Handbook of Pipe C OMPRISING tables, charts and other useful information relating to the subject of the car- rying of fluids and gases by pipe; pipe instal- lation and test data. More particularly that having to do with large diameter steel pipe together with the story of “LOCK-BAR” and Riveted Steel pipe as manufactured by — The East Jersey Pipe Company New York, N. Y. 1920 THE EAST JERSEY PIPE COMPANY New York, N. Y. THE EAST JERSEY PIPE COMPANY General Offices 50 CHURCH STREET, New York, N. Y. Branch Offices UNION ARCADE BUILDING, Pittsburgh, Penna. Works PATERSON, N. J. Associated with T. A. Gillespie Company Engineers and Contractors 50 CHURCH ST., UNION ARCADE BLDG., New York, N. Y. Pittsburgh, Penna. CONTENTS Preface . 11 Materials Specification 13 Class, 13; Process, 13; Chemical and Physical Properties, 13; Analyses, 13; Elongation, 13; Bend Tests, 13; Tests, 15; variations, 15; Inspection, 15. Fabricating 17 Planing and up-setting, 17; Truing, Punching and Beveling, 17; Crimping and rolling, 19; Assembling, 19; Testing, 19; Coating, 21. Weights. ...... .* 25 Notes, 25; Manufacturers’ Standard Practice, 26, 27; Double Lock-Bar Pipe, 25; Double Riveted Steel Pipe, 31. Joints 36 Taper, 36; Flange, 37; Butt Strap, 37; High Pres- sure Flexible, 38; Expansion, 39; Submarine, 40; Flexible Submarine, 41. Fittings 42 Manholes, 42; Straight Saddles, 43; Blow-offs, 44; Socket Saddles, 45; Y-s and Tees, 46; Riveted Spi- rals, 47 ; Reducers, 48. Test Heads 49 Working Pressures 50 Lock-Bar Pipe, 50, 52; Riveted Pipe, 51, 53. Thickness of Pipe 54, 55 Strength of Riveted Joints 56 to 61 Rivets 62 In Circular Seams, 62; Wearing and Bearing Valve, 63, 64. Pipe Data 65 Temperature Stresses, 65; Anchorages, 65; Bends, 68; Superiority of Lock-Bar Pipe, 68; Strength, 68; Physical Tests, 70, 71; Carrying Capacity, 73. Corrosion 74 to 78 Electrolysis 79 to 81 Insulating Wrappings 82, 83 Coating Qualities 84 Bibliography 85 Cost of Pipe 86 Failures of Pipe Lines 87 to 94 Testimony 96 to 113 Hydraulics . 116 to 140 Weir Measurements 141 to 151 Water Power 152 to 158 Water Supply 159 to 167 Testing Lines 168 Installations of Pipe Lines 169 to 172 Distribution of Water 174 to 177 Water Consumption 178 to 184 Useful Data and Formulae 185 to 211 10 PREFACE T HE increased demand for additional water, gas and oil pipe lines throughout the country, to- gether with the apparent need for an engineer- ing exposition of the subject of steel pipe, which will be useful to Engineers, has caused the Company to depart from its usual practice of merely cataloging briefly the merits of the prod- ucts it manufactures and to issue in convenient form, for the man in the field as well as the man in the office, this “Handbook of Pipe.” Certain subjects closely related to the use of pipe have been incorporated herein, and also such general information and engineering data as is germane to the subject. In the compilation of the engineering data, the work of only competent authorities has been resorted to and wherever use has been made of such material, due credit has been given. It is hoped that the “Handbook” may be of as much service to those receiving it, as the measure of pleasure which the Company derives in presenting it, with its compliments. THE EAST JERSEY PIPE COMPANY 11 12 Materials — Specifications FROM RAW MATERIAL TO FINISHED PIPE While to many users, the construction and manufacture of steel pipe is perhaps no secret, yet there are many novel processes involved in the manufacture of “LOCK-BAR” steel pipe which are of peculiar interest and are more or less unknown. It is for this reason that a brief, non-technical description is given herewith. Material Covered Process 1. This Specification covers three classes of material, namely: plates, lock-bars and rivet steel. 2. The steel shall be made by the open-hearth process. Discard 3. A sufficient discard shall be made from each ingot to insure sound material. Chemical 4. (a) The steel shall conform to the following requirements as to and Physical c ^ em i ca i an< 4 physical properties: Properties Properties Considered Plates Lock-Bars Rivet Steel Phosphorus 04 .04 .04 Sulphur .05 .05 045 Yield Point, Min. lb. per sq. in 0.5 T.S. 0.5 T.S. 0.5 T.S. Tensile Strength, Min. lb. per sq. in . 55/65000 40/50000 46/56000 Elongation 1,500,000 1,500,000 1,500,000 * See Section 7. T.S. T.S. T.S. but need not exceed 30 % (b) The yield point shall be determined by the drop of the beam of the testing machine. Ladle Analyses Check Analyses Modifica- tions in Elongation Bend Tests 5. An analysis of each melt of steel shall be made by the manu- facturer to determine the percentages of carbon, manganese, phos- phorus and sulphur. This analysis shall be made from a test ingot taken during the pouring of the melt. The chemical composition thus determined shall conform to the requirements specified in Section 4 (a) and shall be reported to the purchaser or his representative if requested. 6. Analyses may be made by the purchaser from finished material representing each melt. The phosphorus and sulphur content thus determined shall not exceed that specified in Section 4 (a) by more than 25%. 7. (a) For plates over %" in thickness, a deduction of 1 from the percentage of elongation specified in Section 4 (a) shall be made for each increase of Ys" in thickness above . (b) For plates under fa" in thickness, a deduction of 2.5 from the percentage of elongation specified in Section 4 (a) shall be made for each decrease of fa" in thickness below fa". 8. (a) The test specimen for plates shall be bent cold through 180° without cracking on the outside of the bent portion, as follows: For material or under in thickness, flat on itself; for material over YY' in thickness, around a pin the diameter of which is equal to the thickness of the specimen. 13 East Jersey Pipe 14 Inspection and Test — Lock-Bars Test Specimens Number of Tests Permissible Variations Finish Marking Inspection (b) The test specimen for Lock-Bar bars and rivet steel shall be bent cold through 180° flat on itself without cracking on the outside of the bent portion. 9. (a) Tension and bend test specimens shall be taken from rolled steel in the condition in which it comes from the rolls and shall be of the full thickness or diameter of material as rolled except as specified in Paragraph (c). (b) Tension and bend test specimens for plates may be machined to the form and dimensions shown herewith or with both edges parallel. t » ** 1 1 * PARALLEL SECTION ♦ “"notTebs than' 9'"* i 1 — A 1 ♦ -J? T i i ‘r ! v * j i t J ■ • i • k!>!<-T--»K-ETCr* r*- 8- *i H ABOUT 18- * (c) Tension and bend test specimens for lock-bars may be machined to a rectangular section. 10. (a) One tension and one bend test shall be made from each melt; except that if material from one melt differs or more in thickness, one tension and one bend test shall be made from both the thickest and the thinnest material rolled. (b) If any test specimen show's defective machining or develops flaws, it may be discarded and another specimen substituted. (c) If the percentage of elongation of any tension test specimen is less than that specified in Section 4 (a) and any part of the fracture is outside the middle third of the gauge le ngth, as indicated by scribe scratches marked on the specimen before testing, a retest shall be allowed. 11. The thickness of each plate shall not vary under the gauge specified more than 0.01". The over weight shall be within the limits adopted by The Association of American Steel Manufacturers for plates ordered to gauge. 12. The finished material shall be free from injurious defects and shall have a workmanlike finish. 13. The melt number shall be legibly stamped on all finished material, except that rivet steel and Lock-Bar bars may be shipped in securely fastened bundles with the melt number legibly stamped on attached metal tags. The melt number shall be legibly marked, by stamping if practicable, on each test specimen. 14. The Inspector representing the purchaser shall have free entry at all times while work on the contract of the purchaser is being per- formed, to all parts of the manufacturer’s works which concern the manufacture of the material ordered. The manufacturer shall afford the inspector, free of cost, all reasonable facilities to satisfy him that the material is being furnished in accordance with these specifications. All tests (except check analyses) and inspection shall be made at the place of manufacture prior to shipment, unless otherwise specified, and shall be so conducted as not to interfere unnecessarily with the opera- tion of the works. 15 Fabricating “Lock-Bar” 16 Fabricating SPECIFICATIONS FOR COATING See page 21. FABRICATING The steel plates are delivered to the shop where they travel in pro- gressive method of manufacture, from machine to machine, each designed to perform a particular part of the work, in a manner that insures within the machine itself, exact conformity to the specification requirements. PLANING AND UP-SETTING The design of “LOCK-BAR” pipe requires that the longitudinal edges of the plates shall be planed to the proper dimension and the edges up-set to a sufficient degree to form the necessary shoulder for engaging the lock-bar. The steel plate 30 feet long, except where necessary to fit pipe to plan and profile of line, after passing inspection, is delivered to the planing and up -setting machine shown in Figure 3, and each longitudinal edge planed and up-set by a traveling carriage equipped with cutter and up-setting rolls, while being held fixedly in position by a hydraulic clamp running the full length of the machine. Figure 4 shows a close-up of the planing process and Figure 5 the up-setting. When the plate leaves the planing and up-setting machine it is of taper section, to provide for taper joint laying. Before proceeding further the edges are tested by gauging for up-set. TRUING, PUNCHING AND BEVELING The plate is then laid out for truing, punching and beveling on the ends, passing to the combination shearing and punching machine shown in Figure 6. It is trued and then punched by sharp, clean punches and dies, leaving clean holes without burrs. From here it passes to the machine shown in Figure 7, where the ends are bevel-sheared for caulking purposes in laying, the bevel on each end being on opposite sides of the plate. Figure 8 shows a bevel-sheared end as it comes from the machine. 17 18 Testing CRIMPING AND ROLLING The plate passes to the crimping machine shown in Figure 9 where the longitudinal edges are crimped to the proper radius preparatory to rolling. The crimping is done so as to eliminate damage to the up-set edges in the rolls. The plate is next cold rolled as shown in Figure 10, to the radius of the cylinder of the pipe. ASSEMBLING Assembling then begins, in pits arranged to accommodate them, passing through the several stages as follows: Figure 11, applying the lock-bars, previously scarf milled at opposite ends, see Figure 12. Figure 13, lowering mate-half into lock-bar. Figure 14, drawing up the several sections by means of heavy steel clamps. The assembled pipe is now ready for the final fabricating process. It passes into the pressing machine shown in Figure 15, where both lock-bars are pressed down over the up-set edges of the plates by a hydraulic press, exerting a pressure of 350 tons per lineal foot of pipe. TESTING The pipe is now ready for testing. It is conveyed to the hydraulic testing machine, Figure 16, and subjected to a test l-A times the working pressure, undergoing a rigid inspection for leakage over the entire length of the lock-bar joints. 19 20 Protective Coatings COATING PIPE Each length of pipe is thoroughly cleaned, all loose scale, rust, grease and'dirt being removed. It then passes to the coating room where it is heated in the oven shown in Figure 17, to a temperature of from 350° F. to 400° F. Upon removal the pipe is then immersed in a vertical dipping tank, Figure 18, containing a bath of specially prepared coating which is also maintained at the correct temperature for dipping. This bath is deep enough to permit entire vertical submergence of the pipe. It receives a strongly adhering coating, ^ inch or more in thickness, free from blisters and bubbles. This coating after setting will not become soft enough to flow at a temperature of 150° F. nor brittle enough to crack or scale off in freezing temperature. After the pipe sections have been removed from the bath, they are set in vertical position, Figure 19, for cooling and when the coating has become hard are ready for loading. Every engineer having to do with pipe lines knows that they should be protected against corrosion, inside and out. Lock-Bar steel pipe is dipped vertically into a bath of specially pre- pared pipe-coating which embodies all the qualities that long experience in this field has shown to be essential. This coating is proof against the corrosive action of ground water and^of the acids and alkalis of the soil, and has the mechanical properties — toughness, tenacity and pliability — that are required to resist the abrasion and other abuse to which pipe is subject in handling and laying. It is unaffected by the extremes of atmospheric temperature. It will neither crack and crocodile under the cold of winter, nor soften and run under the hottest summer sun. Throughout this entire range of temper- ature its consistency remains practically unchanged, and its sturdy tough- ness is as much in evidence at one extreme as at the other. Such a coating makes for economy in two ways. Not only does it prolong the life of the pipe, but it also prevents the formation of tubercles and the resulting loss in carrying capacity. Taken together with the unobstructed cross-section and the smooth interior surface that are distinctive features of Lock-Bar pipe, this brings about a greater carrying capacity throughout the entire life of the pipe and insures the maximum of pipe-line efficiency. 