. 
 
 Fig. 175, which represents a view of the wheel from below. 
 The latter is surrounded by a bell- shaped casing H, which at 
 
 1 Verhandlgn. d. Ver. zur Be/ordering des Gewerbft. in Prcuszen, 1865. 
 
v ROTARY PUMPS 245 
 
 its upper end L communicates with the delivery pipe D. In 
 L is suspended a bowl-shaped casting E, provided at the bottom 
 with a stuffing box G for the shaft, which is supported by a 
 collar bearing at K. The water which passes from the suction 
 pipe C into the casing is flung outward by the wheel, and 
 flows along the curved surfaces of H into the delivery pipe, 
 where it rises to a height corresponding to its velocity and 
 hydraulic pressure. The upper part of the casing H is pro- 
 vided on the inside with a number of guide blades /, which are 
 given a gradual curvature, so as to guide the water, which has 
 received a rotary motion from the wheel, without shock into 
 the radial direction, and thus prevent the formation of eddies 
 and consequent loss of efficiency, which otherwise would occur. 
 In some instances guide blades have been applied, as in tur- 
 bines, to lead the water into the wheel, but such is not the 
 case in the majority of centrifugal pumps ; neither are, as a 
 rule, such guides employed for the discharge in the horizontal 
 types, inasmuch as the latter usually have a casing of such a 
 form that it may be regarded as a single guide blade. 
 
 In centrifugal pumps with a vertical shaft the foot valve 
 may be dispensed with, provided the wheel is placed below the 
 lower water-level. It must be noted, however, that for great 
 lifts difficulties may be encountered in the erection of the long 
 shaft and in retaining it in its vertical position, particularly 
 as experience shows that the ground below the suction pipe is 
 considerably loosened by the violent flow of water to the pump 
 when the latter is in vigorous operation. 
 
 We may discuss the action of a centrifugal wheel on the 
 water in a manner similar to that employed in tracing the. 
 effect of the driving water on the floats of turbines (see vol. 
 on Hydraulics). For this purpose let AB (Fig. 176) be a 
 blade which makes, with the inner circle of radius r : and the 
 outer circle of radius r 2 , the angles a and respectively. Let 
 us now assume the ordinary case that water is led to the inner 
 circle without guide blades, that is, in a radial direction, and 
 let us represent the absolute entrance velocity AE of the water 
 by v lt and the circumferential velocity AF of the inner circle 
 A by u v Then, in order that a shock may be prevented, the 
 first element of the blade at A must have a velocity in the 
 direction AL equal to the initial velocity of the water relatively 
 
246 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 to the rotating wheel. This condition is expressed by the 
 equation 
 
 In consequence of the initial velocity v l of the water and the 
 simultaneous rotation of the wheel, a particle of water entering 
 at A will traverse an absolute path represented, say, by the curve 
 AD, which cuts the outer circumference at the angle KDO = S. 
 
 Fig. 176. 
 
 Let v 2 represent the absolute velocity with which the water 
 leaves the wheel in the direction DK, and u% = DO = BH the 
 tangential velocity of the wheel at the outer circumference ; 
 then the relative velocity c 2 with which the water moves along 
 the last element B of the blade AB will be the resultant BJ of 
 the absolute velocity BG = v 2t and the velocity GJ = HB = u z 
 equal and opposite to that of the wheel. The triangle GBJ 
 therefore gives the equation 
 
 c 2 2 = vf + u* - 2v 2 u 2 cos 8 . . - . (2) 
 
ROTARY PU 
 
 ing me wheel 
 $1, which may be repre- 
 
 in like 
 
 In addition to its velocity v l the 
 at A has a certain hydraulic pressu 
 
 sented by a water column of the 
 
 may represent the hydraulic pressure of the water leaving 
 7 
 
 the wheel at B with the absolute velocity v%. These pressures 
 may be easily determined. For, let b be the height of the 
 water barometer, ^ the height of suction estimated from the 
 lower water-level up to the axis C, h. 2 the height of delivery 
 measured from C to the upper water-level O, and let \ and 2 
 be the heads corresponding to the resistances to motion in the 
 suction and delivery pipes respectively. As may be seen from 
 the figure, we then have 
 
 (3). 
 
 Since the water that leaves the wheel with a velocity v 2 and 
 a hydraulic pressure p% must be capable not only of overcoming 
 the delivery head h 2 , the atmospheric pressure b, and the resist- 
 ance f 2 , but also of maintaining the velocity of discharge w t 
 we further have 
 
 Now, in order to determine the velocity u 2 of the wheel, which 
 will give to the water the desired efficacy, it should be noted 
 that, owing to the action of the centrifugal force, the water 
 in passing through the wheel from A to B has its living force 
 increased by an amount corresponding to the head 
 
 _ 
 
 29 29' 
 
 less the head f r , which represents the resistance between the 
 blades of the wheel. Accordingly, the action of the rotating 
 wheel on the water passing through it will be represented by 
 the following equation : 
 
 y 
 
 (5). 
 
248 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 If we here substitute the values c^, c 2 2 , %>i and p. 2 given by 
 equations (1) to (4), we obtain, after some simple reductions, 
 
 cos 8 
 
 or if we let h = li l j f h 2 represent the total lift, and 
 
 denote the sum of all the heads corresponding to the hydraulic 
 resistances, we get 
 
 /t + f+ |! = ^ cos8 . I . (6) . 
 
 From this relation we can determine the velocity u 2 of the 
 outer circumference of the wheel by combining it with the 
 equation 
 
 sin/3 
 
 obtained from the triangle BGH, thus finding 
 
 sin (p + 6) 
 
 From this follows the absolute velocity with which the water 
 flows from the wheel 
 
 sili /tf 
 
 cos 8 sin (fi + 8) 
 
 Equation (7) will enable us to compute the velocity of the 
 outer circumference of the wheel, when 8, /3, , and w are 
 known. According to Grove} we may assume for the angles 
 8 and 
 
 tan 8 = 0-5; hence 8=26 34', 
 and 
 
 tan /3 = 0-3; hence j3= 16 42'. 
 
 It is also sufficiently accurate to place the head due to 
 the velocity of discharge w equal to about 3 per cent of the 
 
 1 Mittheil. des Gew.-Ter. f. Hannover, 1869, p. 130. 
 
v ROTARY PUMPS 249 
 
 lift h. Moreover, if we assume, in accordance with existing 
 experimental results, the head f representing the resistances 
 equal to 0*4 2 k, we shall get for the velocity of the outer part 
 of the wheel 
 
 i.e. about 40 per cent greater than the velocity which would 
 be acquired in falling through the height h of the lift. From 
 this follows the absolute velocity with which the water leaves 
 the wheel 
 
 If we denote the inner radius of the wheel by ^ and the outer 
 one by r a , the number of revolutions per minute is expressed by 
 
 30-M 2 . K w 2 
 n = = 9 '55 3. 
 
 WT 2 r 2 
 
 The clear width &., of the wheel at the outer circumference 
 can be found as follows. Let z represent the number of blades, 
 s their normal thickness, and Q the quantity of water that is 
 to be discharged per second, then we have 
 
 Q = (27rr 2 sin ft Z$)b 2 v 2 . 
 
 In like manner for the entrance of the water we have the 
 equation 
 
 sin a 
 
 from which we may obtain either of the three quantities b lf v v 
 and TJ when suitable values are assumed for the others. For 
 instance, if with Grove we assume a constant value for the 
 radial component of the velocity of the water in its passage 
 through the wheel, i.e. that 
 
 v l = v 2 sin 8, 
 then, since 
 
 v l = u l tan a = -u 2 tan a, 
 
 7> 2 
 
 we shall have 
 
 rt> 
 
 v 9 sin 8 = u 9 tan a, 
 
250 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 which gives for the angle a which the blade makes with the 
 inner circumference 
 
 r 2 v* . r 2 sin /3 sin 3 
 tan a = -2 - sm 8 = -^ -T- -. 
 T-J u 2 T-J sm (ft + 8) 
 
 /y* 
 
 Hence, if we accept the customary ratio = 2, and make 
 
 r i 
 
 use of the values ft = 16 42 r and & = 26 34' given above, we 
 obtain 
 
 tan a = 0-375,' or a = 20 30'. 
 
 We may further make the assumption that the area of the 
 openings through which the water is admitted to the wheel is 
 equal to the sectional area of the supply pipe, and hence, if we 
 neglect the thickness of the blades, we have Trr-f = 2irr l b 1 , 
 which gives for the clear width at the inner circle of the 
 
 wheel &! = -^, etc. 
 A 
 
 As regards the number and thickness of the blades, we may 
 apply the same rules as in the case of turbines, in which the 
 usual number of blades for wheels of moderate size varies 
 from 4 to 10, and the thickness from 5 to 10 mm. [0'2 to 
 0-4 in.] 
 
 After thus computing the angles a and ft which the blades 
 make with the inner and outer circumferences, it is necessary 
 to make some definite assumption from which to determine the 
 form of the blades. This is due to the fact that, since the 
 resistances experienced by the water in the wheel cannot be 
 represented by analytical expressions, it is impossible to ascer- 
 tain by calculation the most advantageous form of blade, or 
 that which reduces the internal resistances to a minimum. If 
 no such resistances were encountered, any form of blade inter- 
 secting the circumferences at the required angles a and ft 
 would evidently answer the purpose. 
 
 As a basis on which to proceed in designing the blades, 
 suppositions have been made with respect to the law according 
 to which the velocity of the water should vary in the wheel. 
 
 For instance, it has been suggested that the radial com- 
 ponent of the velocity of the water should remain constant, 
 and that the tangential velocity should increase according to a 
 
ROTARY PUMPS 
 
 251 
 
 certain law, 1 and hence the absolute path of the water and 
 finally the form of the blade has been determined, as in 
 turbines (see vol. on Hydraulics). The arbitrariness of all 
 such suppositions may justify us in assuming directly as simple 
 a form as possible for the blades, say a circular arc that cuts 
 the two circumferences at the desired angles a and @. To 
 draw such an arc, 2 lay off at any point B of the outer circum- 
 ference (Fig. 1*77) a line BJ making with the tangent BH the 
 angle HBJ = $, and at the point C lay off a line. CN" making 
 
 L 
 
 Fig. 177. 
 
 with the radius CB an angle BCN = a + j3. This second line 
 cuts the inner circumference at N, and if we connect this inter- 
 section with the point B and prolong the line thus obtained 
 until it intersects the inner circle at a second point A, then the 
 circular arc passed through A and B with a centre K lying on 
 the perpendicular to BJ at B will satisfy the required con- 
 dition, as may be seen from the figure ; for, the isosceles 
 triangle CNA gives CNA = CAN O ra + + a? = y + + a;, from 
 which we obtain CAK = y = a. 
 