21 Fabricating 22 Fabricating 23 Fig. 9— CRIMPING EDGE PREPARATORY TO ROLLING 24 Notes on Weights GENERAL NOTES 1 . All weights are figured on the basis of one cubic inch of ^steel weighing 0.2833 pounds. 2. All gross weights are figured on the basis of 30 foot lengths. 3. All weights given are limited to two decimal places. 4. All pipe diameter designations are inside dimensions. 25 26 27 Fabricating Fig. ll Applying The “Lock-Bars” Fig. 14 Drawing up Before Pressing Fig. 13 Assembling Halves Fig. 12 Scarfed “Lock-Bar” 28 Fabricating 29 Weight of “Lock-Bar” Pipe APPROXIMATE FINISHED WEIGHTS PER FOOT OF DOUBLE LOCK-BAR PIPE Including Plate, Lock-bars, Rivets and Coating Dia . 3 // 16 M" 5 ft 16 w 7 tr 16 Vi" Lb. Lb. Lb. Lb. Lb. Lb. 20 " 57.03 74.00 91.30 113.50 137.30 150.80 22 " 61.74 79.62 98.10 122.06 146.70 162.50 24 " 66.46 85.24 104.85 130.60 156.00 174.40 26 " 71.18 91.32 112.47 138.90 165.60 185.37 28 " 75.90 97.23 119.85 147.52 175.20 196.34 30 " 80.64 102.95 126.96 156.47 184.81 207.31 32 " 85.11 108.87 134.38 165.11 195.22 219.27 34 " 89.58 114.98 141.95 173.43 205.88 231.23 36 " 94.06 121.25 149.60 181.40 216.72 243.20 38 " 98.43 127.83 157.82 191.72 226.32 255.87 40 " 102.80 134.19 165.45 200.67 236.94 268.54 42 " 107.18 140.30 172.49 208.29 248.47 281.22 44 " 112.67 147.33 181.57 218.59 259.18 291.69 46 " 118.16 154.36 190.65 228.89 269.89 302.16 48 " 123.67 161.40 199.72 239.20 280.60 312.60 50 " 168.01 206.53 248.13 290.94 324.61 52 " 174.62 213.34 257.06 301.28 336.62 54 " 181.25 220.15 266.00 311.62 348.65 56 " 187.52 228.78 274.97 323.24 361.93 58 " 193.79 237.41 283.94 334.86 375.21 60 " 200.05 246.05 292.90 346.50 388.50 62 " 208.00 254.34 307.28 357.84 401.50 64 " 215.95 262.63 317.60 369.18 414.50 66 " 223.91 270.94 323.86 380.52 427.52 68 " 231.19 280 23 333.83 391.68 439.52 70 " 238.47 289.52 343.80 402.84 451.52 72 " 245.76 298.81 353.76 414.00 463.53 30 Weight of Riveted Pipe APPROXIMATE FINISHED WEIGHTS PER FOOT OF DOUBLE RIVETED STEEL PIPE Including Plate, Rivets and Coating Dia. 3 II 16 M M _5_ll 16 H" _7_ll 16 y 2 " Lb. Lb. Lb. Lb. Lb. Lb. 20" 52.50 70.20 89.20 108.10 125.98 145.10 22" 57.22 76.45 96.55 117.25 136.89 157.70 24" 61.95 82.70 103.90 126.40 147.80 170.30 26" 66.61 88.98 111.15 134.81 158.71 181.61 28" 71.27 95.26 118.40 143.22 169.62 192.92 30" 76.00 101.55 125.65 151.65 180.55 204.25 32" 80.90 107.73 133.23 160.66 191.53 216.00 34" 85.80 113.91 140.81 169.67 202.51 227.75 • 36" 90.70 120.10 148.40 178.70 213.50 239.50 38" 95.88 126.61 155.81 188.50 224.62 252.08 40" 101.06 133.12 163.22 198.30 235.71 264.66 42" 106.25 139.65 170.65 208.05 246.85 277.25 44" 111.03 145.76 179.63 217.50 256.90 289.83 46" 115.81 151.87 188.61 226.45 266.95 302.41 48" 120.60 158.00 197.60 236.40 277.00 315.00 50" 124.99 164.15 205.31 246.08 288.61 326.85 52" 129.38 170.30 213.02 255.76 300.22 338.70 54" 133.75 176.45 220.75 265.45 311.85 350.55 56" 138.46 182.86 228.13 274.56 322.63 363.76 58" 143.17 189.27 235.51 283.67 333.41 374.97 60" 147.90 195.70 242.90 292.80 344.20 387.20 62" 153.70 202.30 251.65 302.28 355.08 399.25 64" 159.50 208.90 260.40 311.76 365.96 411.30 66" 165.25 215.50 269.15 321.25 376.85 423.35 68" 171.10 222.17 277.20 ^ 330.70 387.43 435.70 70" 176.90 228.84 285.25 340.15 398.01 448.05 72" 182.70 235.50 293.30 349.60 408.60 460.40 31 Fig. 16— TESTING “LOCK-BAR” PIPE Protective Coatings Fig. 17 — Oven where Lock-Bar is heated before Dipping in Coating 33 Coating-Pipe Fig. 18 — VERTICALLY DIPPING “LOCK-BAR” PIPE 34 Fig. 19 — “LOCK-BAR” PIPE COOLING AFTER DIPPING Coating Pipe End Joints TAPER JOINT The most successful type of field seam for ordinary installations where the pipe diameter is sufficiently large for riveting and caulking on the inside. The larger end of the pipe fits over the smaller or taper end of the contiguous pipe. After riveting, the joint is caulked both inside and out. All interior seams point in the direction of the line of flow. 36 End Joints Fig. 21 FLANGE JOINT Flanges are cast steel. These joints are suitable for both high and low pressure service. They are furnished riveted onto pipe ends, ready for connecting. BUTT STRAP JOINT Butt Strap Joints are sometimes furnished to meet peculiar condi- tions of installation. i 37 High Pressure Joints Fig. 23 HIGH PRESSURE FLEXIBLE COUPLING (Patented) This joint is suitable for all high pressure work and forms a perfect expansion joint and flexible coupling, permitting deflection of the line at each joint. It consists of rolled steel follower rings, through-bolted, and seated on rubber gaskets against a steel center ring. It has given eminently satisfactory service wherever used. Especially adapted for gas lines. Advantageously used for diameters too small for riveted taper joint. Expansion Joints Fig. 24 EAST JERSEY EXPANSION JOINT (Patented) An expansion joint that functions perfectly under all conditions of service. It stays tight and puts the minimum strain on the line. Two mchorage angles are shown in the above cut at the right of joint. 39 Submarine Joints Fig. 25 SUBMARINE JOINT (Patented) A desirable joint for submerged lines because of the ease with which the joint is assembled and made tight under working conditions. A follower ring seating on a rub- ber gasket and drawn to closed position by large bolts, seals the joint. This design also constitutes an expansion joint and will permit considerable deflection. 40 Flexible Joints Fig. 26 FLEXIBLE SUBMARINE JOINT Occasionally used on submarine lines requiring exceptional deflection. 41 Pipe Fittings— Manholes Type Description Number of holes Diameter of holes Weight A For *" Plate B For \i n and fz" Plate . C For and Plate . D For y 2 " Plate tt" tt" 15 // 16 1A" 215 lbs. 215 lbs. 215 lbs. 215 lbs. STANDARD MANHOLES Conforming to all the requirements of safety and convenience. Manu- factured of cast steel with cast iron cover and arches. It is provided with a strong anchor chain. The Manhole opening is 14" x 16" oval. Made in four types. Fig. 27 Patented Pipe Fittings STRAIGHT SADDLES— 125 lbs. pressure Manufactured of cast steel and amply heavy to stand up under duty without fear of breakage. Provided with flange end and made in the several sizes listed. Diam. D II Length L Thickness t Thickness T < Saddle Flange Straight Flange 0) a >» H No. of Holes Dia. of Holes Q 6 d w No. of Holes Size of Holes 4 4 X X 5 A B C 20 16 12 H *t 1 re 9 7% 8 % 6 4f Vs 1 5y 2 A B C 24 20 16 ii H 1 16 11 9 X 8 . Vs 8 4f % 1 5% A B C 28 24 16 H l* 13 H nx 8 Vs 10 41 % 1 6 A B C 28 24 16 tt 13 . 16 16 14X 12 1 12 51 A IX ex A B C 32 28 20 H tt Its 19 17 12 1 16 51 Vs IX 6 X A B C 36 32 24 tt rf 1* 23 % 21 X 16 IVs 20 61 Vs ■IX m A B C 48 44 36 tt « I*' 27 H 25 20 1% 24 61 Vs IX 6 x A B C 48 44 36 tt tt 32 29 V 20 IX 30 8 l IX 7 A B C 56 32 44 « « i* 38 % 36 28 IX 36 10 IX IX 7 X A B C 64 60 52 8 46 42% 32 IVs 48 10 IX IX 7 X A B C 76 72 64 8 1* 59% 56 44 IX 43 Pipe Fittings -*1 ^ l * - * Type A for 3 ^ and 34 Plate “ B “ A “ % “ “ C « * « 34 “ STANDARD BLOW OFF CONNECTIONS Manufactured of cast steel, with ample metal at all points. Flange joint connection. Built in the several sizes listed. Diam-D II Length L Thickness t Thickness T Radius R Saddle Flange Straight Flange a a >> H No. of Holes Dia. of Holes Q o' d No. of Holes Size of Holes 4" 3" K" Vs" 5" 6" A B c 20 16 12 11 " 16 13 // 16 1 A" 9" 7K" | ! 8 1 X" 6" 4" 4" 1 • K" K" i 1 1" 5K" 7" ^ A B C 24 20 16 A" it" 1 A" 11" j 9)2" 8 Vs" 8" 10" 1" 5K" 8K" A B C 28 24 16 A" A" 1A" 13 K" 11 K" 8 1 K"J 4" K" 1" 6" 8 A" A B C 28 24 16 A" ii" 1A" 16" 14 K" : 12 1" 12" 5" K" 1 Vs" 6 K" 9K" A B C 32 28 20 A" 13// 16 1A" 19" 17" 1 12 1" 16" 5" Vs" IX" 6K" 11" A B C 36 32 24 A" iS" 23 K" 21 K" 16 IK" 20" 1 r Vs" IX" 6K" 13 K" A B C 48 44 36 A" H" l A" 27 K" 25" 20 IK" 24" 5" ’ Vs" IK" 6K" 16" A B C 48 44 36 A" H" 1 A" 32" 29 K" 20 | 1)4" 30" 5" 1 „ 1" IK" 7" 19" A B C 56 32 44 A" if 38 H" 36" 28 36" 6" IX" 1)4" : 7M" 22" A B C 64 60 52 A" H" 1A" 46" 42 %” j 32 48" 7" IX" IK" 7K" 28" A B C 76 ! H" 72 | H" 64 1 A" 59 K" 56" 44 IK" 44 Pipe Fittings STANDARD SOCKET SADDLES New England Water Works Association Standard. Dia, D Length L Thickness t < Saddle Flange Type No. of Holes Dia of Holes A 24 it 6" 4^" W 5V 2 " B 20 it" C 16 irirSB A 28 w 7 m 8" 4 X" X” 5H" B 24 it" C 16 i*" A 28 it" 10" 4 X" X" 6" B 24 it" C 16 1*" A 32 ft" 12" 5X" X" 6 X" B • 28 it" C 20 1*" A 36 iJL" 16" 5 H" Vs" ' 6 X" B 32 M" C 24 i*" A 48 it" 20" 6 Vs" %" 6H" B 44 it" C 36 1*" A 48 it" 2-1" 6 W Vs" 6 H" B 44 it" C 36 1*" A 36 it" 30" 8" 1" 7" B 52 it" . C 44 1*" A 64 it" 36" 10" IX" 7 V" B 60 it" C 52 l*" , A 76 it" 48" 10" i x" 7 X" B 72 it" C * 64 1*" A 16 it" 4" 6M" Vs" 4" B 12 it" C 8 1*" 45 Pipe Fittings Fig. 32 Y’s AND TEES Specials are manufactured to meet all conditions. They are fabricated of steel plate and furnished with either riveted or flanged connections. 46 Pipe Fittings Fig. 34 TYPES OF RIVETED SPECIALS Fig. 35 47 Pipe Fittings Fig. 37 Fig. 36 REDUCERS Riveted Steel Plate Reducers are made up to meet all conditions. 48 Field Test Heads Fig. 38 FIELD TEST HEAD (Patented) The Company is prepared to rent field test apparatus to be used by the field contractor for testing the tightness of pipe joints after riveting in the field. This apparatus comprises a steel plate dished head riveted to a cast iron ring and provided with a rubber gasket. In using this device an angle ring which is provided is bolted inside the pipe end after placing the head and rubber gasket inside the pipe. Two hook bolts and cross members are used to draw the head forward against the rubber gasket forcing it against the angle ring. This test apparatus has been widely used and has given entire satis- faction. It is built with a wide factor of safety. 49 Working Pressures SAFE WORKING PRESSURE FOR LOCK-BAR PIPE Dia. _ 3 _" 16 X" 5 // 16 Vs" 7 n 16 Dia. 3 tt 16 X" 5 // 16 Vi" 7 n 16 Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. 20" 258 344 430 515 601 47" 110 146 183 219 256 21" 246 328 410 490 573 48" 107 143 179 214 250 22" 234 312 391 469 545 49" 105 140 176 210 245 23" 224 298 374 447 522 50" 103 137 172 206 240 24" 215 286 358 430 501 51" 101 135 169 202 236 25" 206 274 344 412 480 52" 99 132 165 198 231 26" 198 264 331 396 462 53" 97 130 162 194 227 27" 191 254 318 382 445 54" 96 127 159 191 223 28" 184 244 308 368 428 55" 94 125 156 188 218 29" 178 236 297 356 414 56" 92 122 153 184 214 30" 172 229 287 344 400 57" 90 120 151 180 211 31" 166 222 # 278 332 388 58" 89 118 148 178 207 32" 161 214 269 322 375 59" 87 116 146 175 204 33" 156 208 260 312 364 60" 86 114 143 172 200 34" 152 202 253 304 354 61" 84 112 141 169 197 35" 147 196 246 294 343 62" 83 111 139 166 194 36" 143 191 239 286 334 63" 82 109 136 164 190 37" 139 185 232 278 324 64" 80 107 134 161 188 38" 136 181 226 271 317 65"- 79 106 132 158 185 39" 132 176 220 264 308 66" 78 104 130 156 182 40" 129 172 215 258 300 67" 77 102 128 153 179 41" 126 167 210 252 393 68"- 76 101 126 151 177 42" 123 163 205 246 286 69" 75 100 125 149 175 43" 120 159 200 240 280 70" 73 98 123 147 171 44" 117 156 195 234 274 71" 72 97 121 145 170 45" 115 152 191 229 268 72" 72 95 119 143 167 46" 112 149 187 224 262 T.S. =55,000 lbs. P x r x f f =4 factor of safety t= r = Radius ^.S. e = 100% eff. of joint t x T.S. P = Safe working pressure P= t = Thickness of plate r x f Safe working pressure for double riveted pipe 70% of pressure given in table. 50 Working Pressures SAFE WORKING PRESSURE FOR RIVETED PIPE 70% Joint Efficiency Dia. 3 t> 16 K" 5 n 16 y%" 7 n 16 Dia. 3 n 16 M" 5 n 16 Vs" 7 // re Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. 20" 180 240 300 360 420 47" 77 103 128 154 180 21" 172 230 287 343 400 48" 75 100 125 150 175 22" 163 218 271 326 380 49" 73 98 122 146 170 23" 156 208 260 312 364 50" 72 96 120 144 168 24" 150 200 250 300 350 51" 71 95 118 142 165 25" 144 192 240 288 336 52" 69 92 115 138 160 26" 139 185 232 278 324 53" 68 91 113 136 158 27" 134 178 223 268 312 54" 67 89 112 134 156 28" 129 171 215 258 300 55" 66 88 110 132 154 29" 125 167 208 250 292 56" 64 85 107 128 149 30" 120 160 200 240 280 57" 63 84 105 126 147 31" 116 155 193 232 270 58" 62 83 103 124 145 32" 113 150 188 226 264 59" 61 81 102 122 142 33" 109 145 182 218 254 60" 60 80 100 120 140 34" 106 141 176 212 247 61" 59 79 98 118 137 35" 103 137 171 206 240 62" 58 77 97 116 135 36" 100 133 167 200 234 63" 57 76 95 114 133 37" 98 130 163 196 228 64" 56 75 93 112 130 38" 95 127 158 190 222 65" 55 73 92 110 128 39" 92 123 153 184 214 66" 54 72 90 108 126 40" 90 120 150 180 210 67" 54 72 90 108 126 41" 88 117 147 176 205 68" 53 71 88 106 123 42" 86 115 143 172 200 69" 52 69 87 104 121 43" 84 112 140 168 196 70" 51 68 85 102 119 44" 82 109 136 164 191 71" 50 67 83 100 117 45" 81 108 135 162 189 72" 50 67 83 100 117 46" 78 104 130 156 182 51 52 Working Pressures 53 54 Thickness of Pipe Steel Pipe, either Riveted or Lock-Bar, within ordinary limits can bo made of any required diameter. In this respect it differs from cast iron pipe, which is commonly made only of the sizes for which the foundries have molds. The diameter should always be specified as the smallest diameter of the smallest ring, where the rings are not all of the same size. Weight of Steel Pipe. The finished weight of steel pipe per lineal foot, either Riveted or Lock-Bar, including the excess weight of plates rolled so that the thinnest points in the plate will be approximately of the nominal thickness, and including the laps, rivets and lock bars, material in the joints and coating, may be found approximately by the formula: Weight in lbs. per foot = (12.5 x diameter x thickness) + 10 lbs. in which diameter and thickness are to be taken in inches. The weight of commonly used sizes are given in the tables on pages 30 and 31 . Thickness of Steel Pipe. (See formula on charts, pages 50 and 54.) Riveted Pipe. The older lines of steel pipe prior to the introduction of Lock-Bar and Welded, were all riveted. Generally riveted pipe is made up of steel plates seven or eight feet wide, which are bent so that one sheet goes entirely around, forming one section of pipe. Four of these sheets are riveted together in the shop, making a length of pipe 28 to 30 feet long. This is tested for tightness and dipped in protective coating, and then shipped to the place where it is to be used. The circular seams may be single riveted. The longitudinal seams which alone are required to carry the stress due to the pressure of the water are at least double riveted, except where the pressure is very low. IN-AND-OUT courses are used, alternate rings being larger and smaller. Taper Lengths are also used in which one end of each pipe is smaller than the other end and will slip into the large end of the next length. Pipes have also been made with all the lengths the same size fastened together with butt straps on the outside, but as this is a more expensive method it has not J)een often used. Continuous Riveting has been used in nearly all American steel pipe lines; that is, each length of pipe in the field has been tightly riveted to its neighbors. Practical experience with this system of construction has been satisfactory. 