 The guiding apparatus which receives the water that leaves 
 
 1 See Fink, Theorie der Centrifugalpumpen Zeitsclir. d. Ing., 1868, S. 1. 
 
 2 See Article by Grove, Mittheilungcn d. Gew.-Ver.f. Hannover, 1869. 
 
252 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 the circumference of the wheel at the angle S and gradually 
 leads it into the direction of the delivery pipe, is formed, in 
 horizontal centrifugal pumps, by the casing, whose circumference 
 may be regarded as a single guide blade. This casing is 
 brought almost in contact with the wheel at a point D, and 
 is here given the direction of the issuing water by making the 
 angle NDO equal to 8. A suitable form is obtained for the 
 casing by shaping it as an involute DFG of a circle, which is 
 concentric to the wheel and has the radius CE = r 2 sin 8. At 
 any point E of the circumference of the wheel the sectional 
 area ES furnished by the casing for the issuing water will 
 then be equal to the area of efflux DTE, which discharges the 
 delivered water through ES. For, if we denote the angle 
 
 DOE = ECV by <fc 
 then 
 
 ES = arc VE = r 2 sin 8 . < ; 
 
 hence the sectional area offered to the water at this place is 
 fr/ 2 </> sin 8, where & 9 is the clear width of the wheel. But this 
 is evidently equal to the area offered by the arc DTE = r^ to 
 the water issuing at the angle 8, the diminution of area due to 
 the thickness of the blades being neglected. The casing is pro- 
 vided with a neck GLMD which connects with the delivery pipe. 
 The power needed to drive the pump is equal to that re- 
 quired to lift a quantity of water Q per second to the height 
 
 expressed in horse-power, this is given by 
 75 \ 2aJ \ 2g) 
 
 As the water is actually lifted to the height li only, the 
 efficiency of the pump will be expressed by 
 
 r) = 
 
v ROTARY PUMPS 253 
 
 With the above assumed average values of f=0*42A and 
 _ = 0'037^ the efficiency of the pump becomes 
 
 '-OT- - 69 - 
 
 
 This does not include the resistances due to the pull of the 
 belt and the weight of the wheel, which resistances must be 
 specially determined for each particular case. 
 
 EXAMPLE. What dimensions must be given to a centrifugal 
 pump which is to raise 6 cub. m. [2 11 '9 cub. ft.] of water per minute 
 to a height of 5 m. [16 '4 ft.] 1 
 
 If we assume /3 = 15, 8 = 25, and 
 
 we obtain from (7) for the velocity of the outer circumference of 
 the wheel 
 
 = V9-81 x 5 x 1-5(1 + 0-4t>6 x 373) = 14-20 m. [46 '6 ft.], 
 and for the absolute velocity of efflux, according to equation (8), 
 
 ^2 = x/9-81 x 5 x 1-5 ^"t 1 . , ft0 - = 572 m. [18'8 ft.] 
 
 V cos 25 sm 40 
 
 The radial component of the velocity of efflux is therefore 
 
 v 2 sin 5 = 5 72x0 -423 = 2 -42m. [7 '94 ft] 
 
 If we suppose the water to enter the wheel and pass through 
 the suction pipe with this velocity, the diameter d of the latter will 
 be obtained from 
 
 2 sin d = Q, which gives rf= * ^.^ = 0-230 m. [9 '06 ins.] 
 
 If, therefore, we give to the wheel an inner diameter of 0*24 m. 
 [9'44 ins.], that is, a radius ^ = 0-12 m. [4*72 ins.], and assume 
 r 2 = 2r l = 0'24 m. [9'44 ins.], we get for the velocity at the inner 
 circumference 
 
 Ul = r -lu 2 =l 14-2 = 7-1 m. [23'3 ft], 
 r 2 Z 
 
 and for the angle a at the inner circumference 
 
254 MECHANICS OF PUMPING MACHINERY CHAP, v 
 
 which gives a= 18 40'. Now, assuming 6 blades, each 6 mm. [0*24 
 in.] thick, we obtain the clear width b l at the inner circumference 
 from 
 
 or 
 
 which gives & 1 = 0'065 m. [2*56 ins.]; in like manner the width 
 at the outer circumference is obtained from 
 
 Q=(2^ 2 -^)t- 2 sin5/, 2 , 
 giving 
 
 -= 0-030 m. [118 ins.] 
 
 Finally, we have for the number of revolutions of the wheel 
 per minute 
 
 ,_60w 2 _ 30x14-20 " 
 
 '~27rr~3'14 xO*24 ' 
 
 and for the horse-power required to drive it 
 
CHAPTER VI 
 
 ADDITIONAL WATER-RAISING MACHINES 
 
 46. The Hydraulic Ram. Instead of making use of a 
 swiftly rotating wheel for imparting to the water a velocity 
 which will carry it to the required height, we can, when a fall 
 of sufficient head is available, employ for the purpose the living 
 force possessed by the water while in motion in a pipe. It is 
 on this principle that the hydraulic ram depends. By this 
 
 Fig. 178. 
 
 apparatus, which was invented by Montgolfier in 1796, a 
 portion of the driving water is forced to an elevation which is 
 greater than that from which it has fallen. The arrangement 
 of a hydraulic ram is essentially as follows. The reservoir 
 HA (Fig. 178), from which the water is supplied, connects by 
 means of a pipe ABC with the air chamber E, from which the 
 delivery pipe DE leads to the tank LM, where the lifted water 
 
256 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 is received. At C, where the supply pipe enters the air 
 chamber, a delivery valve W, opening upward, is placed, and in 
 the short branch pipe BK is located a so-called waMe valve 
 which opens downward. 
 
 In order to explain the action of the machine, let us first 
 assume the two valves Y and W to be closed, and that the two 
 pipes ABC and DE are full of water, the air chamber E being 
 at the same time filled partly with water and partly with air. 
 Now, if the aperture K is opened by pressing down the 
 valve V, water will discharge through K and a fresh supply 
 will flow from the reservoir AH into the pipe AB. Since the 
 hydraulic pressure on the upper surface of the waste valve is 
 less than that on the lower surface, on account of the greater 
 velocity of the water passing through the valve opening, the 
 valve will close again as soon as the velocity of efflux has 
 become sufficient to cause an upward excess of pressure greater 
 than the weight of the valve. This closing of the waste valve 
 causes the water moving in AB to open the delivery valve, 
 and consequently water is forced into the air chamber K till 
 the living force of the water in the supply pipe is wholly 
 destroyed by the operation. The incoming water causes a 
 compression of the air, and compresses the air in the chamber, 
 thus causing a discharge from the orifice E of the delivery 
 pipe DE. After the water has been brought to rest in AB it 
 gradually begins to move in the opposite direction from B to 
 A under the influence of the greater pressure in the air 
 chamber. As this flow soon closes the delivery valve W, 
 water ceases to flow from D, and the atmospheric pressure now 
 becoming greater than the pressure of the water in B, pushes 
 down the waste valve, thus automatically causing a new series 
 of operations to begin. The hydraulic ram represented in 
 Fig. 179 was built by Monty olfier, and differs from that just 
 described principally in having two air chambers. AB is the 
 end of the supply pipe, V the waste valve, E the air chamber, 
 and DE the delivery pipe leading from the latter ; another air 
 chamber S connects by the pipe C with the valve chamber 
 BK, and by the valves WW with the outer air chamber E. 
 The inner air chamber is employed to diminish the hurtful 
 effects of the shocks that accompany the sudden opening and 
 closing of the waste valve, thus not only diminishing the wear 
 
ADDITIONAL WATER-RAISING MACHINES 
 
 257 
 
 of the machine, but also increasing its efficiency. The water 
 in the chamber R is subjected to a pressure exceeding that of 
 the atmosphere, and consequently it absorbs a portion of the 
 air and carries it along to the delivery pipe. To make good 
 the loss of air thus caused, an air valve H opening inward 
 is inserted at the bottom of the air chamber R When the 
 return flow takes place in the supply pipe and the pressure in 
 the latter becomes less than the atmosphere, this valve opens 
 and admits, during each series of operations, a small quantity 
 
 Fig. 179. 
 
 of air into the chambers S and R to replace that which has 
 escaped through the delivery pipe. 
 
 The hydraulic ram can also be arranged to lift water by 
 suction. A ram of this kind was built by Boulton? and was 
 described by Hachette in his TraiU EUmentaire des Machines, 
 under the name of Btlier aspirateur. Since that time the 
 Belgian engineer Z/eblanc 2 has constructed a double-acting 
 suction ram for draining excavations. It is shown in Fig. 
 180. A is the supply reservoir, BCD the driving pipe, SG- 
 
 1 Journal des Mines, Bd. II. 
 
 2 Annales des ponts et chaussees, 3, Ser. 7, ann6e 1858, and Civil Ingenieur, 
 Bd. 5. 
 
 S 
 
258 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 the upper part of the suction pipe, E an air chamber, and BE 
 a branch pipe joining the chamber with the driving pipe. The 
 waste valve of the ordinary ram is here replaced by the admis- 
 sion valve V, and the delivery valve of the ordinary ram by 
 the suction valve W. When V is open water flows from A 
 into the driving pipe, which leads to the well U. After the 
 water has attained a certain velocity in BCD, the valve V is 
 pressed down by the water above it, and, as the supply is 
 now cut off from A, the pressure at B falls below that of the 
 
 Fig. 180. 
 
 atmosphere, with the result that the excess of pressure of the 
 rarefied air filling the chamber opens the suction valve W. Con- 
 sequently the atmospheric pressure causes water to rise in the 
 pipe SG, from which it passes by the path EWB into the driving 
 pipe, and from there into the discharge well U. This motion 
 lasts but a short time, however, for, as soon as the living force 
 of the water in the driving pipe has been destroyed, the pres- 
 sure in the pipe BC will overcome that in EW, since the 
 water-level U is higher than the level from which the suction 
 pipe S draws its supply. The result is that the valve W again 
 closes, and after the water in the driving pipe has been brought 
 to rest the valve V opens, and a new series of operations begins. 
 
vi ADDITIONAL WATER-RAISING 
 
 In this description we have assumed only one driVihg^pipe, one. 
 admission valve, etc., while in LeUancs doirffe-acting ram all 
 the parts, with the exception of suction pipB^^rti^r chamber, 
 are duplicated, i.e. there are two driving 
 supply reservoir, each having an admission valve, am 
 chamber is connected to each driving pipe by a separate branch 
 pipe. To avoid severe shocks, the valves Wj and their 
 seats are formed of compressed leather discs, and the suction 
 clacks are also made of leather. Moreover, both of the former 
 are attached by stems to an equal-armed lever HKHj attached 
 to the horizontal shaft KK ; consequently the closing of one 
 valve will be accompanied by the opening of the other, and 
 the two f suction valves W will therefore also be alternately 
 opened and closed. 
 
 In the double-acting ram just described the diameter of all 
 the pipes and apertures is 0*2 m. [7*87 ins.], the length of the 
 driving pipe is 3*29 m. [10*79 ft], the fall is 1*7 m. [5*58 ft], 
 and the lift 2*25 m. [7*38 ft] We are in possession of no 
 exact data concerning the performance of this ram, but it is 
 claimed that its capacity equals that of six wooden pumps, 
 each requiring in its operation the combined efforts of twelve 
 labourers. 
 
 Eytelwein has made very complete tests of two hydraulic 
 rams of the ordinary type. The results are contained in a 
 paper entitled " Bemerkungen uber die Wirkung und vortheil- 
 hafte Anwendung des Stoszhebers," von J. A. Eytelwein, Berlin, 
 1805. The larger of the rams had a horizontal driving pipe 
 65 mm. [2*56 ins.] in diameter, a delivery pipe 26 mm. 
 [1*02 in.], and a copper air chamber 0*235 m. [9*25 ins.] in 
 diameter and 0*314 m. [12*36 ins.] high. The lengths of the 
 pipes, the fall and the lift, were all frequently changed within 
 wide limits. The smallest length of the driving pipe was 
 3*6 m. [11-8 ft], the greatest length 13'65 m. [44*77 ft], the 
 length of the delivery pipe varied from 10 to 15*5 m. [32*8 to 
 50*84 ft], and the lift from 4*7 to 14*8 m. [15*42 to 48*54 
 ft.] Moreover, in the experiments with the larger rain five 
 different dish-shaped waste valves were employed, only one of 
 which had a passage through it, the area of which was 23*9 sq. 
 cm. [3*7 sq. in.], or nearly equal to the sectional area 25*24 sq. 
 cm. [3'91 sq. in.] of the driving pipe. The delivery valve was 
 
260 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 of brass, and was either a hanging clack or a disc valve that 
 moved horizontally. The number of operations or strokes per 
 minute ranged from 10 to 180, the corresponding waste water 
 varied from 0'0044 to 0170 cub. in. [0'155 to 6'004 cub. ft.], 
 and the lifted water from 0'75 to 31 litres [0*0265 to 1-0948 
 cub. ft.] 
 