5 55 Strength of Riveted Joints •Designed and Recommended by Hartford Stm. Blr. Insp. and Ins. Co. SINGLE RIVETED LAP GIRTH JOINTS Designed and Recommended by Hartford Stm. Blr. Insp. and Ins. Co. For use when Rivets of same diameter are used in Girth and Longitudinal Joints. Diameter of Cold Rivet, Inches l A A K H K « X H 1 l* IK lA IK Maximum Diameter of Rivet Hole, Inches A K % « x >8 1 1 A IK Ift IK lA Pitch of Rivets “P,” Inches l X IK IK 2 2 K 2K 2A 2K 3A IK 3K Gauge “A,” Inches A 1* 1 K IK 1A lA 1H 1H itt itt 2 56 Strength of Riveted Joints DOUBLE RIVETED LAP JOINTS T.S.— 55,000 pounds. S.S.— 42,000 pounds. Thickness * of Plate ' Inches Diameter of Cold Rivet Inches Maximum Diameter of Rivet Hole Inches Efficiency in Per Cent Pitch of Rivets “P” Inches Space “A” Inches Gauge “B” Inches A Vi TS 75.0 2^ 1A H A Vi TS 75.0 2 A l A H *A TS Vs 73.6 2Vs l A M A Vs H 71.8 2 TS 1H l A *A TS Vs 72.0 2A 1H H T7 Vs H 71.8 2 rs 1 32 1 A * A Vs H 71.8 2 TS l» 1 A A 72.0 2R 1M IVs A 71.7 2Vs 1^ 1A A if 70.0 2H 1 la I A * A Vs H 70.0 3V 8 IVs Vs 70.0 3Vs IVs in H l 70.3 3Vs 2 i h Vi 1 1A 70.4 3 if 2^ in if 1 1A 70.4 3 if 2 A in A 1 1A 66.9 3 if 2Vs m H 1 1 A 63.4 3 if 2 Ys in Vs l 60.2 3 if 2Vs in U IVs 1A 65.9 3 If 2 n in H lVs 1A 62.9 3 If 2H in H IVs 1A 60.2 3 If 2H in A IVs 1A 57.7 3 If 2ii in n 1 A 1A 60.8 4 if 2H in H IA 1A 58.5 4M 2Vl in M 1 A 1 A 56.3 4H 2H in A 1 A 1A 54.3 4 ii 2H in ^Designed and Recommended by Hartford Stm. Blr. Insp. and Ins. Co. 57 Strength of Riveted, Joints TRIPLE RIVETED LAP JOINTS T.S. — 55,000 pounds. S.S. — 42,000 pounds Thickness of Plate Inches Diameter of Cold Rivet Inches Maximum Diameter of Rivet Hole Inches Efficiency in Per Cent Pitch of Rivets “P” Inches Space “A” Inches Gauge “B” Inches fa X !%■ 78.5 2 X IX Vz fa Vt. fa 78.5 2Vz IX Vz X Vi fa 78.5 2 Y% IVz Vz *X fa Vz 78.2 2% ix tt 'fa fa Vz 78.2 2% IX H fa vz ii 77.0 3 IVz 1* 'fa Vz ft 77.0 3 IX 1 fa Vz » 77.0 3 IVz 1 fa •H X H 75.0 3X 2Vs 1 fa X It 75.0 SX 2Vs Ifa *fa H Vz 75.0 3 X 2X Ifa fa Vs it 75.0 3/4 2% lit Vz H 75.0 3X 2% lit *k Vz H 75.0 3X 2 X lit a X H 75.0 3X 2Vs lit fa Vz It 74.9 3X 2Vs 1 it « 1 1* 75.0 4X 2H lit % » 1 1* 75.0 4X 2« lit 1 1* 72.8 4X 2» lit 1 69.5 4X 2tt lit ft 1 66.4 4X 2H lit X IX l* 71.2 4% 2ft 1ft if 1 Vz l* 68.3 4 X 2H iff ft IVz 1* 65.7 4X 2ft 1ft ft 1 Vz 1* 63.3 4X 2H 1ft K l X 1* 70.8 5 2Vs Iff ft 1 X ifa 68.4 5 2Vs Iff It IX Ifa 66.1 5 2Vs lfi ft IX ifa 63.9 5 2Vs lfi IX ifa 62.0 5 2 Vs lfi ^Designed and Recommended by Hartford Stm. Blr. lnsp. and Ins. Co. 58 59 Strength of Riveted Joints TRIPLE RIVETED BUTT JOINTS SP SP SP /-J \ _ Yi 6 /? ft 77^ 3 y y ^ □ Lv Ct $ /? ft ft 4 1 v % $ h s y z: ir Ji £ < Jr j 7? 5T m 2 ST *~A ST J5 n f - >4 [y. ■f u pu y y. » "i r ft I J 0Q| . N 7^5 y 7—^ ii_ A bv 1 1 V ! r . ^ 7" v y a.c-S < £«S • T3-S S3 <13 „ • j • 3 H . O QJ -P fe a £ P STe/: Sftun 340* & r< W.& / , r /en sw. si m . o%c. e sir. si m . <&,. s/r.o?. &tt. Sim. °)PaUr tyPorL Sls*n. don Ju /tiny (Engineer. 6 10-&/-/- S$Ielo/is, QE/ft/inn. DeC« 29, IS 11 TO WHOM IT MAT CONCERN: I beg, to herewith submit my experience with riveted steel pipe. lines^o^tirCity 1 iIimie ^ C)lis 1 ^ occasion in 1397 to build two large pipe Alter a thorough investigation I was convinced that steel pipe would in eve— «as satisfy the existing conditions, but to please the advocates c* Ca 3 t-iron bids ..ere received lor both steel and cast-iron pipes. The steel was fifty * incnes in aiameter, the cast iron pipe forty-eight inches; Maxima pressure 12o pounds per square inch; Total length of pipe 33, GOC feet, of which 1 5CC feet «ere submerged, crossing the Mississippi River. Lowest Cast-iron bid Lowest steel pipe bid $477, 500. CO 343,726.00 On June 13,1697, contract for steel pipe was awarded to the T. A.Gillespie oaipany of Pittsburgn and the entire Job finished November 9th of the suite l 9 ** “ u ^ 03t r^rxaole record - ana I cannot too highly recommend the T. A. Gillespie Company for doing splenaid .»ork in every respect. I nave several times had occasion- to examine tr.is pipe line ; ersonally botn inside and outside, and found the coatin^ Just as ^coa as new. * The coating used was the so-called Rubber Aspholtum, manufactured by the Assyrian Asphalt Company of Chicago, now the American Asphaltum 1 Rubber Company of Chicago. I determined the use of this particular coating af- ter exhaustive tests and experiments. We have never had a leak on the entire line since the tfater was turned on, fourteen years ago. We have on the other hand a constant trouble with submerged cast iron line of which we have three across the Mississippi, I have also been connected tfitn the 6 to 3 miles long 42 inch steel pipe lines for Seattle, Washington Water Works, with entirely satisfactory re- sulte. I have also put in steel intakes on very exposed places on Lake Superior. The steel mains stood the racket, but the cast iron specials in connection with the work did not. # Taxing tne saving and everything else into consideration, I recommend large steel pipe instead of cast iron pipe. Of course with the .revise mat the steel pipe is properly designed, manufactured and laid. Respectfully, 105 Testimony WATER DEPARTMENT Office of the Chief Engineer WILMINGTON, DEL. Mr. T. A. Gillespie, New York, N. Y. April 8, 1907 Dear Sir: When the duty devolved upon us to decide on the class of pipe to be used for the mains for the extension of the water supply system of this city, the first question was as to the relative merits of steel and cast-iron, and this was decided purely on economic grounds, the saving to the city by the adoption of steel pipe being approximately $40,000 or 25% of the cost of cast-iron pipe. The second question was to decide betw r een the ordinary riveted and the lock-bar pipe. At that time the lock bar pipe was an innovation in this country, and there being no pre- cedent to follow, it was necessary to arrive at a conclusion based solely on our own judg- ment of the mechanical merits of the lock-bar as a serviceable joint, as compared with the usual longitudinal riveted joint, having in mind the unbroken interior surface presented by the lock-bar pipe, with the consequent reduction in friction, and for your satisfaction I am presenting herein the reasons which actuated the final decision to adopt lock-bar pipe, apart from any slight difference in cost between it and riveted pipe. It is an established fact that a riveted joint, such as is usually presented in the all-riveted pipe, under most favorable conditions will not develop over eighty per cent of the tensile strength of the plate, and in consequence of this it becomes necessary to use a plate 25 per cent thicker than would otherwise be required to overcome the weakness of the joint. A satisfactory series of tests having established the fact that the lock-bar pipe, when properly , proportioned, will produce a joint as strong as the plate itself, it becomes apparent that by utilizing this style of joint, one of two results is obtained: either a plate 25 per cent thinner than for riveted pipe may be used, or if the same thickness of metal is retained, 25 per cent greater strength is obtained. Whichever way it may be taken, there is a gain in this point of 25 per cent in favor of the lock-bar joint. Assuming that in the average pipe themstal represents one half of the final cost of the pipe, the economic advantages would, therefore, be 12^ per cent in favor of the lock-bar pipe. Regarding the relative carrying capacity of the lock-bar pipe with its continuously regu- lar inside surface, and the ordinary riveted pipe with inner and outer sheet forming a break in the continuity of the surface every seven feet, it becomes self evident that the frictional resistance of the latter will be largely in excess, and inversely the velocity and carrying capacity of the lock-bar pipe proportionately greater. There is no data extant at this time t to demonstrate conclusively the actual difference in velocity of flow between these two forms of pipe, but in an endeavor to reach a fair conception of this difference, it has been assumed that a variation of .001 in the co-efficient of the Kutter formula would probably result in as close an approximation as circumstances would warrant. Based on this as- sumption, the capacity of the lock-bar pipe, 48 inches in diameter, would be 8 ^percent greater than a riveted pipe of the same diameter. Other sizes would vary proportionately. As a resume, therefore, it may be stated that the lock-bar pipe possesses two points of marked supremacy over riveted pipe, first, an advantage of 12 ^ per cent in the value of the pipe due to its increased strength, and second, 8}4 per cent on account of greater capacity, a total of 21 per cent to the credit of the lock-bar pipe. These deductions may be open to some alterations due to conditions; cost of manufact- ure; size of pipe, and some other minor points, although in general they may be accepted as fair. But making due allowance for some such criticism it may be stated broadly that the net value of the lock -bar pipe is from 15 to 20 per cent greater than riveted pipe of the same diameter and thickness. Respectfully, (Signed) THEODORE A. LEI SEN 106 Testimony BUREAU OF WATER PHILADELPHIA, PA. August, 7, 1908 East Jersey Pipe Company, New York City. Dear Sirs: Complying with your request for an expression of my opinion of the strength, carrying capacity and durability of Lock-Bar Steel Pipe corn* pared with riveted steel pipe, I would say that the City of Philadelphia has completed the installation of some 54,000 feet of 48-inch and 36 inch Lock-Bar Steel Pipe, which was laid under most adverse circumstances, and I believe this pipe to be from twenty to thirty per cent stronger than double riveted pipe made of the same thickness of plate, because double riveted joints, such as are generally used in the manufacture of riveted steel pipe, have from twenty to thirty per cent less tensile strength than the plates thus joined, while tests have shown Lock-Bar joints, when pro- perly made, to have strength equal to the plates themselves. The carrying capacity of Lock-Bar Steel Pipe is probably ten to twelve per cent greater than that of the ordinary in and out or taper sheet, riveted pipe. As far as I know there have been no tests made to deter- mine this point, but in my opinion, the continuously regular inside surface of the Lock-Bar Pipe, with circular joints thirty feet apart, will produce no greater frictional resistance than well coated cast iron pipe with joints every twelve feet. The natural life of Lock-Bar Steel Pipe is undoubtedly greater than that of ordinary riveted steel pipe similarly coated because it is made with smooth, continuous inside surface, with circular joints at thirty feet inter- vals only and few projecting rivets, while riveted steel pipe has circular joints at least every seven and one-half feet and many projecting rivets, and at each the coating, which prolongs the life of steel, is more easily torn or worn off, thus exposing the bare metal to corrosive action, and further on account of the fewer number of joints 'and fewer rivets the leakage of the Lock-Bar Steel Pipe is less than that of the ordinary riveted steel pipe. Yours very truly, (Signed) F. C. DUNLAP, Chief of Bureau. 