 Let Q represent the quantity of water flowing through the 
 waste valve, Q l the quantity discharged from the delivery 
 pipe, h the fall OK (Fig. 181) or distance of the water-level H 
 in the supply reservoir above the outlet K of the waste valve, 
 
 R 
 
 
 Fig. 181. 
 
 and /&]_ the lift or distance OL between the water-levels in the 
 upper and lower reservoirs ; the efficiency of the ram is then 
 expressed by 
 
 QA 
 
 VI = -- 
 
 In all, Eytelwein made 1123 experiments, partly with the 
 larger and partly with the smaller ram. From these experi- 
 ments he deduced the formula 
 
 7?=M2-0-2 ^/^, 
 whence we obtain the following table for the efficiency, 
 
 Al 
 
 h = 
 
 1 
 
 2 
 
 3 
 0-774 
 
 4 
 
 5 
 
 6 
 
 8,' 
 
 10 
 
 12 
 
 15 
 
 20 
 
 1?= 
 
 0-920 
 
 0-837 
 
 0-720 
 
 0-673 
 
 0-630 
 
 0-555 
 
 0-488 
 
 0-427 
 
 0-345 
 
 0-226 
 
vi ADDITIONAL WATER-RAISING MACHINES 261 
 
 This shows that for a given fall h the efficiency decreases 
 with an increased lift h lt and Eytdwein therefore suggests that, 
 for great lifts, instead of a single ram several be employed, the 
 first supplying water to the one above it, and so on. He also 
 deduces from his experiments the following important rules. 
 
 1. The total quantity (Q-f Q x ) of water consumed varies 
 as the square of the diameter (d) of the supply pipe, and 
 if CC^Q-j-Qi) represents the quantity of water used per 
 minute, in cubic inches, the diameter of this pipe will be given by 
 
 ,7 1 . , 
 
 d = - 12 :*!/ inches, 
 
 2i\. 
 
 or, when Q + Q x is expressed in cubic metres, it would be 
 approximately 
 
 d = 300 >/60(Q + Q x ) mm. 
 
 2. The length I of the supply pipe depends on the delivery 
 head h lt and may be found from the formula 
 
 3. The diameter d 1 of the delivery pipe has a subordinate 
 influence on the action of the machine ; it suffices to take 
 d! = %d. 
 
 4. The aperture of the waste valve should have the same 
 sectional area as the driving pipe. 
 
 5. The weight of the waste valve should be as small as is 
 consistent with sufficient strength. 
 
 6. The waste valve may be placed under water without 
 interfering with the effect of the machine. 
 
 7. The two valves should be located as closely together as 
 possible. 
 
 8. The air chamber diminishes the shocks and increases 
 the effect of the machine. It is sufficient to make the cubic 
 contents of the air chamber equal to that of the delivery pipe. 
 
 EXAMPLE. An hydraulic ram is to be constructed to work with 
 a fall of 2 m. [6'56 ft.], and to raise 30 litres [1-059 cub. ft.] of 
 water per minute to a height of 8 m. [26*25 ft.] 
 
 We have h = 2, h^ = 8, and consequently the efficiency 
 
262 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 The required driving water will therefore be 
 
 WQ=60^=^~~|0-167 cub. m. [5'898 cub. ft.], 
 
 and the total consumption of water per minute 
 
 60(Q + Q 1 ) = 0-03 + 0167 = 0-197 cub. m. [6 '957 cub. ft.] 
 
 The diameters of supply pipe and valve openings should there- 
 fore be 
 
 d = 300V60(Q+~Qi) = 300\/0-197 = 133 mm. [5 '24 ins.], , 
 
 while for the delivery pipe d = ^d = 66 mm. [2 '6 2 ins.] will suffice. 
 For the length of supply pipe we have 
 
 ^ = A 1 + 0'3^=8 + 0-3| = 9-2 m. [3918. ft.], 
 
 /b 2t 
 
 The volume of the air chamber we make equal to that of the 
 delivery pipe, or 
 
 ird 2 
 
 W = -^ AJ = 7854 xO'66 2 x 80 = 27 '4 litres [0'968 cub. ft.], 
 
 and if we choose the cylindrical form and a diameter of 0'3 m. 
 
 2 7 '4 
 [0-98 ft.] we obtain for the height of the chamber = 0'388 m. 
 
 [1-27 ft.] 
 
 The general theory of the hydraulic ram is quite compli- 
 cated, and involves the use of unusual analytical methods 
 (see Navier's Eesume des Lemons sur V application de la Mecanique, 
 part ii., and also Venturoli's Elementi di Meccanica e d'Idraidica, 
 vol. ii.) Moreover, as it is insufficient for the determination of 
 the effect of the machine, which always requires empirical results, 
 we will in the following present a theory which, though only 
 approximately correct, yet the more closely approaches to the 
 truth the greater the quantity of water in the supply pipe, 
 and the greater the number of revolutions of the ram per 
 minute. 
 
 Let F denote the sectional area and I the length of the 
 supply pipe, and h the fall, then the inert quantity of water 
 which must be set in motion when the waste valve opens by 
 
 F/7 
 the force F/z/y will be , and consequently its acceleration 
 
 t/ 
 
 Thy h 
 
vi ADDITIONAL WATER-RAISING MACHINES 263 
 
 Owing to this constant acceleration the velocity acquired after 
 t seconds will be 
 
 h . 
 
 and if the waste opening has the same area F as the supply 
 pipe, the volume of water which flows out during the time t 
 will be 
 
 Now, if the volume of water in the delivery pipe is small 
 in comparison with that in the supply pipe, the retardation of 
 the latter mass caused by the back pressure F/^7 in the 
 delivery pipe, when the waste valve closes and the delivery 
 opens, will be given by 
 
 and consequently the velocity of the water in the supply pipe 
 will, when ^ seconds have elapsed after the opening of the 
 delivery valve, amount to 
 
 h, 
 
 v l = v-p l t l = v--lgt r 
 
 The time ^ required to bring the whole volume of water to rest 
 will now be obtained by placing v 1 = 0, which gives 
 
 t - l v - h t 
 
 * i~V 
 
 and determines the volume which, in the meantime, has flown 
 into the air chamber to 
 
 v -v't -^ ^ 2 _^^ 
 
 2 l \ 2g hj 2 ' 
 
 Assuming the delivery valve to remain open for a short 
 interval t z after the subsequent return flow into the supply 
 pipe has commenced, the driving force I\7 will give to the 
 volume F/7 a velocity 
 
 = 
 
264 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 and therefore the volume returned from the air chamber will be 
 
 Finally, when the delivery valve closes and the waste valve 
 opens, the mass of water Ffy will move with a retardation 
 
 h 
 
 2V* 7* 
 
 and accordingly, after the time t y it has attained a velocity 
 
 Ji 
 
 The volume Ffy is now again brought to rest, that is, v 3 
 becomes zero, and a new stroke begins after the time 
 
 during which a volume 
 
 V * = ~2~ ''~fh t2 = ~l^"f 
 
 returns, and an equal quantity of air or water flows in through 
 the waste valve. 
 
 The driving or waste water required by the ram per minute 
 is now given by 
 
 Q = $ + 7+7+7' 
 
 or approximately, when V 3 , t v and t s , owing to their insigni- 
 ficance, are neglected, 
 
 "\T "\T 7, "GT,. 7, Z, ~t 
 
 Q = 
 
 Further, the volume of water lifted per second will be 
 
 T^ J. i J. i J. i -/ ' 
 
 or approximately 
 
 n v i h i Yi _ h ^ - ll h-$gt 
 t h + h^ 2 h + h^ I 2' 
 
vi ADDITIONAL WATER-RAISING MACHINES 265 
 
 and consequently the ratio of the lifted water to the driving 
 or waste water 
 
 Si 1 
 
 Q V 
 The total volume of water consumed will be 
 
 which, like the experiments of Eytelwein, indicates that the 
 sectional area F of the supply pipe should be proportional to 
 the quantity Q -f Q x of water consumed. 
 
 Under the supposition that the volume of water sucked in 
 
 through the waste valve during the return flow is V 3 = 
 we obtain for the efficiency of the hydraulic ram 
 
 h 
 
 _ 
 
 ~ 
 
 On the other hand, if there is no such suction through the 
 waste valve, the efficiency will be given by 
 
 _h?P - lift? _ _ 
 
 \h 
 
 that is to say, that, as has also been proved by experience, it 
 
 will approach more closely to unity the smaller the ratio 
 
 h 
 
 of delivery height to fall, and the shorter the time during 
 which the delivery valve remains open after the return flow 
 commences. 
 
 NOTE. In regard to the efficiencies 77 = 0-57 to 0*67 of five 
 hydraulic rams which are in operation in France, see Fwmules, Tables, 
 etc., par Claudel, Paris, 1854. 
 
 47. Ejectors and Injectors. On the suction produced by 
 a jet of water various water-raising contrivances have been 
 based, which may be employed to advantage for some purposes. 
 
266 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 To this class belongs the ejector designed by James Thomson l 
 and shown in Fig. 182. The driving water is supplied by 
 the pipe EA, and flows through a conical nozzle into a horizontal 
 
 discharge pipe which widens 
 toward the end F. Owing 
 to the reduction in pressure 
 which is hereby produced 
 in the chamber D (as in the 
 case of the blast pipe of a 
 locomotive), water will be 
 sucked through the pipe CD, 
 ascending from the reservoir 
 C, and will be discharged, 
 together with the driving 
 water, at F. 
 
 According to tests of the 
 apparatus made by Thom- 
 son, the maximum effect 
 was obtained for a suction 
 h = 0'9A, where h is the 
 fall of the driving water; 
 
 for this case the water raised Q 1 equalled ^ of the driving water 
 Q, which performance corresponds to the trifling efficiency of 
 
 1, = $ x 0-9 = <H8. 
 
 This small efficiency explains why ejectors of this kind 
 have gained but little application, more economical methods 
 being available for the employment of water power. On the 
 other hand, the apparatus constructed by Nagdf and based on 
 the same principle, has been used to advantage in the temporary 
 work of draining excavations, etc., the slight efficiency often 
 being of no consequence in such cases. An arrangement used 
 by Nagel for draining the excavations for a turbine plant is 
 shown in Figs. 183 and 184. By opening the gate B water 
 is admitted at A to the wooden trough CDE, which is secured 
 to the bottom of the outlet channel FF. The trough is made 
 of rectangular section, and obtains its smallest height at D, 
 
 1 Report of the British Association, 1852, and Rankine, Manual of the Steam 
 Engine, etc. 
 
 2 Ztschr. deutsch. Ing., 1866, p. 121. 
 
vr 
 
 ADDITIONAL WATER-RAISING MACHINES 
 
 267 
 
 whence it widens towards E, so that it has its minimum cross- 
 section at D. At this point the suction pipe H enters it from 
 above, being carried from the excavation G-, which is protected 
 by the dam K. A flap L at the end E of the trough permits 
 of filling the latter with water before starting ; when the flap 
 
 Fig. 18o. 
 
 is dropped the flow of water through the trough will create a 
 suction in the pipe H. The latter is at its lower end pro- 
 vided with a foot valve, which prevents the water from flowing 
 out of the suction pipe when the action of the apparatus is 
 interrupted by the closing of the gate B. The desired object 
 
 Fig. 184. 
 
 was completely achieved in the instance referred to, when the 
 excavation, which measured 24*3 m. [79'7 ft.] in length by 
 5'6 m. [18'4 ft.] in width, and contained water to a depth of 
 2-4 m. [7-9 ft,], was emptied in half an hour and kept entirely 
 free from water during the building operations. It is claimed 
 that the apparatus worked equally well when the height of 
 suction considerably exceeded that of the fall. 
 