107 Testimony KANSAS NATURAL GAS COMPANY FARMERS BANK BUILDING Pittsburgh, Pa. December 19, 1911 T. A. Gillespie, President, The T. A. Gillespie Company, 71 Broadway, New York. Dear Sir: In the year 1901, while general manager of the Philadelphia Company of this city, I lifted some twelve miles of 36 inch riveted steel pipe laid by you for that company about the year 1886-1887, from the Murrays ville Field to Pittsburg. I found this pipe in per- fect condition; in fact, the mill bloom was scarcely off the iron in many places, and not a joint of it was lost or a patch used in relaying. None of the lateral seams required caulking. This line had expan- sion joints (a device of your own) about every 175 feet, that is the most perfect working expansion joint that. I ever had any ex- perience with. The line has been in successful operation under a pressure of from 65 lbs. to 100 lbs., has never given any trouble, and is a perfect line today, seemingly as perfect as when first laid. I have knowledge of other steel lines of smaller size that have been in good service from fifteen to twenty years, and are apparently in as good condition today as when first laid. Yours very truly, (Signed) J. C. McDOWELL 108 Testimony MORRIS R.SHERRERO, •1ES C. HALLOCK, Srpartmrnt uf thiblir IBorka BOARD OF STREET AND WATER COMMISSIONERS, NEWARK, N. J. City Haul. ;£ eCa 35 th, 1511 T. A. Gillespie Company 50 Church Street, He* York City, N. Y. Gentlemen: Replying to your inquiry in regard to the condition 0 f the steel p ipe lines wnich your company laid in connection with the new water supply lor the City of Newark, I would advise you that tne first line, laid in 1591, consisting of 21 aides of .45 inch and 5 axles of 56 incn rivet ted steel *ipe, and the second line, laid in 1596, consisting of 5 ax lee of 45 inch and 16 miles of 42 inch rivetted steel pipe, ana the third line, laid in 1904, 7 miles of 60 inch rivetted steel pipe, have all given very satisfactory ser- vice, and have been in continuous use since laid. The only serious difficulty .ve nave had with any of the lines was at one spot, where for a distance of about 1200 feet, two lines of pipe ware laid through a peat swamp, the soil of which was of a peculiar nature ana was back-filled directly against the pipe. , Electrolytic ac- tion has taken place at this point dither from stray currents from tne trolleys, or from local action in the soil. We .vara able to repair 'without difficulty slight leaks dn this section, and have filled around the pipes with gravel. The trouble happened over a year ago, but we nave not been bothered since. • The nature of the swamp was such that it would seem very probable cast-iron pipe would also be affected in a serious manner. You will remember that in asking for bids for the 60 inch pipe line referred to above, we also asked for bids for cast iron pipe, and found that the difference in cost was so great that we could have renewed the steel pipe in 13 or 14 years for the difference, and that our decision was at that time favorable to steel pipe. Considering the difference in first cost, I am satis- fied that it has been of advantage to us to lay steel pipe, and that it would generally be advantageous to use this class of ma- terial for supply pipe lines when the same are well constructed and te iven a tenacious asphalt covering. Very truiy^yours. YZ. w Cnief Engineer 109 Toe East Jersey Pipe Co*, 50 Church Street, New York City, N. Y* Dear Sirs:- Repiying to your letter asking for info rmat ion as to the carrying capacity of lock bar pipe, we beg to hand you the following. We have a line approximately 36,000 feet in length and are pumping into this at the rate of 11,800 U. S. gallons per minute by Venturi Meter. At a point 13,000 feet from the pump station water is drawn at the rate of 2, 333 U. S. gallons per minute, also measured by Venturi Lister. Readings of pressure ,vere taxen with Bristol recording pressure gauges, and the gauges tested by meane of a Croeby gauge tester before and after the 12 hours records* Elevations of gauges were well established. The average friction loss for three hours while conditions were constant in the whole line was 23.27 feet. The figure given in Coffins tables for clean cast-iron pipes under the above conditions is 30.7 feet, and, in our experience the actual friction loss in cast-iron pipes that has been in service a few years is about 5<$ higher than is given in these tables. Hence we estimate that if this line were laid in cat-iron, the friction would be at least 45 feat or 59. 2> more than the observed friction in our steel main. The first section of this main, 12, 00C feet, was laid in 19C7 and 19C3 and the balance in 1909. Diet. WHS Yours truly. MONTREAL WATER & °0WER COMPANY 'AsstT Eng - 110 Preferences PREFERENCES ACCORDED LOCK-BAR PIPE IN COMPETITION WITH OTHER TYPES. The high longitudinal joint efficiency of Lock-Bar Pipe permits the safe utilization of a given thickness of plate against a higher working pres- sure than would be possible for the same plate thickness if incorporated in a pipe of lower joint efficiency. This fact is usually considered by Engineers and is instrumental in effecting considerable saving in plate tonnage, particularly in long supply lines where a gradual but consistent increase of pressure is encountered. The carrying capacity of Lock-Bar Pipe, owing to the smooth interior unobstructed by rivets, is from 10% to 15% greater than that of riveted pipe. This means that in order to carry a given volume of water under s .milar conditions a riveted pipe must be of greater diameter than a Lock- Bar Pipe. By reason of these features Lock-Bar Pipe is usually given prefer- ence for strength when in competition with welded pipe and for both strength and carrying capacity when in competition with riveted pipe. In some instances this is stipulated as a 10% money preference in price on pipe laid. In others the specifications provide that riveted pipe shall be of larger diameter and of greater plate thickness than Lock-Bar Pipe. Ill Testimony Some Steel Pipe Lines Manufactured by the East Jersey Pipe Company Year Location Kind Size in. Length ft. 1891 Newark, N. J Riveted 48 and 36 142,000 1896 Newark, N. J ci 48 and 42 126,000 1897 Paterson, N. J. “ 42 40,000 1899 Seattle, Wash u 42 32,000 1899 Newark, N. J “ 51 47,500 1900 Utica, N. Y . . . “ 96 1,000 1902 Jersey City, N. J . . 72 93,000 1903 Newark, N. J u 60 39,300 1903 Troy, N. Y “ 33 35,300 1903 Schenectady, N. Y u 36 24,000 1904 Astoria, Long Island ci 60 15,000 1905 Pittsburgh, Pa Lock-Bar 30 2,500 1905 Paterson , N. J “ 48 and 42 11,000 1905 Lynchburg, Ya CC 30 15,000 1905 Wilmington, Del “ 48 and 43 20,000 1906 Brooklyn, N. Y Riveted 72 42,300 1906 Honolulu, T. H Lock-Bar 30 8,000 1906 Philadelphia, Pa “ 48 and 36 55,300 1907 Gary, Ind a 36 4,000 1907 Trenton, N. J. . u 48 10,000 1907 Montreal, P. Q . . . ci 36 11,000 1907 Lockport, N. Y. Cl 30 68,500 1907 Vancouver, B. C ci 22 5,000 1908 Michigan City, Ind Cl 30 4,000 1908 Philadelphia, Pa Riveted 132 3,180 1908 Montreal, P. Q Lock-Bar 36 25,000 1908 Springfield, Mass 54 and 42 63,500 1909 Brooklyn, N. Y Cl 72 83,000 1909 Portland, Ore ll 48 to 24 9,600 1910 Brooklyn, N. Y Cl 48 16,200 1910 Ensley, Ala “ 50 8,840 1910 Pittsburgh, Pa Cl 24 5,000 1910 Cuba Cl 36 and 28 1,300 1910 Washington, D. C Cl 30 1,220 1910 Seattle, Wash Cl 32 4,050 1910 Seattle, Wash Lock-Bar 42 to 24 12,300 1910 Portland, Ore “ 52 and 44 128,000 1910 Butte, Mont. “ 42 1,200 1910 New York City, N. Y Cl 48 to 30 1,200 1910 Catskill Aqueduct, N. Y . . . . Riveted 135, 117 and 114 33,000 1911 Catskill Aqueduct, N. Y . . . . Lock-Bar and Riv. 66 17,020 1911 Lakeland, Fla Lock-Bar 20 4,020 1911 Pennsylvania R. R “ 20 7,770 1911 Massena, N. Y 24 1,320 1911 Seattle, Wash “ 42, 40, 36 and 24 16,945 1911 Montreal, P. Q “ 48, 36 and 30 7,300 1911 Denver, Colo Lock-Bar 60 1,200 1911 Marquette, Mich 66 8,000 1912 Chihuahua, Mexico Riveted 102 1,400 1912 Union Bay, B. C Lock-Bar 50 1,320 1912 Rochester, N. Y “ 66 9,254 1912 Ottawa, Ont “ 42 2,400 1912 Omaha, Neb “ 48 10,550 1912 Akron, Ohio “ 36 55,870 1912 Winnipeg, Man “ 36 42,500 1913 Minneapolis, Minn 54, 50 and 48 39,725 112 Testimony Year Location Kind Size in. Length ft. 1913 Montclair, N. J Lock-Bar 24 7,295 1913 Massena, N. Y “ 24 1,200 1913 Utica, N. Y “ 36 1,000 1913 Wilkesbarre, Pa 36 1,335 1913 Schenectady, N. Y U 24 2,420 1913 Kansas City, Mo Riveted 48 1,220 1913 Croghan, N. Y . “ 114 2,555 1914 Schenectady, N. Y Lock-Bar 36 10,500 1914 Essex Junction, Vt Lock-Bar and Riv. 108 and 36 2,440 1914 Rutland, Vt u u u 54 2,750 1914 Winnipeg, Man Lock-Bar 36 24,000 1914 Brooklyn, N. Y “ 66 12,200 1914 Rochester, N. Y U 66 and 48 1,120 1915 Minneapolis, Minn Lock-Bar and Riv. 40 and 48 7,355 1915 Ottawa, Ont Lock-Bar 51 15,000 1916 Seattle, Wash “ 42 1,324 1916 Ottawa, Ont U 51 1,945 1916 Minneapolis, Minn Lock-Bar and Riv. 40 and 48 7,341 1916 Seattle, Wash Lock-Bar 42 1,301 1916 Rochester, N. Y “ 37 50,754 1916 St. Louis, Mo u 36 26,700 1916 Brandon, Vt. “ 36 2,344 1916 Gary, Ind u 36 1,865 1917 Eastman Kodak Co “ 42 7,910 1917 Rochester, N. Y “ 37 42,140 1917 Carnegie Natural Gas Co . . . “ 54, 40, 36 and 30 48,537 1918 Carnegie Natural Gas Co . . . u 40 12,000 1919 Akron, Ohio “ 48 12,000 1919 Jersey City, N. J “ 72 88,000 1920 Elyria, Ohio “ 36 24,500 1920 Port Henry. Vermont “ 36 and 40 3,000 1920 Passaic Water Co u 30 12,300 1920 Salt Lake City, Utah “ 36 1,200 1920 Bayonne, N. J “ 48 44,000 1920 Akron, Ohio “ 48 21,250 1920 Detroit, Michigan 48 21,930 Submarine Pipe Lines 114 Submarine Pipe Lines 115 Fig. 60— TOWING LOCK-BAR PIPE INTO PLACE IN A SUBAQUEOUS LINE. Hydraulics — Water . WATER Water is composed of two gases, hydrogen and oxygen, in the ratio of two volumes of the former to one of the latter. It is never found pure in nature, owing to the readiness with which it absorbs impurities from the air and soil. Water boils under atmospheric pressure (14.7 pounds at sea level) at 212°, passing off as steam. Its greatest density is at 39.1°F., when it weighs 62.425 pounds per cubic foot. Weight of Water per Cubic Foot at Different Temperatures Temper- ature °F Weight per cubic foot, pounds Temper- ature °F Weight per cubic foot, pounds Temper- ature °F Weight per cubic foot, pounds Temper- ature °F Weight per cubic foot, pounds Temper- ature °F Weight per cubic foot, pounds 32 62.42 150 61.18 260 58.55 380 54.36 500 48.7 40 62.42 160 60.98 270 58.26 390 53.94 510 48.1 50 62.41 170 60.77 280 57.96 400 53.5 520 47.6 60 62.37 180 60.55 290 57.65 410 53.0 530 47.0 70 62.31 190 60.32 300 57.33 420 52.6 540 46.3 80 62.23 200 60.12 310 57.00 430 52.2 550 45.6 90 62.13 210 59.88 320 56.66 440 51.7 560 44.9 100 62.02 212 59.83 330 56.30 450 51.2 570 44.1 110 61.89 220 59.63 340 55.94 460 50.7 580 43.3 120 61.74 230 59.37 350 55.57 470 50.2 590 42.6 130 61.56 240 59.11 360 55.18 480 49.7 600 41.8 140 61.37 250 58.83 370 54.78 490 49.2 1 Volume of Water Cent. Fahr. Volume Cent. Fahr. Volume Cent. Fahr. Volume 4° 39.1° 1.00000 35° 95° 1.00586 70° 158° 1.02241 5 41 1.00001 40 104 1.00767 75 167 1.02548 10 50 1.00025 45 113 1.00967 80 176 1.02872 15 59 1.00083 50 122 1.01186 85 185 1.03213 20 68 1.00171 55 131 1.01423 90 194 1 .03570 25 77 1.00286 60 140 1.01678 95 203 1.03943 30 86 1 .00425 65 149 1.01951 100 212 1.04332 116 Water Pressure WATER PRESSURE (From Kent’s Mechanical Engineers’ Pocket Book.) Comparison of Heads of Water in Feet with Pressures in Various Units One foot of water at 39.1° F. One foot of water at 39.1° F. One foot of water at 39.1° F. One foot of water at 39.1° F. One foot of water at 39.1° F. 62.425 pounds per square foot; 0.4335 pound per square inch; 0 . 0295 atmosphere ; 0.8826 inch of mercury at 30° F; ( feet of air at 32° F. and atmospheric 773.3 •< pressure; One pound on the square foot, at 39.1° F. One pound on the square inch, at 39.1° F. One atmosphere of 29.922 inches of mercury One inch of mercury at 32° F One foot of air at 32° F. and 1 atmosphere One foot of average sea- water One foot of water at 62° F One foot of water at 62° F One inch of water at 62° F. = 0 . 5774 ounce One pound of water on the square inch at 62° F One ounce of water on the square inch at 62° F = 0 .01602 foot of water; = 2.307 feet of water; = 33.9 feet of water; = 1 . 133 feet of water; = 0 .001293 foot of water; = 1 .026 feet of pure water; = 62 . 355 pounds per square foot; = 0 .43302 pound per square inch; = 0.036085 pound per square inch; = 2.3094 feet of water; = 1.732 inches of water Pressure of Water Due to Its Weight. The pressure of still water in pounds per square inch against the sides of any pipe, channel, or vessel of any shape whatever is due solely to the “head” or height of the level surface of the water above the point at which the pressure is considered, and is equal to 0.43302 pound per square inch for every foot of head, or 62.355 pounds per square foot for every foot of head (at 62 °F.) The pressure per square inch is equal in all directions, downwards, upwards, or sideways, and is independent of the shape or size of the con- taining vessel. The pressure against a vertical surface, as a retaining-wall, at any point, is in direct ratio to the head above that point, increasing from o at the level surface to a maximum at the bottom. The total pressure against a vertical strip of a unit’s breadth increases as the area of a right-angled triangle whose perpendicular represents the height of the strip and whose base represents the pressure on a unit of surface at the bottom; that is, it increases as the square of the depth. The sum of all the horizontal pressures is represented by the area of the triangle, and the resultant of this sum is equal to this sum exerted at a point one-third of the height from the bottom. (The center of gravity of the area of a triangle is one-third of its height.) The horizontal pressure is the same if the surface is inclined instead of vertical. The amount of pressure on the interior walls of a pipe has no appreciable effect upon the amount of flow. 117 Water Pressure Pressure in Pounds per Square Inch for Different Heads of Water (At 62°F., 1 foot head = 0.433 pound per square inch; 0.433 X 144 = 62,352 pounds per cubic foot.) Head, feet 0 1 2 3 4 5 6 7 8 9 0 0.433 0.866 1.299 1.732 2.165 2.598 3.031 3.464 3.897 10 4.330 4.763 5.196 5.629 6.062 6.495 6.928 7.361 7.794 8.227 20 8.660 9.093 9.526 9.959 10.392 10.825 11.258 11.691 12.124 12.557 30 12.990 13.423 13.856 14.289 14.722 15.155 15.588 16.021 16.454 16.887 40 17.320 17.753 18.186 18.619 19.052 19.485 19.918 20.351 20.784 21.217 50 21.650 22.083 22.516 22.949 23.382 23.815 24.248 24.681 25.114 25.547 60 25.980 26.413 26.846 27.279 27.712 28 . 145 28.578 29.011 29.444 29.877 70 30.310 30.743 31.176 31.609 32.042 32.475 32.908 33.341 33.774 34.207 80 34 . 