268 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 To discuss the action of this ejeetor, let h denote the fall 
 of the driving water measured from the upper level E (Fig. 
 182) to the centre of the nozzle, whose clear aperture will be 
 designated by F ; further, let A T be the height of suction, and 
 F x the sectional area of the suction pipe. Now, if p is the 
 hydraulic pressure in the chamber at the orifice B of the 
 
 /Y\ 
 
 nozzle, and consequently the corresponding water column, 
 
 7 
 
 then, neglecting frictional resistances, we have for the velocity 
 of efflux v of the driving water at B the equation 
 
 and likewise for the velocity v l with which the suction water 
 passes the nozzle 
 
 Letting w represent the velocity with which the mixture 
 of driving and suction water Q and Q 1 is discharged, the living 
 force of the latter will be 
 
 As the two bodies of water suddenly change their velocities 
 v and 0J respectively into w, the resulting losses from impact 
 will (according to Weisbach's Mechanics, vol. i. 7, chap. 4) be 
 given by 
 
 Qfo-w) 2 ^ QA-w) 2 
 
 ~ ~ 
 
 and consequently we obtain the following equation, 
 
 in which the quantity on the left represents the work per- 
 formed by the driving water in falling from the height h, while 
 QJ/^J is the work expended in raising the suction water Q l to 
 the height h^ This equation may also be written thus 
 
vi ADDITIONAL WATER-RAISING 
 
 or, after combining it with (1) and (2), 
 
 ( < 
 
 "D V-W\ f V BL^AxliVI Ll I I LI 
 
 P T, , ,. v " J \ r\ J, r *..v.i a/ \ /q\ 
 
 v 3 )- v v^ 
 
 v v yX 
 
 >'^\ ( N^ 1 1^*'' 
 
 The efficiency will be given by ^^^^ 
 
 ~ Q/i 
 and for determining the cross-sections we have the relations 
 
 Q = Ffly; Q^F^y; Q + Q x = (Ft; + F^Jy = Gwy, 
 
 if G- represents the sectional area of the discharge pipe. 
 
 Assuming, for instance, h = 8 m. [26'25 ft.], 7^ = 3 m. [9'84 ft.], 
 and such dimensions that the velocities v l and w in suction and 
 discharge pipes will be equal to 5 m. [16 '4 ft.], we have 
 
 6-07m. [19-92 ft.], 
 and consequently 
 
 v= tj 2g (b + h-^\ = \/2x 9'81(10'34 + 8 -6'07) = 15'5 m. [50'85 ft.] 
 Hence we obtain 
 
 Q~ p 1*1- u>~ 10-34-6-07 ~4-27 
 
 7 g 
 and accordingly the efficiency will be 
 
 = 0-094. 
 
 ~-~ 
 
 The Gifford Injector, which in modern times has gained 
 such an extended application as a means of feeding boilers, 
 also belongs to the class of apparatus which raise water by the 
 action of a jet. Its distinguishing feature is that the driving 
 fluid is steam, which, by virtue of its living force, not only 
 sucks water from a certain depth, but also forces it into the 
 boiler against the pressure in the latter, the action being equi- 
 valent to raising the water to a height equal to that of a 
 water column corresponding to the excess of pressure in the 
 boiler. The arrangement and action of this apparatus are 
 
270 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 essentially as follows. The pipe A (Fig. 185) communicates 
 with the steam space of the boiler, and, when the cock H is 
 open, admits steam through a series of holes into a pipe BC 
 
 Fig. 185. 
 
 provided with a nozzle C. This nozzle terminates in a chamber 
 D, which acts as a condenser, and is connected by the suction 
 pipe I with the feed-water supply. This chamber is called 
 the combining tube, and has its outlet in a nozzle E, through 
 
vi ADDITIONAL WATER-RAISING MACHINES 271 
 
 which flows the mixture of water drawn through b and that 
 formed by the condensation of the steam that passes through C. 
 Opposite the tube E is a delivery tube Gr, which receives the 
 water issuing from E and guides it through the gradually 
 widening pipe K and the check valve V into the pipe L com- 
 municating with the water space in the boiler. In this way 
 the steam issuing from C drives a continual stream of water 
 into the boiler. The flow of steam can be regulated by a 
 conical spindle 1ST, which can be moved back and forth by turn- 
 ing the crank M. On the other hand, the amount of feed 
 water can be controlled by moving the receiving tube BC by 
 means of a screw 0, thus varying the annular space between 
 the nozzle C and the bottom of the combining tube D. All 
 the water which is not received by the delivery tube G passes 
 into the overflow chamber E, and is discharged by the pipe S. 
 While the apparatus is working normally no water escapes 
 through the pipe S, for overflow occurs only when the apparatus 
 is started, or when the pressure of the steam has fallen below 
 the requisite amount. By the condensation of the steam this 
 feed water is heated, which circumstance, however, involves no 
 loss in the case of boiler feeds, for practically all the heat thus 
 expended is returned to the boiler. But when the injector is 
 employed as a pump or ejector for raising water to a great 
 height, this heat produces no useful effect, and is the cause of 
 the low efficiency of steam jet pumps or ejectors when em- 
 ployed for the latter purpose. As the action of the injector 
 depends largely on the condensation of the steam jet, we see 
 that it will be more uncertain the hotter the feed water. Of 
 late certain improvements have been made in the apparatus, 
 however, permitting the employment of feed water of 60 C. 
 [140 Fahr.] The height of suction attainable is usually 
 less than in piston pumps, for there is always in the com- 
 bining chamber D a pressure corresponding to that of steam 
 of the temperature of the mixture flowing through the chamber. 
 But aside from these defects, which, especially in boiler feeds, 
 are of slight importance, the injector is a most excellent appa- 
 ratus, and is valued for its uniform action and entire absence 
 of mechanical complications. 
 
 In order to determine the action of the injector, approxi- 
 mately, by calculation, let h represent the height of a water 
 
272 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 column corresponding to the excess of pressure (that is, the 
 gauge pressure) of the steam in the boiler, then, for an excess 
 of pressure equal to n atmospheres we have A=10*34?i 
 metres [k =3 3'9n ft.]; in like manner let 7^ represent the 
 height of suction, and k% the distance of the combining 
 chamber below the water in the boiler. Moreover, let Q be 
 the weight of the steam flowing per second through the steam 
 nozzle with a velocity v, and Q 1 the weight of the feed water 
 which flows per second into the condensing chamber with a 
 velocity v lf Now, let p represent the hydraulic pressure in 
 the latter chamber, then we have, for the suction pipe, the 
 equation 
 
 where i represents the coefficient of resistance for the suction 
 pipe. In like manner we have, for the flow of steam, the 
 approximate equation 
 
 v 2 p 
 
 2 (7 it "y 
 
 where <f> is a coefficient less than unity, which takes into 
 account the reduction of steam pressure due to radiation and 
 friction while the steam passes from the boiler to the apparatus, 
 the excess of pressure of the steam before it issues from the 
 nozzle being therefore expressed by fyli ; p represents the 
 relative volume of this steam, or the ratio of the volume of 
 the steam and that of the water from which it is formed ; the 
 living force contained in the steam Q and water Q lt when 
 flowing into the apparatus, is expressed by 
 
 a portion of this energy is absorbed by the impact accom- 
 panying the change of the velocities v and v l into v 2 , and the 
 remainder is expended in forcing the mixture Q + Qi with a 
 velocity v 2 through the nozzle E of the combining chamber. 
 We therefore obtain the relation 
 
vi ADDITIONAL WATER-RAISING MACHINES 273 
 
 and hence the simple equation 
 
 Q(v-v 2 ) = Q 1 (f; 2 -v 1 ) . (3). 
 
 The jet passes from the combining chamber, where the 
 pressure is p, into the delivery tube, whose orifice is subjected 
 to the atmospheric pressure b in the overflow chamber K ; 
 accordingly, if we neglect the resistances at the entrance, we 
 find the velocity w with which the water enters the delivery 
 tube from 
 
 flo 2 P W 2 
 
 * + ?-iT* 
 
 or 
 
 *-*?- , <> 
 
 This velocity w, with which the jet enters the delivery 
 tube, must be capable not only of forcing the water into the 
 boiler i.e. of lifting it from a height b corresponding to the 
 atmospheric pressure, to a height Ji 2 + h + b corresponding to 
 the pressure in the boiler but also of overcoming the resist- 
 ances in the pipe between the delivery tube and the boiler, and 
 discharging the water into the boiler itself with a velocity w^ 
 
 If f represents the coefficient of resistance in the pipe 
 between the delivery tube and the boiler, we must have the 
 equation 
 
 Is t/ 
 
 or, if we make the sectional area of the delivery pipe m times 
 
 w 
 that of the delivery tube, i.e. make w 1 = t we obtain 
 
 '171 
 
 / 
 1 -- = 
 
 V 
 
 1 + (\W 2 
 \ 
 
 /2g 
 
 From this equation we first compute w, and then assuming 
 a certain entrance velocity v : of the water, determine the 
 hydraulic pressure p from (1) ; subsequently we find from (4) 
 the value v 2 , and from (3) the ratio of the weights Q and Q x 
 of the steam and water. 
 
 This ratio -^ = v also gives the temperature t 2 with which 
 
274 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 the water reaches the boiler, for, calling ^ the temperature of 
 the feed water, we have 
 
 or 
 
 EXAMPLE. Determine the dimensions of an injector which is to 
 furnish a hoiler carrying four atmospheres pressure [58*8 Ibs. gauge 
 pressure] with 10 kg. [22 Ibs.] of water per minute, the height of 
 suction being h^ = 2 m. [6*56 ft.], and the injector being h 9 1*5 m. 
 [4*92 ft.] below the water-level of the boilers. 
 
 Let us assume that the feed water flows through the annular 
 space around the steam nozzle with a velocity ^ = 5 m. [16 "4 ft.], 
 and that the coefficient of resistance for the suction pipe is equal to 
 0'2, then the hydraulic pressure in the combining chamber is found 
 from equation (1) to be 
 
 | = 6-A 1 -(l+ i - 1 )^=10-34-2-l-2^g I = 8-8m. [22 '3 ft] 
 
 If we also assume <=0'75, i.e. that the steam flows into the 
 apparatus with an excess of pressure of three atmospheres [44*1 Ibs. 
 gauge pressure], we must take //, = 448 (see Weisbach's Mechanics, 
 vol. ii., Table of Relative Steam Volumes) ; substituting these values 
 in equation (2) we obtain the velocity of efflux of the steam 
 
 v= \/2~x 9-81 x 448 x (3 x 10'34 + 10'34- 6'8) = 551 m. [1807 ft. per sec.] 
 