640 35.073 35.506 35.939 36.372 36.805 37.238 37.671 38.104 38 .537 90 38.970 39.403 39.836 40.269 40 . 702 41.135 41.568 42.001 42.434 42.867 Head in Feet of Water, Corresponding to Pressures in Pounds per Square Inch 1 pound per square inch = 2.30947 feet head; 1 atmosphere = 14.7 pounds per square inch =33.94 feet head.) Pres- sure, lbs. 0 1 2 3 4 5 6 7 8 9 0 2.309 4.619 6.928 9.238 11.547 13.857 16.166 18.476 20.785 10 23.0947 25.404 27.714 30.023 32.333 34.642 36.952 39.261 41.570 43.880 20 46.1894 48.499 50.808 53.118 55.427 57.737 60.046 62.356 64.665 66.975 30 69.2841 71.594 73.903 76.213 78.522 80.831 83.141 85.450 87.760 90.069 40 92.3788 94.688 96.998 99.307 101.62 103.93 106.24 108.55 110.85 113.16 50 115.4735 117.78 120.09 122.40 124.71 127.02 129.33 131.64 133.95 136.26 60 138.5682 140.88 143.19 145.50 147.81 150.12 152.42 154.73 157.04 159.35 70 161.6629 163.97 166.28 168.59 170.90 173.21 175.52 177.83 180.14 182.45 80 184.7576 187.07 189.38 191.69 194.00 196.31 198.61 200.92 203.23 205.54 90 207.8523 210.16 212.47 214.78 217.09 219.40 221.71 224.02 226.33 228 . 64 Ice and Snow. (From Clark.) 1 cubic foot of ice at 32° F. weighs 57.50 pounds; 1 pound of ice at 32° F. 30.067 cubic inches. has a volume of 0.0174 cubic foot = Relative volume of ice to water at 32° F., 1.0855, the expansion in passing into the solid state being 8.55 per cent, i 0.922, water at 62° F., being 1. Specific gravity of ice = ! At high pressures the melting-point of ice is lower than 32° F., being ! at the rate of 0.0133° F. for each additional atmosphere of pressure. Specific heat of ice is 0.504, that of water being 1. 1 cubic foot of fresh snow, according to humidity of atmosphere, weighs 5 pounds to 12 pounds. 1 cubic foot of snow moistened and compacted by rain weighs 15 pounds to 50 pounds (Trau twine). 118 Flow of Water in Pipes Specific Heat of Water (From Marks and Davis’s Steam Tables.) Degrees F. Specific heat Degrees F. Specific heat Degrees F. Specific heat Degrees F. Specific heat Degrees F. Specific heat Degrees F. Specific heat 20 1.0168 120 0.9974 220 1.007 320 1.035 420 1.072 520 1.123 30 1.0098 130 0.9979 230 1.009 330 1.038 430 1.077 530 1.128 40 1.0045 140 0.9986 240 1.012 340 1.041 440 1.082 540 1.134 50 1.0012 150 0.9994 250 1.015 350 1.045 450 1.086 550 1.140 60 0.9990 160 1.0002 260 1.018 360 1.048 460 1.091 560 1.146 70 0.9977 170 1.0010 270 1.021 370 1.052 470 1.096 570 1.152 80 0.9970 180 1.0019 280 1.023 380 1.056 480 1.101 580 1.158 90 0.9967 190 1.0029 290 1.026 390 1.060 490 1.106 590 1 .165 100 0.9967 200 1.0039 300 1.029 400 1.064 500 1.112 600 1.172 110 0.9970 210 1.0050 310 1.032 410 1 .068 510 1.117 Compressibility of Water. Water is very slightly compressible. Its compressibility is from 0.000040 to 0.000051 for one atmosphere, decreasing with increase of temperature. For each foot of pressure, distilled water will be diminished in volume 0.0000015 to 0.0000013. Water is so incompressible that even at a depth of a mile, a cubic foot of water will weigh only about half a pound more than at the surface. FLOW OF WATER IN PIPES The quantity of water discharged through a pipe depends on the head. If the discharge occurs freely into the air, this head is the difference in level between the surface of the water in the reservoir and the center of the discharge end of the pipe; if the lower end of the pipe is submerged, the head is the difference in elevation between the two water levels. The dis- charge for a given diameter depends also upon the length of the pipe, upon the character of its interior surface as to smoothness and upon the number and sharpness of its bends. The head, instead of being an actual distance between levels, may be caused by pressure, as by pumping, in which case the head is calculated as a vertical distance corresponding to the pressure, 1 pound per square inch being equal to 2.309 feet head, or 1 foot head being equal to a pressure of 0.433 pound per square inch. The total head operating to cause flow is divided into three parts: (1) The velocity head, which is the height through which a body must fall in a vacuum to acquire the velocity with which the water flows in the pipe. This is equal to v 2 -f- 2 g, in which v is the velocity in feet per second, and 2 g =64.32; (2) The entry head, which is required to overcome the resistance to entrance to the pipe. With sharp-edged entrance the entry head equals about one-half of the velocity head;with smooth, rounded entrance the entry head is inappreciable; (3) The friction head, due to the frictional resistance to flow in the pipe. 119 Flow of Water 120 Flow of Water in Pipes In ordinary cases of pipes of considerable length the sum of the entry and velocity heads scarcely exceeds one foot; in the case of long pipes with low heads it is so small that it may be neglected. When the flow becomes steady, the pipe is entirely filled throughout its length, and hence the mean velocity at any section is the same as that at the end, when the size is uniform. This velocity is found to decrease as the length of the pipe increases, other things being equal, and becomes very small for great lengths, which shows that nearly all the head has been lost in overcoming the resistances. The length of the pipe is measured along its axis, following all the curves, if there be any. The velocity considered is the mean velocity, which is equal to the discharge divided by the area of the cross section of the pipe. The actual velocities in the cross section are greater than this mean velocity near the center and less than it near the interior surface of the pipe. The object of the discussion of flow in pipes is to enable the discharge which will occur under given conditions to be determined, or to ascertain the proper size which a pipe should have in order to deliver a given dis- charge. The subject cannot, however, be developed with the definiteness which characterizes the flow from orifices and weirs, partly because the condition of the interior surface of the pipe greatly modifies the dis- charge, partly because of the lack of experimental data, and partly on account of defective theoretical knowledge regarding the laws of flow. In orifices and weirs errors of two or three per cent may be regarded as large with careful work; in pipes such errors are common, and are generally exceeded in most practical investigations. It fortunately happens, however, that in most cases of the design of systems of pipes errors of five and ten per cent are not important, although they are of course to be avoided if possible, or, if not avoided, they should occur on the side of safety. Quantity of Water Discharged The quantity of water which flows through a pipe is the product of the area of its cross section and the mean velocity of flow. That is, Q=av, in which Q is the quantity discharged in cubic feet per second, a is the area in square feet and v is the velocity 'in feet per second. For U. S. gallons per second multiply by 7.4805 For U. S. gallons per minute multiply by 448.83 For U. S. gallons per hour multiply by 26929 . 9 For U. S. gallons per 24 hours multiply by 646317. The diagram, page 123, gives the discharge in gallons per minute, when the velocity in the pipe line is known. 121 Flow of Water FIG. 02. INSTALLING A LOCK-BAR PIPE TWIN LINE THROUGH CITY STREETS 122 Quantity of Water Discharged 123 Flow of Water in Pipes Mean Velocity of Flow The velocity of flow, depending as it does to such a great extent upon the condition of the interior surface of the pipe, is difficult to compute. Below are given the formulae most generally accepted. In the solution of any problem a comparison of the results obtained by the use of these formulae is advisable. There are so many conditions affecting the flow of water that all hydraulic formulae give only approximations to accurate results. Approximate Formula (Trau twine). To find the velocity of water discharged from a pipe line, knowing the head, length and inside diameter, use the following formula: v h D L + 54 D’ in which v = approximate mean velocity in feet per second; m — coefficient from table below; D — diameter of pipe in feet; h = total head in feet; L — total length of line in feet. Values of Coefficient “m” Diameter of Pipe m Diameter of Pipe m Feet Inches Feet Inches 0.1 1.2 23 1.5 18 53 0.2 2.4 30 2.0 24 57 0.3 3.6 34 2.5 30 60 0.4 4.8 37 3.0 36 62 0.5 6.0 39 3.5 42 64 0.6 7.2 42 4.0 48 66 0.7 8.4 44 5.0 60 68 0.8 9.6 46 6.0 72 70 0.9 10.8 47 7.0 84 72 1.0 12.0 48 10.0 120 77 The above coefficients are averages deduced from a large number of experiments. In most cases of pipes carefully laid and in fair condition, they should give results within 5 to 10 per cent of the truth. Example : Given the head, h — 50 feet, the length, L — 5280 feet, and the diameter, D= 2 feet; to find the velocity and quantity of discharge. The value of the coefficient m from the table when D = 2 feet is m = 57. 124 Kutter’s Formula Substituting these values in the formula, we get : ^57Ap pX 2 = 57 ^jOO =57X0.136 = 7.752 feet per sec. ''5280+108 '5388 To find the discharge in cubic feet per second, multiply this velocity by the area of cross section of the pipe in square feet. Thus, 3.1416X(1) 2 X7. 752 = 24.35 cubic feet per second. Since there are 7.48 gallons in a cubic foot, the discharge in gallons per second =24.35X7.48 = 182.1. The above formula is only an approximation, since the flow is modified by bends, joints, incrustations, etc. Wrought pipes are smoother than cast-iron ones, thereby presenting less friction and less encouragement for deposits; and, being in longer lengths, the number of joints is reduced, thus lessening the undesirable effects of eddy currents. Kutter’s Formula. This formula, although originally designed for open channels, can be used in the case of long pipes with low heads. It is the joint production of two eminent Swiss engineers, E. Ganguillet and W. R. Kutter, and is, properly speaking, a formula for finding the coefficient C in the well-known Chezy formula: v=C xrs, in which y = mean velocity in feet per second; r=mean hydraulic radius in feet; s = slope = head -f - length. The mean hydraulic radius is the area of wet cross-section divided by the wet perimeter, which for pipes running full, or exactly half full, is equal to one-quarter of the diameter. According to Kutter the value of this coefficient C is 0.00281 1.811 41.6+ + (j _ s n / 0.0028R n 1+ 4.16+ ) X— V 5 / vr in which s is the slope, r is the mean hydraulic radius in feet and n is the “coefficient of roughness.” The value of n varies from .010 for very smooth pipes to .015 for pipes in a very poor condition. For ordinary wrought pipe .012 can be used. For clean steel riveted pipe .015 can be used. The following table gives values of the coefficient C as obtained by Kutter’s formula for different slopes, hydraulic radii and degrees of rough- ness. Darcy 1 s Formula Table of Coefficient “G” Coeffi- cient .1 .15 .2 .3 .4 .6 .8 1.0 1.5 2.0 104 116 126 138 148 157 166 172 183 190 199 89 101 110 120 129 140 148 154 164 170 179 78 90 97 107 115 126 133 138 148 154 162 69 80 87 96 104 113 121 125 135 141 149 62 71 78 87 94 103 110 115 124 130 138 50 59 65 73 79 87 93 98 106 112 119 43 50 54 62 68 75 81 85 93 98 105 Hydraulic radius in r feet Slope s = . 0004 .009 .010 .011 .012 .013 .015 .017 .009 .010 .011 .012 .013 .015 .017 Slope s = .0010 110 121 129 141 150 161 169 175 184 191 199 94 105 113 124 131 142 150 155 165 171 179 83 92 99 109 117 127 134 139 149 155 163 73 82 89 98 105 115 122 127 136 142 149 65 74 81 89 96 104 111 116 124 130 138 54 61 66 74 80 88 94 99 108 112 119 45 51 57 63 69 76 82 86 93 98 105 .009 .010 .011 .012 .013 .015 .017 Slope s = .0100 no 122 130 143 151 162 170 175 185 191 95 105 114 125 133 143 151 156 165 171 83 93 100 111 119 129 135 141 149 155 74 83 90 100 107 116 123 128 136 142 66 75 81 90 98 106 112 117 125 130 54 62 67 . 76 82 90 95 99 107 112 46 52 57 64 70 77 82 87 94 99 199 179 162 149 138 119 105 For slopes steeper than .01 per unit of length, =52.8 feet per mile, C remains practically the same as at that slope. But the velocity (being CX Vrs) of course continues to increase as the slope becomes steeper. Darcy’s Formula. The simplest form of Darcy’s formula is Cv 2 = Ds, in which v is the velocity in feet per second, D is the diameter of the pipe in feet, s is the slope and C is a coefficient, varying with the diameter and roughness of the pipe. For cast-iron and wrought pipes of the same roughness, the values of C are given below. For rough pipe Darcy doubled the coefficient. 126 Williams and Hazen’s Formula Values of “C” in Darcy’s Formula Diameter, inches Rough pipe Smooth pipe 3 0.00080 0.00040 4 0.00076 0.00038 6 0.00072 0.00036 8 0.00068 0.00034 10 0.00066 0.00033 12 0.00066 0.00033 14 0.00065 0.000325 16 0.00064 0.00032 24 0.00064 0.00032 30 0.00063 0.000315 36 0.00062 0.00031 48 0.00062 0.00031 Williams am! Hazen’s Exponential Formula. From Chezy’s formula, v—C^rs } it would appear that the velocity varies as the square root of the head; this is not true, however, for C is not a constant, but a variable depending upon the roughness of the pipe and upon the hydraulic radius and the slope. Williams, and Hazen as a result of a study of the best records of experiments and plotting them on logarithmic ruled paper, ound an exponential formula t;=CV 0 ' 63 s 0<54 , in which the coefficient C is practically independent of the diameter and the slope, and varies only with the condition of the surface. In order to equalize the numerical value of C to that of the C in the Chezy formula, at a slope of 0.001, they added the factor 0.001- 004 to the formula, so that the working formula of Williams and Hazen is v =Cr°- 63 s°- 54 0.001— 004 . The value of C varies to a great extent, depending on the condition of the interior of the pipe. A fair value for iron or steel pipe is (7 = 100. Computations of the exponential formula are made by logarithms or by the Williams-Hazen hydraulic slide rule. 12 ? 