 Now, taking the sectional area of the delivery pipe at the entrance 
 to the boiler to be ten times that of the delivery tube, i.e. placing 
 m = 1 ; further, assuming the coefficient of resistance for the 
 delivery pipe equal to 2, for the bends equal to 3, and for the clack 
 valve 10, i.e. assuming f = 15, then equation (5) will give us the 
 velocity of the water when it enters the delivery pipe 
 
 - 
 
 19-62 = 31.7 .n, [104 ft.], 
 
 1 ~ToF 
 
 and therefore u\ = 3'17 m. [10*4 ft.] We can now obtain from (4) 
 the velocity v. 2 with which the mixture leaves the combining 
 chamber 
 
 ^2= /v /2x9-8l(|^^-+10-34-6-8J=327m. [107 '3 ft.], 
 and therefore equation (3) gives us the ratio of the weights 
 
vi ADDITIONAL WATER-RAISING MACHINES 275 
 
 The weight of steam used per minute is therefore 
 ~y = 0-535 kg. [l-l81b.] 
 
 The temperature with which the water enters the boiler when 
 the temperature of the feed water is 15 C. [59 F.] is 
 
 640 f 187x15 
 
 1 + 187 
 
 = 467C. [118 F.I 
 
 and consequently the water has been heated about 30 C. [54 F.] 
 The feed water needed per second is given by 
 
 Qi = j^ = 0-167 kg. [0-368 lb.]; 
 
 from this quantity, and the velocities determined above, we can 
 determine the dimensions of the apparatus at various points. The 
 annular area Y l for the suction water will be 
 
 * M * - [0 ' 052 * "! 
 
 the area of the orifice of the combining tube 
 
 and that of the orifice of the delivery tube 
 
 G = Q^i = ^^ = Q-0552 sq. cm. [0 "00856 sq. in.], 
 
 while the feed pipe must have ten times this size, or 
 G 1 = 10G = 0-552 sq. cm. [0'0856 sq. in.] 
 
 As mentioned above, both the steam nozzle and the entrance for the 
 water may be regulated by adjusting screws. 
 
 NOTE. In the above discussion we have neglected the quantity 
 of heat which was transformed into work during the operation of 
 forcing the water into the boiler. With reference to the applica- 
 tion of the mechanical theory of heat to the injector, we refer to 
 Weisbach's Mechanics, vol. ii., Boilers. 
 
 48. Spiral Pumps. Compressed air m'ay also be em- 
 ployed for raising water, the apparatus made use of being then 
 either spiral pumps or the air machine constructed by Holl. 
 The method is, however, seldom employed. 1 The two apparatus 
 
 1 Regarding the use in America of an "air lift pump," constructed by PohU 
 of San Francisco, see Engineering, London, 1894, vol. i. pp. 723 and 754, and 
 {Inland's Technische Rundschau, 1896, pp. 10 and 46. TRANSLATOR'S REMARK. 
 
276 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 just mentioned differ as regards the means introduced for 
 compressing the air, falling water being in Soil's pump the 
 motive agent, while in the spiral pump the air is compressed 
 by revolving a shaft. Like the water screw, the latter consists 
 of a pipe wound spirally around a shaft, only the shaft is not 
 inclined to the horizon, but placed horizontally almost on a 
 level with the surface of the water, and besides the outlet of 
 this pipe does not communicate directly with the outside air, 
 but with the lower end of a vertical pipe into which the lifted 
 water is delivered. In Fig. 186 AB is the shaft, which is con- 
 nected to the delivery pipe MN by means of a stuffing box B, 
 and is revolved by the crank P ; CGL is the thread or 
 worm wound around and firmly secured to the shaft ; it jtf 
 is provided with an enlarged head or inlet at C, and 
 terminates at L in the hollow end of the shaft. 
 
 In order to form a clear idea of the action of this 
 machine, we will assume that the worm is filled with 
 
 Fig. 186. 
 
 water and air occupying alternate arcs, as shown in the figure. 
 At the head CD the air will then have the usual atmospheric 
 pressure, measured by a water column of the height 5, while 
 the air enclosed in the arc EF will have a pressure exceeding b 
 by an amount A x equal to the height of the water arc DE ; 
 further, in the arc GH the pressure will exceed that in EF by 
 the height h of the water column FG, etc. We have, therefore, 
 
 the pressure in EF = b + h 1 
 
 GH = b + h 1 + h 2 
 
 JK = b + h : + h 2 + h s 
 
 
 
 
 
 LM = 
 
 + h. 
 
 4 , etc., 
 
 if the pressures in the remaining water arcs HJ, KL ... be 
 
vi ADDITIONAL WATER-RAISING MACHINES 277 
 
 denoted by h B , li^. ... In order to keep the air enclosed in 
 the space LBM in equilibrium, it is now necessary that a water 
 column of the heiht 
 
 should be contained in the delivery pipe BMN, since the air 
 will then on both sides be acted on by the same force 
 
 When the worm is slowly revolved, the air and water arcs 
 gradually advance to the inlet B of the delivery pipe BMN . . ., 
 and after rising in the latter are finally discharged at the 
 top. If the radius of the worm is gradually reduced 
 from the head C to the end L, so as to correspond to the 
 gradually decreasing arcs of air, and if the head C for 
 every revolution is allowed to take in a water arc and 
 a quantity of air, then the equilibrium of the arcs will 
 not be disturbed while the worm revolves slowly, and 
 consequently there will be a uniform discharge of water 
 
 M 
 
 Fig. 187. 
 
 at the top of the delivery pipe. For instance, in case the 
 shaft AB has revolved half a turn, then the arcs of water 
 and air will have advanced in the direction from A to B through 
 a distance equal to half the pitch of the screw, as shown in 
 Fig. 187. The forward arc KL will then be partially dis- 
 charged into the hollow shaft B and its continuation while the 
 head C has taken in a new supply of water. 
 
 It is quite essential for the proper working of the machine 
 that the head CD (Fig. 188), although scarcely longer than one 
 quarter of the circumference, should be of sufficient capacity to 
 contain a volume of air which will entirely fill the outer half 
 
278 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 coil DE. Then, in the opposite position, shown in Fig. 189, it 
 will, although the inlet apparently has described a semicircle 
 in the water, take in an approximately equal amount of water 
 
 Fig. 188. 
 
 CCi, which, after another half revolution, will fill one half of 
 the outer coil DE, as may be seen in Eig. 188. Eor the 
 fulfilment of this requirement it is necessary that the centre 
 of the shaft should be located somewhat above the water-level 
 
 Fig. 189. 
 
 HE, and that the mean sectional area 7rp 2 of the head should 
 be equal to twice the sectional area Trp 2 of the worm, i.e. we 
 should have 
 
vi ADDITIONAL WATER- RAISING MACHINES 279 
 
 or, in other words, the ratio of the mean. radius p Q of the pipe at 
 the head to the radius p in the remainder of the worm should be 
 
 ^>= N/2 = 1-414, 
 P 
 or about as 7 to 5. 
 
 The rule according to which the radii of the coils are to 
 be decreased from the head end to the delivery pipe may be 
 deduced as follows by the aid of Mariotte's law. Let r be 
 the mean radius BD = BE of the first coil DEF (Fig. 188), 
 and let p be the radius of its cross-section, then the volume of 
 water contained in the arc DE will be 
 
 Vo O O 
 
 Tjyr . TT!\ = rfrf v 
 
 and the height DQ will be 
 
 Denoting by h the height of the water column or the sum 
 of water columns in the delivery pipe, and by 6 that of a column 
 which corresponds to the atmospheric pressure, then the volume 
 of the inner arc, if there are in all n arcs, will be 
 
 and consequently its length 
 
 vp 
 
 b + h ir* b + h 
 
 If we now add to this length that of a water arc I = TTT^ we 
 obtain for. the total length of the coil n 
 
 and hence the required radius 
 
 _ _ b = 
 
 ' ~ 
 
 b + h 72 (b + h) 2' 
 Letting the radii of the coils decrease in arithmetical 
 
280 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 progression from the outside, we shall have as the difference 
 between two successive terms 
 
 r^-rn (b + h) -(b + 111) r^ 
 
 a = = r - 
 
 Ti-1 o + li n- 1 
 
 b + h 2(n-l)' 
 
 and the corresponding progression for the radii of coils will be 
 r p (r 1 -rf),(f 1 -2<J) . . . [;-!-( -1)4 
 
 For the angle ft at the centre, corresponding to the water 
 arc I in the inner coil, we have 
 
 I b + h 
 
 360 
 consequently 
 
 T = 360 
 
 2b + h r n 
 and hence we determine the height of water in this coil 
 
 h n = r n ~ p + r n cos (180 - j3) = r n (\ - cos /?) - p. 
 The mean height of water in all the turns is 
 2b + h 1 - cos 5\ 3 
 
 * 4 
 
 and therefore the total number of coils required is 
 
 2h 
 
 If the shaft makes u revolutions per minute, the quantity 
 of water raised per second will be 
 
 Since the machine not only raises water but also compresses 
 air, the work required will be given by 
 
 L = QAy + Q&y hyp log -|~ = (Ji + b hyp log ^- 
 (See Weisbach's Mechanics, vol. i. 6, chap. 4). 
 
vi ADDITIONAL WATER-RAISING MACHINES 281 
 
 If the air in the delivery pipe mixes uniformly with the 
 water and gradually expands during the ascent, then the 
 delivery height will be increased to 
 
 7 IT. i b + h 
 h + b hyp log -y- ; 
 
 on the other hand, if the air and water remain separated in 
 this pipe, the total delivery height will be equal to the sum of 
 the heights of the air and water columns contained in the 
 latter. Let p 1 be the radius of the delivery pipe, then the 
 length of water column produced in the latter by one water 
 arc will be 
 
 and consequently the number of such columns, as well as 
 columns of air in the delivery pipe, 
 
 Ill 
 
 The air column at the top is compressed by a water column 
 of a length 
 
 and therefore its height is 
 
 b h bh 
 
 h m mb + h ' 
 CM 
 m 
 
 the air column just below it, which is acted on by a water 
 
 column of a length , has a height 
 m 
 
 b h = bh 
 
 b H 
 
 m 
 
 and the next lower air column one of 
 
 bh 
 
 i TTTi e tc. 
 mo + ofi 
 
282 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 Consequently the total delivery height is given by 
 bh bh bh bh 
 
 mb + h mb + 2h mb + 3h ' ' m(b + h) 
 
 L \mb + h mb + 2h mb + 3h ' m(b + h)) J 
 
 If a is the lever arm at which the turning force P acts on 
 the shaft, we have 
 
 b + h\ V- 
 >g ~F 
 
 In the calculation of the quantity of water raised per second 
 
 n u v w 2 2 
 Q = 60 ^60^1, 
 
 no attention has been paid to the helical shape of the worm, 
 since the pitch of the latter, which is of no consequence, can 
 be assumed quite small. If the diameter of pipe in the worm 
 also be taken quite small in comparison with the radius of 
 coils, the axes of the latter might all be placed in the same 
 plane, and thus be made to form a plane spiral. 
 
 NOTE. Spiral pumps have thus far gained but little application, 
 and have been thoroughly discussed only by Eytelwein (see his 
 Handbuch der Mechanik fester Korper und der Hydraulik). On the 
 other hand, machines of this class have been more frequently brought 
 into use as blowing engines. 
 