128 Lock-Bar Pipe 129 ■ n ... . . i . l i l .. . i i i ■ i ■ . i Water Hammer Hydraulic Grade-line. In a straight tube of uniform diameter throughout, running full and discharging freely into the air, the hydraulic grade-line is a straight line drawn from the discharge end to a point im- mediately over the entry end of the pipe, and at a depth below the surface equal to the entry and velocity heads (Trautwine). In a pipe leading from a reservoir, no part of its length should be above the hydraulic grade-line. Air-bound Pipes. A pipe is said to be air-bound when, in conse- quence of air being entrapped at the high points of vertical curves in the line, water will not flow out of the pipe, although the supply is higher than the outlet. The remedy is to provide cocks or valves at the high points, through which the air may be discharged. The valve may be made auto- matic by means of a float. Water Hammer. When a valve in a pipe is closed while the water is flowing, the velocity of the water behind the valve is retarded and a dynamic pressure is produced. When the valve is closed quickly this dynamic pressure may be much greater than that due to the static pressure, and it is then called “water hammer” or “water ram.” This action is ^ dangerous and causes in many cases fracture of the pipe. It is provided against by arrangements which prevent a rapid closing of the valve. The formulae for the pressure produced by this shock are Iv p = 0.027 po + pi, (1) t p = 63v - po + pi, (2) where po =the static pressure when there is no flow, pi =the static pressure when the flow is in progress, p=the maximum dynamic pressure due to the water hammer in excess over the pressure po, v = the velocity in ieet \ per second, 1= length of pipe back from the valve in feet, and t- time of closing of valve in seconds. The pressures in the formulae are expressed in pounds per square inch. Formula (1) is to be used when t is greater than 0.000428 l and formula (2) when t is equal to or less than this. From the first of these formulae the value of t when p — o is found to be t = 0.027 -A- > po-pl which is the time of valve closing in order that there may be no water hammer. To prevent the effects of water hammer, it is customary to arrange valves so that they cannot be closed very quickly, and the last formula furnishes the means of estimating the time required in order that no excess of dynamic pressure over the static pressure po may occur. Long Pipes Formulas for Long Pipes The Chezy Formula. If v is the velocity in the pipe, C a coefficient dependent upon roughness, density, velocity, and diameter, r the Hydraulic, Radius, namely the cross-sectional area divided by the wetted perimeter, hf the frictional loss of head in a length L, and if hf/L be designated by s the inclination or slope, then v-C^rhfjL or v=C^rs in which for new pipes C ranges from 95 to 152 and for old pipes from 60 to 120, the value increasing both with the diameter and the velocity, as shown in the following tables. Values of “C” in Chezy Formula for Cast-iron Pipes Velocities in feet per second of pipe, inches For new pipes For old pipes 1 3 6 10 1 3 6 10 3 95 98 100 102 63 68 71 73 6 96 101 104 106 69 74 77 79 9 98 105 109 112 73 87 80 84 12 100 108 112 117 77 82 85 88 15 102 110 117 122 81 86 89 91 18 105 112 119 125 86 91 94 97 24 111 120 '*126 131 92 98 101 104 30 118 126 .131 136 98 103 106 109 36 124 131 136 140 103 108 111 114 42 130 136 140 144 105 111 114 117 48 135 141 145 148 106 112 115 118 60 142 147 150 152 For steel riveted pipes see next page. Chezy ’s formula is also used for conduits and streams by the coefficient C for such cases is generally ex- pressed in terms of r and s Darcy’s Formula. The original form of Darcy’s equation was rs — av+bv 2 , where a and b were coefficients. This Darcy later reduced to rs = Cv 2 , where C = ci+C2/r. where ci and C2 are constants. For new cast-iron and for wrought-iron pipes of the same roughness, Darcy’s values of these 131 Flow in Pipes and Channels Values of “C” in Chezy Formula for Steel Riveted Pipes Diameter of pipes, inches Velocity in ft. per second 1 3 5 10 3 81 86 89 92 11 92 102 107 115 11 93 99 102 105 15 109 112 114 117 38 113 113 113 113 42 102 106 108 111 48 105 105 105 105 72 110 110 111 111 72 93 101 105 110 103 114 109 106 104 constants are ci = 0.0000773 reduces to &/ =0.00000647 - 1 - 2 D + 1 l tk D r and C 2 = 0.00000162. The formula then u = 394 yj_ D Vrs 12D+1 where D is the diameter of the pipe in feet. For rough pipe Darcy reduced the velocity one-half. Darcy’s formula may be transposed to CV 2 =Ds, in which case C has an average value of 0.00032 for clean pipes of diameters from 8 to 48 inches inclusive, the variation being only 3% from the mean for all except the 8-inch. The table on page 127 gives more accurate values of C for Darcy’s formula in the last form. Fanning’s formula for flow in pipes is or v ^\[2gDhf hs ~ D2g or v ~ where / is a coefficient which ranges from 0.0071 to 0.0028 for new pipes and from 0.0152 to 0.00046 for old ones, the value decreasing as diameter and velocity increase. The other notation is the same as that at the beginning of this article. Values of / in Fanning’s Formula for Cast-iron Pipes Velocity in feet per second of pipe, inches For new pipes For old pipes 1 3 6 10 1 3 6 10 3 .0071 .0067 .0064 .0062 .0152 .0139 .0128 .0122 6 .007 .0063 .006 .0057 .0135 .0117 .0108 .0103 9 .0067 .0058 .0055 .0051 .0122 .0105 .010 .0092 12 .0064 .0056 .0051 .0048 .0108 .0096 .0089 .0084 15 .0062 .0053 .0048 .0043 .0099 .0087 .0081 .0078 18 .0058 .0051 .0045 0041 .0087 .0078 .0073 .0069 24 .0053 .0045 0040 0037 0076 0067 .0063 .0060 30 0046 .0040 .0037 .0035 .0067 .0061 .0057 .0055 36 .0042 .0037 .0035 .0033 .0061 .0056 .0052 .0050 42 .0038 .0035 .0033 .0031 .0058 .0052 .005 .0048 48 60 .0036 .0032 .003 .0030 .0031 .0029 .0029 .0028 .0057 .0051 .0049 .0046 132 Long Pipes Tables for Long Pipes are given on the three following pages. The friction factors 4/ used in computing them differ slightly from those at the foot of the preceeding page and are the same as those given in “Merriman’s Treatise on Hydraulics.” These tables apply to new, clean, straight cast-iron and wrought-iron pipes, either smooth or coated with coal tar, and laid with close joints. A pipe is said to be long when its length is such that the error in computing v by the last formula does not exceed five percent; this will usually be the case when the length of the pipe is greater than 1000 diameters. The discharges given in the tables are accurate in the last figure for the given velocities. Thus for a velocity of 3.4 ft. per sec. the discharges for pipes 6 and 16 in. in diameter are 40.1 and 285 cu. ft. per min. The friction head, given in the second column under each size of pipe, is however liable to an error of one or two units in the second figure; thqs for 3.4 ft. per sec., in the 6-inch pipe the head 0.88 per 100 ft. may actually range from 0.86 to 0.90 for new, clean pipes. Velocities and Discharges for a given pipe may be found from the tables when the friction head is known. For example, let a pipe 3500 ft. long and 6 in. in diameter have a total head of 37.8 ft. Here the friction head per 100 ft. is 100X378/3500=1.08, whence from the table velocity =3.8 ft. per sec., and discharge =44.8 cu. ft. per min. Again, let an 8 -in. pipe 6075 ft. long be under a head of 112.5 ft. then friction head per 100 ft. is lOOx- 112.5/6075 = 1.85, whence velocity =6.1 ft. per sec., and discharge = 199 cu. ft. per sec. These are for new, clean, straight iron pipes. Curves influence results but little unless they are very sharp. For Old Pipes the actual heads should be multiplied by the following numbers before using the table to obtain velocities and discharges: For diameter, 3 6 12 16 24 30 36 in. Multiplier 0.50 0.55 0.60 0.62 0.64 0.65 0.66 For example, let an old pipe 3500 ft. long and 6 in. diameter be under an actual head of 37.8 ft. or 1.08 ft. per 100 ft; the true friction head is 0.55X1.08 =0.59 ft. per 100 ft., whence from the table velocity =2.8 ft. per sec. and discharge =33 cu. ft. per sec. Similarly , for given velocities the true friction heads are found approximately by multiplying the tabular values by the following numbers: For diameter, 3 6 12 16 24 30 36 in. Multiplier 2.00 1.81 1.67 1.61 1.56 1.54 1.52 For example, for a velocity of 60 ft. per sec. the friction head in an old pipe of 12 in. diameter is 1.87 instead of 1.12 ft. per 100 ft. The term old pipe is a vague one, and refers to the amount of corrosion and incrustation rather than to the actual life in years. The Required Diameter for a pipe to furnish a given discharge under a given head may also be roughly found from the tables. For example, to find diameter to furnish 100 cu. ft. min. under a head of 1.2 ft. per 100 ft: for a new, clean pipe the tables give 8 inches as required diameter, for an old pipe, assume multiplier as 0.5, then head becomes, 0.60 ft. per 100 ft. and the table shows that a 10-in. pipe is somewhat too large. The formula for computing the diameter of a long pipe is: D =0.479 (4 flcpjhyti), in which q = discharge in. cu. ft. per min., h =head in ft., I = length of pipe in ft. D = diameter of pipe in ft., and a rough mean value of / being taken as 0.005 for new pipe. After D is computed the velocity is found by »=q/^ 7 rD 2 and thus a better value of / may be obtained from the table at foot of page preceding. Then a new diameter may be re-computed if the change in / seems to warrant it. For example, to find the diameter of a new pipe to deliver 67 cu. ft. per sec. under a head of 24 ft. its length being 4500 ft. Using 4/ as 0.020, the formula gives D =3.35 ft., whence v =6.6 ft. per sec. Then from the table at foot of preceding page a closer value of / is found to be 0.0061, or 4/ =0.025. A second computation now gives D =3.52 ft. so that a 42-inch pipe should be used. With the same data the rough value of 4/ for an old pipe is 0.035 and D is about 48 inches. 133 Exponential Formula for Pipes Kut ter. The Kutter formula was designed for open channels and will be treated under that head. It is sometimes used for pipes, but the results from it, since the coefficients, like those of the Chezy and Fanning formulas, change with the velocity in the same pipe, are usually erroneous, except for a very small range of velocity. For this reason it is not to be recommended for general use in computations for pipes. Exponential Formula for Pipes One form of an exponential formula for flow of water in pipes is hf=KvNL/D 1 25 where the notation is the same as that at beginning of page 135, but where the coefficients K and N may vary with the kind and condition of the pipe. To avoid zeros in the coeffi- cient a unit length of 1000 feet may be taken, when the formula becomes hr KvN n 1 - 25 iooo in which N has a mean value of 1.87 and K ranges from 0 28 to 0.48 with an average value of 0.38 for ordinarily clean pipes. For rough or tubercuJated pipes K may become as high as 0.70. The advantage of the exponential formula is that the coefficient for the same pipe is nearly constant and, if the exponent, its range being from 1.70 to 2. 00, be properly selec- ted, absolutely so, and the variation in all cases is much less than with other formulas, so that with a few average coefficients for different classes of channels, all hydraulic flow problems may be solved with reasonable accuracy without reference to any tables of coeffi- cients. The foregoing formula with the coefficient 0.38 may be expected to give results within 20 % of accuracy for any pipes likely to be encountered which have diameters from one inch to fifteen feet, except those extremely tuberculated, and with velocities from 1 foot to 20 feet per second. For ordinary cast-iron or riveted pipe with any diameter and velocity, the results may be expected to be within 6 % of accuracy. The exponential formula is derived from experiment in the following manner: Any plane curve passing through the origin of coordinates can be represented by an equation of the form y = mxN, in which m and N may be either constant or variable. If the curve be one of single curvature such that the change of inclination of its tangents either contin- uously increases or continuously decreases, both m and N become constants. All curves which are loci of equations expressing the relation between velocity and loss of head in flowing water are of this latter class, and consequently hf=mvN is a general expression for the loss of head in either a pipe or an open channel. If for any pipe line the values of m and N be determined, the equation of flow in that line is established. Expressing the above equation for logarithmic computation, it becomes log hf = log m -r-Mog V and considering the logarithms as mere quantities, this is at once seen to be the equation of a straight line in which log m is the intercept on the hf axis and N is the tangent of the angle which the line makes with the v axis. Both m and N may be found by determining two points in the line representing the plottings of the logarithms. If it be desired to draw the straight line which most nearly coincides with a number of points, it must pass through their center of gravity and also through the centers of gravity of the two groups into whicn the center of gravity of the whole divides them. Having the last two points, the equation of the line is readily determined. The following example will serve to illustrate the process (Fig. 65). The data are from observations on a 12-inch cast-iron water main very carefully laid in a tangent some 3500 feet long, the loss in 1000 feet of which was measured. 