 EXAMPLE. A spiral pump has a worm and delivery pipe of 
 radii /> = p l = 0'08 m. [3'15 ins.], while the radius of the largest coil 
 is r^= 1 m. [3'28 ft.] Determine the radius of the other coils, the 
 height of delivery, and the turning force required, under the sup- 
 position that the latter acts with a lever arm of 0'5 m. [1'64 ft.], 
 and that the height of water column in the delivery pipe is h = 12 m. 
 [3 9 '3 7 ft.] The maximum volume of water raised per revolution is 
 
 V = n*p*r 1 = 9-87 xO'08 2 x 1 = 0'0632 cub. m. [2'232 cub. ft.] ; 
 
 further, if we place the pressure of the atmosphere equal to b 
 10 '34 m. [33*92 ft.] water column, the radius of the smallest coil 
 will be 
 
 _(25 + a)r 1 _20-68 + 12 
 Tn ~ (& + /02 ~ 10-34 + 12' 
 
 and the angle at the centre of the corresponding arc 
 
vi ADDITIONAL WATER-RAISING MACHINES 283 
 
 The height of the water arc in the largest coil is 
 
 /*! = 2(rj - p) = 2(1 -0-08) = 1-84 m. [6'04 ft], 
 
 while that of the smallest is 
 
 7i. B = r n (l-cos /3) -/> = 0-732(1 + 0-407) -0-08 = 0-95 m. [3'12 ft], 
 
 and consequently the mean height of the water arcs 
 fti + 7t = gv9 = 1-395 ln . [4.58 f t ] 
 
 and the number of coils or threads required 
 
 "nrwr* 1 
 
 Now we have 
 
 b hyp log =1U>-S4 hyp log = 7-96 m. [26'12 ft], 
 
 and therefore, when the air and water mix uniformly, the maximum 
 delivery height will be 
 
 h + b hyp log = 12 + 7'96 = 19-96 m. [65-49 ft], 
 and the required driving force 
 
 = 402k S- [886 ' 41 lbS ' ] 
 
 If the machine is to make twelve revolutions per minute, the 
 quantity of water raised per second will be 
 
 Q = ^ V = J| 0-0632 cub. m. -12-6 litres [0'445 cub. ft], 
 oO ou 
 
 and, neglecting wasteful resistances, such as friction at the journals 
 and in the pipes, we obtain for the theoretical amount of work 
 expended 
 
 L = h + b hyp log - Q? = 19-96x12-6 = 251 '5m. kg. [1819-3 ft. Ibs.]. 
 
 The length of each water arc or water column in the delivery 
 pipe is 
 
 I = 7r r 1 = 3-142 m. [10'31 ft], 
 
 and therefore the number of such columns in the delivery pipe, on 
 an average, 
 
 h 12 
 
284 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 The lengths of the air columns in the delivery pipe are as 
 follows : 
 
 = 0-5231, 
 
 which, added together, give 
 
 2-363^ = 2-363 x 3-142 = 7-44 m. [24-41 ft.], 
 and consequently the total delivery height will be 
 
 12 + 7-44 = 19-44 m. [6378ft.] 
 
 49. Roll's Compressed Air Pump. As has already been 
 
 mentioned, the air which is to 
 raise the water is in this machine 
 compressed by the action of fall- 
 ing water, as in the traditional 
 fountain of Hero. Briefly stated, 
 the function of the apparatus is 
 to transmit the motive power 
 stored in a water column, by 
 means of compressed air, to 
 another body of water in such 
 a manner that when the former 
 column descends the latter will 
 be caused to rise. The essential 
 arrangement of this water rais- 
 ing device will be seen from Fig. 
 190. The air enclosed in the 
 reservoir M and the pipe CD is 
 compressed by the water column 
 in the supply pipe AB, and, by 
 virtue of its expansive action, 
 drives the water from the reser- 
 voir N up into the delivery pipe 
 E, which at its lower end is pro- 
 vided with a valve V opening 
 inward, and discharges the water at the top, at Gr. When the 
 
 Fig. 190. 
 
vi ADDITIONAL WATER-RAISING MACHINES 285 
 
 reservoir M is full of water the cocks B and C are closed, and 
 H and K belonging to the upper reservoir, as well as E and S 
 belonging to the lower one, are opened. The upper reservoir 
 M then empties through H into the common receptacle G, 
 while N is filled from the reservoir 0, the foot valve V at the 
 same time closing automatically, and the air which has col- 
 lected in N escaping through S. When the upper tank M has 
 been emptied and the lower 1ST filled, the cocks H, K, R, and S 
 are closed and B and C opened, and a new operation begins. 
 Holl (in 1753) built a machine of this kind in the mine 
 "Amalia" at Chemnitz (see N. Poda, Kurzgefaszte Beschre'ibung der 
 beim Berglau zu Schemnitz errichteten Mascliinen, Prague, 1771), 
 which required two attendants for opening the cocks and other- 
 wise watching the machine. The first automatic apparatus of 
 the kind is described by Bosivell in 1796 (see Hachette's TraiU 
 dementaire des machines). 
 
 Darwin s water- raising machine consists of a series of air 
 machines forcing water one to the other ; further, in Detrou- 
 villes pump the delivery pipe is replaced by a suction pipe, 
 the water being lifted by suction. The hydraulic air com- 
 pressors which were employed in modern times for driving the 
 rock drills at Mount Cenis, but, owing to their insufficiency, 
 were rapidly replaced by blowing engines, were, in the main, 
 nothing but Holl's machines utilised to compress air in- 
 stead of raising water (see article by F. Eeuleaux in Sckweit- 
 zerischen polyteclm. Zeitschrift, Bd. II., on " Die Durchbohrung 
 des Mont -Cenis"; also Riihlmami, Allgem. Maschinenlehre, 
 Bd. IV.) 
 
 The effect of Noll's or the so-called Hungarian machine 
 may be determined as follows. Let h be the fall, measured 
 from the upper water-level at A to the lowest level in M, 
 further, let A x be the height of delivery, counted from the dis- 
 charge orifice G of the delivery pipe to the high water-level in 
 N ; let the water column corresponding to the atmospheric 
 pressure be denoted by I, the sectional area of the tank M by 
 F, and that of 1ST by F 1? and finally, the height through which 
 the water in M rises or falls during each operation by s, and 
 the corresponding height in N by s^ Then we have 
 
 b + li - s = I + A! + s v or h - s = h^ + s v 
 
286 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 and, according to Mariotte's law, 
 
 b + h + s Fs 
 
 consequently the efficiency of the machine is 
 bh, bh, 
 
 _ - _ __ _ * 
 
 *yj _ _ ~ ^ _ _ ; - _ __ _ _____ . , _ _ 
 
 Fsh (b + h^ + sjh (b + /^ + 5 1 )(A 1 + s + s 
 
 To obtain the maximum efficiency it is necessary to make 
 the variations of the tank levels as small as possible (nearly 
 zero). Then we should have 
 
 and consequently a greater value of 97, the smaller the fall h 
 or the height of delivery h ly though not equal to unity until 
 li = h = zero. Tor greater lifts 77 sinks considerably below 
 unity, as, for instance, for k = h 1 = b we have rj = |-, for 
 h l = h=3b we have 77 = J, etc., and therefore the machine is 
 not suitable for raising water to great elevations. (Compare 
 discussion of " Pneumatic Hoists " in the volume on Hoisting 
 Machinery.) 
 
 50. The Pulsometer. The direct pressure of steam has 
 long been used to force liquids to an elevation, the arrangements 
 devised by So/very for lifting water being thus operated. Steam 
 has also for a long time been employed to produce a vacuum 
 in a vessel by replacing the air contained in the latter, and, 
 by being subsequently condensed, allowing the atmospheric 
 pressure to force the liquid up into the vessel. Such is the 
 arrangement, for instance, made use of in sugar refineries for 
 elevating the sugar juice, and the same plan has more recently 
 been applied to emptying sewers and excavations whose thick 
 contents will not allow of the use of valved pumps. In the 
 pneumatic dredging machines steam is likewise employed to 
 produce a vacuum in a chamber, into which the pasty dredging 
 material is then forced by the atmospheric pressure. 
 
 A modern application of the direct pressure of steam for 
 raising water has been made in the apparatus invented by H. 
 Hall of New York (in 1872), and known by the name of the 
 P'ulsometer. This device is very serviceable for certain purposes, 
 because of its simplicity and the ease with which it may be set 
 
VI 
 
 ADDITIONAL WATER-RAISING MACHINES 
 
 287 
 
 up, although it has the defect common to all devices for raising 
 liquids directly by steam pressure, namely, of excessive steam 
 consumption. The pulsometer works like a pump, exerting a 
 suction as well as a forcing action, the greatest suction height 
 
 Fig. 191. 
 
 Fig. 192. 
 
 being, of course, limited by the height of the water barometer 
 (the actual height attained is about 8 m. [26 ft.]), while the 
 height of delivery depends on the excess of pressure of the 
 steam used. The arrangement of one of Hall's pulaometers is 
 shown in Figs. 191 and 192. The apparatus consists of a 
 
288 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 cast-iron casing divided into two pear-shaped spaces A 1 and A 9 , 
 separated by a partition a ; the lower part of the casing is 
 connected with the suction pipe B and the upper part with the 
 steam pipe C, the latter containing a throttle valve V of 
 ordinary construction, by means of which the supply of steam 
 can be regulated. The chambers A are separated from the 
 suction pipe by two rubber valves S x and S 2 , which alternately 
 open and close like the suction valves of a double-acting pump, 
 so that either the water which is driven up the pipe B by the 
 atmospheric pressure enters the chamber A l through the valve 
 Sj when open, while it is shut off from the other chamber A 2 
 by the valve S 0f or the reverse takes place. The space W 
 between A X and A 2 is connected with the suction pipe B by a 
 side passage, and performs for the latter the functions of an air 
 chamber. 
 
 The chambers A l and A 2 are provided at one side with dis- 
 charge passages a^ and a 9 which lead to a valve chest K, each 
 passage being shut off from this chest by a delivery valve D. 
 These valves also open alternately upward, the water being 
 forced through the valve chest K and up the delivery pipe H. 
 It is evident from this arrangement that to drive the apparatus 
 it is only necessary to alternately establish a vacuum and an 
 excess of pressure in each chamber, in such a manner that 
 while there is a vacuum in one chamber there will be an excess 
 of pressure in the other. Thus, water can be drawn up to 
 one chamber from B and forced out of the other up the delivery 
 pipe H ; the action will be similar to that of a double-acting 
 pump, since the two chambers are comparable to the two sides 
 of the piston in a reciprocating pump. In order to effect 
 automatically this alternate action, a bronze ball E is placed 
 at the point where the two chambers unite at the top ; this 
 ball is pressed first to one side and then to the other, now 
 shutting off the chamber A 1 from the steam pipe and placing 
 A 9 in communication with it, and then the reverse. This 
 motion to and fro is effected automatically by the action of the 
 steam, without the help of any special moving pieces, in the 
 following manner. Let us suppose the apparatus filled with 
 water, say to the height 00, which can be done through an 
 opening in the air chamber W, the suction pipe B being pro- 
 vided with a foot valve to prevent the water from flowing out. 
 