134 Flow in Pipes and Channels C = center of gravity or mean point of the whole group A = center of gravity of part of group above C B = center of gravity of part of group below C Ch=hf coordinate of (7, Cv= v coordinate of C Ah =hf coordinate of A, Av = t coordinate of A Bh=hf coordinate of B, Bv = v coordinate of B Observed Data No. V Ft. per sec hf Ft of water log v Logarithms log hf 1 4.794 6.515 0.68071 I 0.81391 | 2 4.667 5.577 .6690 Sum =3.1667 ,7464 Sum =3.4641 3 4.155 5.100 .6186 ^mean =0.63334 .7076' Lmean =0.69282 4 3.998 4.002 .6018 I =Ar .6023 [ =Ah 5 3.950 3.926 . 5966 J 1 .5939J 1 6 3.519 3.566 ,54641 I .55221 1 7 3.252 2.888 .5122 Sum =2.3715 .4606 Sum =2.0046 8 3.208 2.942 ,5062 ?unean =0.47430 .4686 >Mean = 0.40092 9 2.943 2.374 .4688 =Bv .3755 =Bh 10 2.177 1.405 .3379J 1 .1477J 1 Sum mean = 5.5382 = 0.55382 Sum = 5.4687 =Cv mean = 0.54687 =Ch Av—Cv =0.63334—0 . 55382 = 0 . 07952 Ah—Ch = 0 . 69282—0 . 54687 =0 . 14595 Cv—Bv =0 . 55382—0.47430 = 0.07952 Ch—Bh =0.54687—0.40092 =0 . 14595 Since Av — Cv=Cv — Bv and Ah — Ch = Ch — Bh, the three points A, C, and B are in a straight line, which fact checks the accuracy of the work. N = tangent of inclination of line ACB Ah-Ch Ch-Bh Ah-Bh 0-14592 ~ Av-Cv “ Cv-Bv ~ Av-Bv ~ 0 . 07952 — 1 ,835 ss& Since log m =log hj — n log v , using the coordinates of C log m = 0 . 54687—1 . 835X0 . 55382 = 0.54687— 1.01626 =9.53051= log 0.3393, and m = 0.3393 The equation for this 12-inch pipe is therefore hf = 0.3393 cl. 835 L/1000. Remark : Evidently the v coordinates must be divided between the same pair of obser- vations as the hf coordinates. The mathematical determination of what group should include a point whose v coordinate is on one side of C and whose hf coordinate is on the other, depends on whether the point itself is above or below a normal to the line ACB through C. This can usually be established by plotting the logarithms on ordinary cross- section paper, or the observations on logarithmic paper. To introduce the diameter into the equation, a series of values of m and N for pipes of different diameters must be obtained. The range of N is relatively small, the limits for all reliable pipe experiments on record being from 1.70 to 2.08, and if the pipes are of the same character of surface and alignment the value of N will be constant. It is, therefore, only necessary to consider the variation of m, which depends upon the area of the cross- section or upon D and upon the roughness. Evidently m varies inversely as some power of the diameter, and for 1 /D = 0 , m =0 for any velocity, so the curve representing the relation between m and D will be m =KD — x. Proceeding in the same manner as before an average value of x =1.25 will be obtained, and the formula for pipe of the same character as that in the above experiment is _K» 1835 L _o.3sv m . L h f~ D 1-25 • 10 00 or hf ~ D 1 ' 25 ’ 1000 for average conditions, and this may be transposed to v = 73.54 D°' m S °* 535 or v = 185 7*0-66830.535 135 Variations in Diameter Variations in Diameter Relation of Diameter of Pipe to Quantity Discharged. In terms of C for Chezy’s formula. Q =7r/SC^7D5 in terms of Fanning’s coefficient f, Q = 7r/4 \ \4 / L Approximately for rough pipe Q =1000 D^/2s^/2 and for smooth pipe Q =2 X1000 D5/2si/2 Roughness. The effect of roughness in a water pipe is in general to retard the flow or increase the loss in head. This is accomplished by reducing the velocity of the water- at the surface of contact, thus producing a general reduction in velocity and also causing cross currents or eddies which use up the energy in the stream. Roughness decreases C and increases / and K in the foregoing formulas. It also increases N somewaht in the exponential formula. Curvature. The effect of curvature is to increase the loss of head. This increased loss is partly due to the cross currents and eddies set up in the bend, but also to the changes of velocity along the stream lines and increased friction along the walls of the channels due to increased velocities over part of the circumference. The loss of head due to a curve may be stated in terms of the velocity head hv or, better, in terms of the equivalent length of straight pipe which would give the same loss as the curve. Experiments upon the loss of head in pipes show the radius of the curve of minimum resistance for a right-angled bend to be about three diameters of the pipe. For six-inch pipe the loss due to such a curve is about the same as that in eight feet of straight pipe, and for a thirty-inch pipe about the same as that in forty feet of straight pipe. For intermediate sizes the loss may be expected to fall between these limits and to vary approxi- mately as the diameter. Fig. 65. Logarithmic Plotting Expansions when sudden always produce eddies which increase the loss of head. Consider two sections of a pipe, 1 and 2; 1 to be taken at a point where normal condition of flow exists before expansion and 2 after expansion. 136 Flow in Pipes and Channels If vi and V 2 are the velocities and A 1 and A 2 the areas at the two sections then the loss of head due to this sudden enlargement hfe = ^± 2 or hfe= — 2 g ' [_Ai J zg According to St. Venant, this quantity should be increased by v 2 /18 g, but this correction is so small as a rule that it can be neglected, and more recent experiments indicate that the formula is as likely to give results in excess as otherwise. Contraction when sudden produces an effect upon a stream very similar to a sharp orifice; that is, just beyond the contraction occurs the point of minimum cross-section of the stream or the “vena contracta. ,, There result not only the loss of head due to the contraction of the stream, but also that due to the reenlargement of it after passing the “vena con- tracta.” If v is the velocity under conditions of normal flow in the pipe after passing the contraction and C is the coefficient of contraction, the same in this case as for a sharp orifice, then the loss of head due to the contraction is According to St. Venant this quantity should be increased by v 2 /18 g. Also it may be written hfc= Ccv 2 /2 g, where Cc varies from 0.42 to 0.53. A fair assumption to make is Cc =0.5. This may also be taken as the loss of head due to sharp-edged entrance into a pipe. The value of C is probably too high for small pipes and too low for large pipes. Obstructions. If the sectional area of a pipe be gradually decreased and then gradually increased as in the case of a Venturi meter, the loss of head for moderate velocities is not much increased over that due to normal flow. When the obstruction causes a sudden contraction or expansion of the stream or there is discontinuity of the pipe wall, the loss of head is increased. Valves. The losses due to valves in pipe lines have been investigated with accuracy in only a few instances. From these experiments it appears that a fully open gate valve in a pipe causes a loss of head corresponding to about six diameters of length of the pipe. 137 Measurement of Flowing Water MEASUREMENT OF FLOWING WATER (From Kent’s Mechanical Engineers’ Pocket Book.) Piezometer. If a vertical or oblique tube be inserted into a pipe con- taining water under pressure, the water will rise in the former, and the vertical height to which it rises will be the head producing the pressure at the point where the tube is attached. Such a tube is called a piezom- eter or pressure measure. If the water in the piezometer falls below its proper level it shows that the pressure in the main pipe has been reduced by an obstruction between the piezometer and the reservoir. If the water rises above its proper level it indicates that the pressure there has been increased by an obstruction beyond the piezometer. If we imagine a pipe full of water to be provided with a number of piezometers, then a line joining the tops of the columns of water in them is the hydraulic grade-line. Pitot Tube. The Pitot tube is used for measuring the velocity of fluids in motion. It has been used with great success in measuring the flow of natural gas. (S. W. Robinson, Report Ohio Geol. Survey, 1890.) (See also Van Nostrand’s Mag., Vol. XXXV.) It is simply a tube so bent that a short leg extends into the current of fluid flowing from a tube, with the plane of the entering orifice opposed at right angles to the direction of the current. The pressure caused by the impact of the current is transmitted through the tube to a pressure-gage of any kind, such as a column of water or of mercury, or a Bourdon spring-gage. From the pressure thus indicated and the known density and temperature of the flowing fluid is obtained the head corresponding to the pressure, and from this the velocity. In a modification of the Pitot tube described by Professor Robinson, there are two tubes inserted into the pipe conveying the gas, one of which has the plane of the orifice at right angles to the current, to receive the static pressure plus the pressure due to impact; the other has the plane of its orifice parallel to the current so as to receive the static pressure only. These tubes are connected to the legs of a U tube partly filled with mercury, which then registers the difference in pressure in the two tubes, from which the velocity may be calculated. Comparative tests of Pitot tubes with gas-meters, for measurement of the flow, of natural gas, have shown an agreement within 3%. It appears from experiments made by W. M. White, described in a paper before the Louisiana Eng’s Socy., 1901, by Williams, Hubbell and Fenkel (Trans, A. S. C. E., 1901), and by W. B. Gregory (Tra ns, A. S. M. E., 1903), that in the formula for the Pitot tube, V- c V 2gH , in which V is the velocity of the current in feet per second, H the head in feet of the fluid corresponding to the pressure measured by the tube, and c an experimental coefficient, c = 1 when the plane at the point of the tube is exactly at right angles with the direction of the current, and when the static pressure is correctly measured. The total pressure pro- 138 Measurement of Flowing Water duced by a jet striking an extended plane surface at right angles to it, and escaping parallel to the plate, equals twice the product of the area of the jet into the pressure calculated from the “head due to the velocity/’ and for this case H — 2X — , instead of — ;but as found in White’s 2 g 2 g experiments the maximum pressure at the point on the plate exactly V 2 . opposite the jet corresponds to h — — . Experiments made with four differ- 2 9 ent shapes of nozzles placed under the center of a falling stream of water showed that the pressure produced was capable of sustaining a column of water almost exactly equal to the height of the falling water. Tests by J. A. Knesche (Indust. Eng’g, Nov., 1909), in which a Pitot tube was inserted in a 4-inch water pipe, gave <7 = about 0.77 for veloci- ties of 2.5 to 8 feet per second, and smaller values for lower velocities. He holds that the coefficient of a tube should be determined by experiment before its readings can be considered accurate. Maximum and Mean Velocities in Pipes. Williams, Hubbell and Fenkel (Trans. A. S. C. E., 1901) found a ratio of 0.84 between the mean and the maximum velocities of water flowing in closed circular conduits, under normal conditions, at ordinary velocities; whereby obser- vations of velocity taken at the center under such conditions, with a properly rated Pitot tube, may be relied on to give results within 3% of correctness. The Venturi Meter, invented by Clemens Herschel, and described in a pamphlet issued by the Builders’ Iron Foundry of Providence, R. I., is named for Venturi, who first called attention, in 1796, to the relation between the velocities and pressures of fluids when flowing through con- verging and diverging tubes. It consists of two parts, — the tube, through which the water flows, and the recorder, which registers the quantity of water that passes through the tube. The tube takes the shape of two truncated cones joined in their smallest diameters by a short throat-piece. At the up-stream end and at the throat there are pressure-chambers, at which points the pressures are taken. The action of the tube is based on that property which causes the small section of a gently expanding frustum of a cone to receive, without material resultant loss of head, as much water at the smallest diameter as is discharged at the large end, and on that further property which causes the pressure of the water flowing through the throat to be less, by virtue of its greater velocity, than the pressure at the up-stream end of the tube, each pressure being at the same time a function of the velocity at that point and of the hydrostatic pressure which would obtain were the water motionless within the pipe. 139 Measurement by Venturi Tubes — - The recorder is connected with the tube by pressure-pipes which lead to it from the chambers surrounding the up-stream end and the throat of the tube. It may be placed in any convenient position within 1000 feet of the meter. It is operated by a weight and clockwork. The difference of pressure or head at the entrance and at the throat of the meter is bal- anced in the recorder by the difference of level in two columns of mercury in cylindrical receivers, one within the other. The inner carries a float, the position of which is indicative of the quantity of water flowing through the tube. By its rise and fall the float varies the time of contact between an integrating drum and the counters by which the successive readings are registered. There is no limit to the sizes of the meters nor the quantity of water that may be measured. Meters with 24-inch, 36-inch, 48-inch, and even 20-foot tubes can be readily made. Measurement by Venturi Tubes (Trans. A. S. C. E., Nov., 1887. and Jan., 1888). Mr. Herschel recommends the use of a Venturi tube inserted in the force main of the pumping engine, for determining the quantity of water discharged. Such a tube applied to a 24-inch main has a total length of about 20 feet. At a distance of 4 feet from the end nearest ' the engine the inside diameter of the tube is contracted to a throat having a diameter of about 8 inches. A pressure gage is attached to each of two chambers, the one surrounding and communicating with the entrance ! or mam pipe, the other with the throat. According to experiments made upon two tubes of this kind, one 4 inches in diameter at the throat and 12 inches at the entrance, and the other about 36 inches in diameter at the throat and 9 feet at its entrance, the quantity of water which passes through the tube is very nearly the theoretical discharge through an opening having an area equal to that of the throat, and a velocity which is that due to the difference in head shown by the two gages. Mr. Herschel states that the coefficient for these two widely varying sizes of tubes, and for a wide range : of velocity through the pipe, was found to be within 2%, either way, of 98%. In other words, the quantity of water flowing through the tube per second is expressed within two per cent by the formula W = 0.98 A^Tjh, in which A is the area of the throat of the tube, h the head, in feet, corres- ponding to the difference in the pressure of the water entering the tube and that found at the throat, and g = 32.16. i 140 The Miner’s Inch THE MINER’S INCH (From Merriman’s Treatise on Hydraulics.) The miner’s inch may be roughly defined to be the quantity of water which will flow from a vertical standard orifice one inch square, when the head on the center of the orifice is inches. The coefficient of discharge is about 0.623, and accordingly the actual discharge from the orifice in cubic feet per second is g = — X0. 