vi ADDITIONAL WATER-RAISING MACHINES 289 
 
 Now, if the throttle valve is opened steam will enter one of 
 the chambers, say A 2 , and will force the water through the 
 passage ., and the delivery valve D 2 to the delivery pipe 
 H. This operation will last till the water level in the chamber 
 A., has fallen below the upper edge of the discharge passage 
 a 2 ; from this instant considerable steam will escape through 
 the latter opening into the delivery pipe, where it will be 
 quickly condensed by the return flow of water. A vacuum 
 will thus be created in the chamber A 9 , in consequence of 
 which the ball E will be thrown over to the right by the 
 greater pressure in the chamber A r This completely shuts 
 off steam from the chamber A 9 , and the vacuum in A 2 now 
 causes water to flow in from the suction pipe B through the 
 opening valve S 2 ; the delivery valve D 2 closes, and thus pre- 
 vents further return of the water delivered to H. Moreover, 
 the shifting of the ball E admits steam to the chamber Aj_ and 
 the operation described above is repeated till the water-level 
 sinks below the upper edge of the discharge passage a^ At 
 this instant there will likewise be a swift condensation of steam, 
 and the ball valve will be pushed over to the left by the excess 
 of pressure in the chamber A . During the process just 
 described care must be taken to allow a small quantity of air 
 to be drawn into the chamber where suction is exerted. For 
 this purpose each chamber is provided at the upper end with a 
 small air valve L lt L 2 opening inward. The suction is thereby 
 somewhat injured, but a means is at the same time provided of 
 regulating the apparatus. For, by adjusting the air valve the 
 quantity of air drawn in can be regulated, and thus the dura- 
 tion of suction controlled. On the other hand, the throttle 
 valve enables us to control the duration of the forcing action, 
 within certain limits, and it is in our power to so regulate the 
 apparatus that the suction in one chamber and the forcing 
 action in the other will be completed in the same space of 
 time. The air entering the chamber during suction also per- 
 forms another function, for in the following forcing period it 
 acts as a non-conducting layer between the water below and 
 the steam above, the assumption being made that when the 
 latter enters it pushes the air before it. In consequence of 
 the slight conducting power of air, this layer greatly diminishes 
 the premature condensation of the steam during the forcing 
 
 U 
 
290 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 period, and when the water-level sinks below the upper edge 
 of the discharge passage, it is always the greater portion of the 
 air drawn in during the preceding suction that first escapes. 
 
 This air also plays an important part in moving the ball 
 valve; its action may be described as follows. When a 
 vacuum has been produced in a chamber by sudden condensa- 
 tion of the steam at the end of the forcing period, water rushes 
 in from the suction .pipe with an acceleration which is greater 
 the more the pressure in the air chamber exceeds that which 
 exists in the chamber A. The accelerated motion of the water 
 only lasts till the pressures in the two spaces are equalised. 
 The water-level in the chamber will not come to rest at this 
 instant, however, for the water will pass beyond the position of 
 equilibrium by virtue of its velocity, and, as it rises, will com- 
 press the air above it. It is the pressure thus brought to bear 
 on the ball, combined with the vacuum in the other chamber, 
 that causes the ball to shift its position. 
 
 Tests of the pulsometer, particularly those made by 
 Sclialteribrand} confirm the remark made above, that consider- 
 able loss of heat is connected with the direct action of steam 
 on the water. In the tests referred to the lifts varied between 
 6 and 10'18 m. [19'68 and 33'39 ft,], -and the consumption 
 of steam per hour, for every horse-power actually expended in 
 raising water, varied between 122 and 235 kg. [268 and 517 
 Ibs.], which consumption greatly exceeds that of good pumps 
 driven by steam engines. 
 
 The results obtained by Eicliler 2 point to a more favour- 
 able performance due to certain improvements made in the 
 pulsometer, the consumption of steam per minute being 1*43 
 kg. [3*15 Ibs.] for every effective horse-power. Pulsometers 
 may therefore be recommended for use in mines where a 
 moderate cost, ease of erection, and occupation of the smallest 
 possible space are prime requirements of the water-raising 
 apparatus, and where the lift does not exceed 40 m. [130 ft.] 
 They are also to be recommended for temporary service, for 
 instance the draining of excavations connected with building 
 operations. So far as simplicity of arrangement and ease of 
 
 1 Schaltenbrand, Der Pulsometer, Berlin, 1877. 
 
 2 C. Eichler, Die Anwendung der Pulsometer auf Adolph-Scliacht bei 
 Reiclienwalde. 
 
vi ADDITIONAL WATER-RAISING MACHINES 291 
 
 setting up are concerned, the pulsometer is all that can be 
 desired, since it not even requires a fixed foundation, but may 
 be set in action while kept suspended from a rope over the 
 excavation. In Schalteribrand's experiments the number of 
 pulsations or single throws of the ball per minute varied 
 between 43 and 128, while in the larger pulsometers tested 
 by Eichler, which operated with a lift of 25 m. [82 ft.], each 
 pulsation required from 4 to 4j seconds. For further data 
 reference must be made to the sources mentioned. 
 
 51. Siphons. Strictly speaking, a siphon is not a water- 
 raising machine, since by its use water is not raised to a 
 higher point, but only transferred across an elevation ; for this 
 reason it is rather to be considered as a water conduit with 
 an upward bend. The small siphons used in every laboratory 
 are too well known to require explanation, and we will there- 
 fore only discuss the apparatus of this class employed on a 
 large scale in hydraulic constructions. In the volume on 
 Hydraulics a short siphon of this kind is described in con- 
 nection with the means employed for regulating the water-level 
 in canals. As another example may be mentioned the so- 
 called periodical springs, as shown in ABCDE (Fig. 193). 
 When the water contained in the cavity W has risen above 
 the highest point D of A 
 
 the siphon-shaped, subter- 
 ranean canal ODE, it will 
 drive the air out of the 
 latter and discharge through 
 E until the water level in 
 W has fallen below the 
 inlet at C. The interrup- 
 tion which then takes place 
 will last as long as the water- 
 level remains below the 
 
 point D ; when the cavity again becomes full of water, which 
 flows in through the cleft AB, up to the level of D, the dis- 
 charge through CDE will begin anew. 
 
 In Fig. 194 is shown the arrangement of a simple siphon 
 employed for draining a marsh or ditch. It consists essen- 
 tially of three cast-iron pipes, AB for the upward, CD for the 
 downward flow, and the horizontal connection BC. A gate 
 
292 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 valve S is placed at the inlet A, a clack valve E at the outlet 
 D, and in the middle pipe BC a short branch pipe K, which 
 may be closed by a plug, is inserted. When the siphon is to 
 be set in operation the valves S and E are closed and water is 
 poured in through K until all the pipes are filled. If now K 
 is closed up tight, S opened and E released, the action of the 
 siphon begins, a continuous stream of water flowing through it 
 in the direction ABCD. 
 
 |This flow is, however, dependent on the fulfilment of two 
 conditions. In the first place, it is necessary that the water- 
 
 .B UK C 
 
 S. 
 
 E 
 
 Fig. 194. 
 
 level H in the feed reservoir AH should be above the discharge 
 orifice E, for the velocity of efflux v at E is 
 
 if p is the coefficient of discharge, and h the head or vertical 
 distance KE of the level H above the orifice E, and conse- 
 quently for h = we have v=0. 
 
 In the second place, the height KO = 7^ of the middle pipe 
 BC or summit K of the siphon above the level H of the feed 
 reservoir must not exceed the height of the water barometer 
 1= 10-34 m. [33'9 ft.], for the pressure of the water at the 
 highest point is & h 1} and thus becomes zero for 7^ = 6. In 
 case 7^ should be greater than b, a vacuum would be created 
 at K which would interrupt the continuity of the current 
 ABCD. 
 
 As the pressure b 7^ at the vertex always falls short 
 of the atmospheric pressure, the air contained in the water 
 supplied gradually separates from the latter at this point, and 
 soon accumulates to such an extent as to impede the dis- 
 charge of the water. It is therefore necessary to remove the 
 
vi ADDITIONAL WATER-RAISING MACHINES 293 
 
 air at intervals; in the simple apparatus shown in Fig. 194 
 this can be done only by closing the apertures S and E and 
 refilling with water at the vertex, while in more perfect con- 
 structions an air pump is used for this purpose. 
 
 A larger and more complete siphon is illustrated in Fig. 
 195. It was constructed by F. Allay? of the Belgian Engineer 
 Corps, for the purpose of furnishing water to the trenches of 
 the fort St. Marie near Antwerp from the river Schelde, which 
 runs close by. The conduit ABCD is made of cast-iron pipes 
 0*2 m. [7*87 ins.] in diameter, and of a total length of 36 m. 
 [118 ft.] At the extremities there are two iron wells AH 
 and DK of rectangular section, located in such a manner that 
 their tops are on the same level HOE, and provided with iron 
 
 Fig. 195. 
 
 gratings. By means of this arrangement the two apertures A 
 and D are always kept under water, and no air can therefore 
 enter the siphon even when, at low tide, the surface W of the 
 Schelde falls below the water-level E in the trench. To pre- 
 vent the water in the siphon from running backwards when 
 this occurs, the discharge orifice at D is provided with a clack 
 valve E opening outward. At low tide the level of the river 
 stands 1'4 m. [4'59 ft.] below that of the trench, while at high 
 tide it rises from 2'7 to 3'2 m. [8'86 to 10'5 ft.] above the 
 latter. To remove the air which accumulates at the vertex C 
 of the siphon, an air chamber S and a suction pump P are 
 made use of, the whole being enclosed in a shelter built of 
 masonry. For military reasons the whole siphon, together 
 with the shelter containing the air pump, is covered with 
 1 See Annales des Traveaux publics de Belgiquc, Tome ix., 1850 and 1851. 
 
294 
 
 MECHANICS OF PUMPING MACHINERY 
 
 CHAP. 
 
 earth. By the cock K, which can be turned by means of 
 gears operated by a crank, the flow of water in the siphon 
 may be either started or discontinued, as may be required. 
 
 The construction of the suction pump used may be seen from 
 the vertical section in Fig. 196. AC A is a receiver attached 
 to the vertex of the siphon and provided with a float S, whose 
 pointer (not visible in the figure) plays up and down in a glass 
 tube and may be observed from without; further, B is the 
 E pump cylinder communicating with the receiver 
 by means of a narrow pipe, K is the plunger, and 
 EDF the hand lever having its fulcrum at D. 
 At V the suction and at W the discharge valve 
 are seen, and at II a small cock by means of 
 which the pump may be shut off from the re- 
 ceiver with a view to preventing leakage of air 
 into the latter. 
 
 When the siphon is to be set in operation, the 
 two reservoirs AH and ED (Fig. 195) must be filled 
 with water and the air pump started ; after a 
 while the siphon becomes filled with water and its 
 action begins. This action will be discontinued 
 when the water-level W sinks below E, but com- 
 mences again as soon as W rises above E. The air 
 accumulating in ACA (Fig. 196) must evidently 
 now and then be removed by the air pump. 
 
 It is especially difficult to maintain a steady 
 flow of water in a siphon when the pipes are not 
 perfectly air-tight. For this reason it is im- 
 possible to keep water flowing for any length 
 of time in a siphon made of wooden pipes unless an air pump 
 be permanently employed to remove the air. When the middle 
 pipe is long there is a good chance for the air to accumulate, 
 and in such cases it is necessary to give a slight pitch to the 
 pipe and locate the air pump at the highest point directly 
 above the branch in which the flow is downward, so as to 
 carry the air bubbles to the receiver and away with the de- 
 scending water. In regard to the results obtained in Saxon 
 mines and in the Hartz with siphons having very long middle 
 pipes, see Jahrbuck fur den Sachs. Berg- und Huttenmann, 
 1843, and Die lerg- und huttenmannische Zeitwwj, 1858. 
 
 Fig. 196. 
 
VI 
 
 ADDITIONAL WATER-RAISING MACHINES 
 
 295 
 
 The theory of the siphon is the same as that applying to the 
 motion of water in ordinary pipe conduits (see vols. i. and ii. 
 of Weisbach's Mechanics. Let h be the head or height EE, 
 (Fig. 197) of the upper water-level H above the lower level, I 
 the total length of pipes in the siphon, d their diameter, v the 
 velocity of discharge, the coefficient of resistance for the 
 
 Fig. 197. 
 
 inlet at A, f the coefficient of friction for the flow of water in 
 the pipes, and ^ and 9 the coefficients of resistance for the 
 bends B and C. We then have 
 
 (1), 
 
 Hence follows the 
 
 if we place l + ?- + f +f l + 
 velocity of the discharging water 
 
 and the quantity discharged per second 
 
 Further, letting \ denote the height KO of the vertex above 
 the high water-level, ^ the length of the pipe leading from 
 the aperture A to the summit, and z the pressure of the water 
 at the summit, we obtain the equation 
 
 (2), 
 
296 MECHANICS OF PUMPING MACHINERY CHAP. 
 
 if for the sake of brevity we place 1 + f + + f -,_ = fa. From 
 
 cv 
 
 (1) and (2) follows 
 
 whence we obtain the pressure z at the summit of the siphon 
 
 . * = &_*,-* .. . . (3). 
 
 9 
 
 When the middle or summit pipe is very long, and con- 
 sequently /j nearly equal to l t we can with sufficient accuracy 
 place < = fa, and then obtain 
 
 z = b-(h + hj). 
 
 To obtain a steady flow, both h and z must be positive, and 
 consequently we must have, according to (3), 
 
 &'*+*.<4 
 
 9 
 
 or, when the middle pipe is very long, 
 
 h + A! < 1) ; 
 
 that is to say, the height KU = h + h\ of the summit above the 
 lowest water-level must be less than that of the water barometer 
 b. For, if only the height KO = 7^ falls short of b, but 
 KU = h -f Aj exceeds it, then, although water will rise to the 
 summit pipe, it will not be supplied as rapidly as it is carried 
 away by the other branch of the siphon. As a consequence, the 
 flow of water will no longer be continuous, unless the discharge 
 orifice D obtains a correspondingly smaller diameter ^ than the 
 pipes. For the latter event let v 1 be the velocity of discharge 
 and the coefficient of resistance for the nozzle, then we have, 
 
 Combined with (2) this equation gives 
 
vi ADDITIONAL WATER-RAISING MACHINES 297 
 
 whence we obtain the pressure z of the water in the summit 
 pipe 
 
 2 = 1)-]^ 
 
 In order that a steady flow shall be maintained, z must be 
 positive, i.e. we must have 
 
 * / /7\4 ^ 
 
 Now, if d l is much smaller than d, we can place 
 
 ^ -. = 0. 
 
 and then obtain as the condition of continuous flow merely 
 that 7^ < b, which relation must always be maintained in order 
 that any flow at all may take place. 
 
 EXAMPLE. A siphon is 100 m. [328 ft.] long and is made of 
 pipes O'l m. [3 '9 4 ins.] in diameter at every point; the coefficient 
 of resistance f = 0'100, the coefficients for the two bends are 
 = f 2 = 0'3, and the fall is h = 3 m. [9'84 ft.] The corresponding 
 velocity of discharge is 
 
 fy/A /2x9-81 x3 
 
 I ~~ V 17 + lOOOf' 
 
 I ' 
 
 or, if we assume f = 0*02, 
 
 /ro.og 
 
 ^-=1 -65m. [5-41 ft.] 
 
 & 
 
 According to Weisbach's Mechanics, vol. i., we should have for 
 v = 1*6 m. f = 0'0219, and therefore a more accurate value would be 
 
 "= \A-lllhr 1 - 58m -[ 5 ' 18ft -] 
 
 Hence we obtain the quantity of water discharged per second 
 Q = 3-14xO'05 2 x 1-58 = 0-0124 cub. m.=12'4 litres [0-438 cub. ft.] 
 
 To produce a steady flow in the siphon, the vertex pipe of which 
 is, say, ^ = 80 m. [2 6 2 '5 ft.] from the inlet, we must have 
 
298 MECHANICS OF PUMPING MACHINERY CHAP, vi 
 
 that is, 
 
 80 
 
 j+ 0-1 + 0-6 
 
 or, in other words, the height h t must not exceed 10 '34 -2 '41 
 = 7'93 m. [26 ft.] Otherwise, the discharge orifice must be corre- 
 spondingly contracted. 
 
 NOTE. A large number of special articles on water-raising 
 machinery may be found in the various technical journals (compare 
 pp. 232 and 233). In addition to the references made in the text 
 to literary sources, we will here mention the following works on the 
 subject : Eytelwein's Handbuch der MechaniJc und Hydraulik, Berlin, 
 1842 ; Gerstner's Handbuch der Mechanik, vols. ii. and iii. ; Kaiser's 
 Handbuch der MechaniJc, Karlsruhe, 1842 ; Langsdorf's Follstandiges 
 System der Maschinenkunde, Leipzig, 1828 ; Jeep, Der Bau der 
 Pumpen und Spritzen, Leipzig, 1891 ; Hagen's Handbuch der Wasw- 
 baukunde, vol. i. ; Hachette, Traite~ eUmentaire des Machines, Paris, 
 1819; Borgnis, TraiU complet de Mdcanique aplique'e ; vol. iv. of 
 Machines hydrauliques, Paris, 1819; Navier, Resumd des Lemons sur 
 I' application de la Mechanique, part ii., Paris, 1838; D'Aubuisson, 
 Trait4 d' Hydraulique, Paris, 1840 ; Morin, Machines et appareils 
 destines a VdUvation des eaux, Paris, 1863. 
 
 Mining pumps are extensively treated of in the large work Die 
 Wasserhaltungsmaschinen, von J. v. Hauer, where a complete list of 
 literature on the subject may also be found. We may further 
 mention Serlo's Bergbaukunde, Bittinger's Erfahrungen im berg- und 
 huttenmannischen Maschinenbau- und Aufbereitungswesen, Biedler's 
 JExcursionsbericht, and Combes, TraiU de V exploration des Mines, T. 
 iii., Paris, 1845. 
 
 With reference to city waterworks information may be obtained 
 from Salbach, Die Dresdener PFasserwerke, Halle, and W'asserwerk der 
 Stadt Halle, 1871, as well as several articles by the same author in 
 Schilling's Journal fur Gasbeleuchtung ; Hydraulica, an historical and 
 descriptive account of the waterworks of London, 1835. In regard 
 to drainage see Trending, Ueber Ent- und Bewasserung von Lcindereien, 
 Zeitschr. des Hannov. Arch- und Ing.-Fer., 1864 and 1865 ; Gevers 
 van Endegeest, Over de droogmaking van het Haarlemer Meer, Amster- 
 dam, 1857 ; in German in Forster's Bauzeitung, 1865. In addition 
 we may mention Elementi di Meccanica e D'idraulica di G. Venturoli, 
 Naples, 1833 ; John Bobison, A System of Mechanical Philosophy, 
 with notes by Brewster, vol. ii., 1822. An extensive list of refer- 
 ences pertaining to the subject is contained in the often cited work> 
 Ruhlmann's Allgemeine Maschinenlehre, vol. iv. 
 
INDEX 
 
 ACCUMULATOR, 222 
 Air-chamber, 87, 106, 218 
 Air-chamber, volume of, 92, 111, 117 
 Air escape, 75 
 Archimedean screw, 29 
 
 BAILING, 4 
 Balance valve, 59 
 Box pump, 76 
 Brakes, 140 
 Bramah pump 234 
 Bucket pump, 47 
 Bucket wheel, 12 
 
 CALCULATIONS for fire engines, 149 
 California pump, 137 
 Cataract, 193 
 Cave's wheel, 14 
 Centrifugal pump, 240 
 Chain pump, 18, 21, 23 
 Chaplet, 18 
 
 Chinese scoop-wheel, 10 
 Coefficient of discharge 82 
 Coefficient of resistance, 123 
 Compensating attachment, 230 
 Compound pumping engine, 201 
 Compressed air pump, 275, 284 
 Cornish pumping engine, 191 
 Crank and fly-wheel pump, 214 
 Cup leather, 65 
 
 DIAGRAM for steam cylinders, 203, 209 
 
 Diagram for water cylinder, 116 
 
 Diaphragm pump, 140 
 
 Direct pumping into mains, 227 
 
 Double-acting pump, 76, 211 
 
 Double pump, 53 
 
 Driving gear for pumps, 155 
 
 Drum-wheel, 14 
 
 Duplex pump, 188 
 
 Dutch scoop, 6 
 
 Dutch water-screw, 37 
 
 EFFECT of chain pump, 23 
 Effect of scoop-wheels, 15 
 
 Efficiency of reciprocating pumps 125 
 Ejector, 265 
 Electric pump, 156 
 
 FIRE engine, 137 
 Flash-wheel, 7 
 
 Forcing action in pumps, 101 
 Frankish scoop- wheel, 11 
 
 GARDEN pump, 137 
 Gaskill pump, 225 
 Gifford's injector, 269 
 
 HALL'S pulsometer, 286 
 Hall's pump, 188 
 Hand pump, 134 
 Hero's fountain, 284 
 Holl's pump, 276, 284 
 Hydraulic ram, 255 
 
 INJECTOR, 265 
 KNOWLES' pump, 186 
 LAFAYE'S wheel, 14 
 MINE pump, 162 
 
 NORIA, 18 
 
 Norton's tube- well, 136 
 
 PAPPENHEIM'S pump, 239 
 
 Paternoster pump, 18 
 
 Perronet's wheel, 14 
 
 Piston, 64 
 
 Piston displacement, 80 
 
 Plunger, 64 
 
 Plunger pump, 49, 51 
 
 Pneumatic dredging machine, 286 
 
 Pohle pump, 275 
 
 Pulsometer, 286 
 
 Pump cylinder, 56 
 
 Pump rod, 159 
 
 Pump valve, 59, 61 
 
300 
 
 MECHANICS OF PUMPING MACHINERY 
 
 QUANTITY of water delivered, 80 
 
 RAM, hydraulic, 255 
 
 Keciprocating pump, 46 
 
 Kefereiices to literature on pumps, 232, 
 
 298 
 
 Kepsold's pump, 238 
 Boot's pump, 239 
 Rosary pump, 18 
 Rotary pump, 234 
 Rotative pumping engine, 214 
 
 SCOOP, 6 
 
 Scoop- wheel, 9 
 
 Separation of water in pumps, 85 
 
 Sinking pump, 184 
 
 Siphon, 291 
 
 Speeds of pumps, 57 
 
 Spiral pump, 275 
 
 Spiral wheel, 14 
 
 Stand pipe, 143, 218 
 
 Steam fire engine, 147 
 
 Steam pump, 180 
 
 Suction, 83, 92 
 Suction and force pump, 73 
 Suction and lift pump, 68 
 Sump, 58 
 
 TELESCOPE pump, 70 
 Throwing, 6 
 Tube well, 136 
 Tympanum, 14 
 
 VALVES, 59 
 Valved piston, 65 
 
 WASTEFUL resistances, 120, 128 
 Water balance, 6 
 
 pressure pump, 166, 173 
 
 screw, 37, 42 
 
 snail, 29 
 
 work's pump, 218 
 Watt's pumping engine, 192 
 Worthington's pump, 187 
 
 high-duty pump, 228 
 
 THE END 
 
 Printed by K. & R. CLARK, LIMITED, Edinburgh 
 
M289318 
 
 THE UNIVERSITY OF CALIFORNIA LIBRARY