623X8. 02 \f— = 0.0255, 144 12 and the discharge in one minute is 60x0.0255 = 1.53 cubic feet. The mean value of one miner’s inch is therefore about 1.5 cubic feet per minute. The actual value of the miner’s inch, however, differs considerably in different localities. Bowie states that in different counties of Cali- fornia it ranges from 1.20 to 1.76 cubic feet per minute. The reason for these variations is due to the fact that when water is bought for mining or irrigating purposes, a much larger quantity than one miner’s inch is required, and hence larger orifices than one square inch are needed. Thus at Smarts ville, a vertical orifice or module, 4 inches deep and 250 inches long, with a head of 7 inches above the top edge, is said to furnish 1000 miner’s inches. Again at Columbia Hill, a module 12 inches deep and 12 % inches wide, with a head of 6 inches above the upper edge, is said to furnish 200 miner’s inches. In Montana the customary method of measurement is through a vertical rectangle, one inch deep, with a head on the center of the orifice of 4 inches, and the number of miner’s inches is said to be the same as the number of linear inches in the rectangle ; thus under the given head an orifice one inch deep and 60 inches long would furnish 60 miner’s inches. The discharge of this is said to be about 1.25 cubic feet per minute, or 75 cubic feet per hour. The following are the values of the miner’s inch in different parts of the United States. In California and Montana it is established by law that 40 miner’s inches shall be the equivalent of one cubic foot per second, and in Colorado 38.4 miner’s inches is the equivalent. In other States and Territories there is no legal value, but by common agreement 50 miner’s inches is the equivalent of one cubic foot per second in Arizona, Idaho, Nevada, and Utah; this makes the miner’s inch equal to 1.2 cubic feet per minute. A module is an orifice which is used in selling water, and which under a constant head is to furnish a given number of miner’s inches, or a given quantity per second. The size and proportions of modules vary greatly in different localities, but in all cases the important feature to be observed is that the head should be maintained nearly constant in order that the consumer may receive the amount of water for which he bargains and no more. 141 The Miner’s Inch The simplest method of maintaining a constant head is by placing the module in a chamber which is provided with a gate that regulates the entrance of water from the main reservoir or canal. This gate is raised or lowered by an inspector once or twice a day so as to keep the surface of the water in the chamber at a given mark. This plan is a costly one, on account of the wages of the inspector, except in works where many modules are used and where a daily inspection is necessary in any event, and it is not well adapted to cases where there are frequent and considerable fluctuations in the surface of the water in the feeding canal. Numerous methods have been devised to secure a constant head by automatic appliances; for instance, the gate which admits water into the chamber may be made to rise and fall by means of a float upon the surface; the module itself may be made to decrease in size when the water rises, and to increase when it falls, by a gate or by a tapering plug which moves in and out and whose motion is controlled by a float. These self- acting contrivances, however, are liable to get out of order, and require to be inspected more or less frequently. Another method is to have the water flow over the crest of a weir as soon as it reaches a certain height. The use of the miner’s inch, or of a module, as a standard for selling water, is awkward and confusing, and for the sake of uniformity it is greatly to be desired that water should always be bought and sold by the CU P er secon d- Only in this way can comparison readily be made, and the consumer be sure of obtaining exact value for his money. The cut, Fig. 66, shows the form of measuring-box ordinarily used, and the following table gives the discharge in cubic feet per minute of a miner’s inch of water, as measured under the various heads and different lengths and heights of apertures used in California. Weirs Sharp- edged Weirs. When an obstruction is placed in an open channel, so that water is caused to flow over it, it is called a dam or weir. If the top of the weir be a thin straight edge, the conditions of flow are similar to those that would exist in an orifice in a thin wall if the side contractions were suppressed and the head fell so low that the water did not fill the orifice to its top. If the portions of the dam near the walls of the channel are raised above the level of the rest so that water Fig/65— SHARP-EDGED WEIR does not flow over them, the overflow- ing jet is contracted at the sides as in the case" of an orifice. The general expr essio n for the discharge of water over a weir is Q = %CLH ^ 2 gH wherein H is the height above the creskof the weir to the level of still water 142 The Miner's Inch FIG. 66. MINER’S INCHgMEASURING BOX Miner’s Inch Measurements (Pelton Water Wheel Company) Length of opening in inches Opening 2 inches high Opening 4 inches high Head to center, 5 inches Head to center, 6 inches Head to center, 7 inches Head to center, 5 inches Head to center, 6 inches Head to center, 7 inches Cubic feet Cubic feet Cubic feet Cubic feet Cubic feet Cubic feet 4 1.348 1.473 1 .589 1.320 1.450 1.570 6 1 .355 1.480 1 .596 1.336 1.470 1.595 8 1 . 359 1.484 1 .600 1.344 1.481 1.608 10 1.361 1.485 1 .602 1.349 1.487 1.615 12 1.363 1.487 1 .604 1.352 1.491 1.620 14 1.364 1.488 1 .604 1.354 1.494 1.623 16 1 . 365 1.489 1 .605 1.356 1.496 1.626 18 1.365 1.489 1 .606 1.357 '1.498 1.628 20 1.365 1.490 1 .606 1.359 1.499 1 .630 22 1.366 1.490 1 .607 1.359 1.500 1.631 24 1.366 1.490 1 .607 1.360 1.501 1.632 26 1.366 1.490 1 .607 1.361 1.502 1.633 28 1.367 1.491 1 .607 1.361 1.503 1.634 30 1.367 1.491 1 .608 1.362 1.503 1.635 40 1,367 1.492 1 .608 1.363 1.505 1.637 50 1.368 1.493 1 . .609 1.364 1.507 1.639 60 1.368 1.493 1 . .609 1.365 1.508 1.640 70 1 .368 1.493 1 . ,609 1.365 1.508 1.641 80 1.368 1.493 1 . 609 1.366 1.509 1.641 90 1.369 1.493 1 . 610 1.366 1.509 1.641 100 1.369 1.494 1 . 610 1 . 36 & 1.509 1.642 — ■ Weirs and L is the length of the crest over which the water flows. Practically, it is not possible to measure H, but a head h may be observed to the surface of the stream above the curve of depression caused by the weir, and to this the velocity head hv due to the velocity v a with which the water approaches the weir, may be added when the result is approximately equal to H. If the velocity of approach be small, h as observed may be treated as equal to H. C is a coefficient which depends upon the height and form of the weir, whether or not there be end contractions, the character of the weir surface and the condition of the water on the downstream side. In weir formulas it is customary to combine one or more of the factors % } C, and 2 g into a single coefficient. Four Recognized Formulas for the discharge of weirs are as follows, but the first arid the fourth are the most important. The Francis Formula <2 = 3.33 LW'h or Q =3.33 L[(h+hv) s / 2 -hv 3 h] The Fteley and Stearns Formula Q = 3.31 LH 3 /2+0.007L or Q = 3.31L(/i + l .5/w) 3/2 +0.007L The Hamilton Smith Formula <2 = 3.29(L+H/7)ffV2 or Q =3 .29 (h+iyhv) 3 /* The Bazin Formula Q =mLh yl2gh, where ra = ^0.405+ ^'^-^ £l+0.55^“^ J in which a is the height of the crest of the weir above the bottom of the channel of approach. For weirs with end contractions, Francis concluded that L in the above formulas should be replaced by L -0.1 nH, where n is the number of full end contractions. This correction has been generally accepted, but it is by no means accurate, and for exact work in measuring water a weir without end contractions is to be preferred. These formulas all apply to a weir with a vertical upstream face, a sharp edge and with free access of air to the under side of the overfalling sheet of water. Triangular or V-shaped Weir. This form of weir, suggested by Prof. Thomson of Dublin, possesses the peculiarity that, whatever the heads, the sections of the stream are similar, and hence it may be expected to have a coefficient more nearly constant than the ordinary weir and be particularly well adapt- ed to the measurement of water where the flow varies through a considerable range. The coefficient will vary for different inclinations of the sides of the notch. For a sharp-edged weir in which the sides make an angle of 90° with each other, since L = 2 h, the discharge is Q =2.6 /F/2. No experiments have been made upon weirs of this type when other than sharp edged with vertical faces, but the effects of inclination and rounding Fig. 67-Triangular Weir may be expected to affect them similarly to rectangular weirs. 144 Weirs Rounding the Upstream Corner of the crest of a weir increases the discharge. With flat-crested weirs Bazin found this effect to amount to as much as 13% where the radius of the rounding was 4 inches and the breadth of crest 6.56 feet. Fteley and Stearns, with weirs up to one inch in breadth, found the rounding to be equivalent to increasing the head by hR = 0.7 R, where R is the radius of the rounding. Inclining the Upstream Face away from the current decreases the contraction and increases the discharge as much as 10% when the slope is one of 45°. If the inclination be in the opposite direction, the contraction is increased and the discharge decreased. With a 45° slope, the decrease may be as much as 7%. Inclining the DOWN STREAM FACE does not materially alter the discharge until the slope becomes at least 3 horizontal to 1 vertical, when the discharge is reduced. Rounding the Entire Crest reduces the discharge for low heads, but increases it for those wherein the curve of the crest approaches the curve of the natural under side of the sheet. By a combination of a rounded crest and an inclined upstream slope, the discharge may be increased 20% above that of the sharp-edged weir. Flat Crests descrease the discharge until the head becomes so high that the sheet jumps clear of the downstream corner, when they have no effect. A broad flat crest may reduce the discharge 25% below that of the sharp edge. The Sheet of Water adhering to the downstream face of a vertical sharp-edged weir has increased the discharge about 28%. The sheet being wetted, that is depressed and the space between it and the weir filled with water, due to the formation there of a partial vacuum, has increased the discharge about 15%. The sheet being depressed, but the space only partially filled with water, has increased the discharge about 6%. Submerged Weirs. When water on the downstream side of the weir rises above the level of the crest, the weir is said to be submerged. If h u is the head observed on the upstream side and h is the difference of head on the two sides, the usual formula for the discharge of a submerged weir is Q = CL V 2gh(hu-h/3 ) where C for a sharp edge varies from 0.58 to 0.63. On account of the difficulty of measuring hi, the Fig. 68— Submerged Weir head in the lower pool, because of the turbulence there, accurate results with this formula are impossible. Experiment shows that so long as the water flowing over the weir plunges to the bottom of the channel below or dives under that in the lower pool, the discharge of the weir is not decreased more than 10% by the submergence. In rounded weirs it is possible to submerge the crests to fully 30% of hu without vary- ing the discharge from that for a free weir under the head hu more than the above percent; and for submergences of less than 10% of hu the discharge is likely to be increased by the exclusion of air behind the sheet. 145 Installation FIG. 69 A LOCK-BAR PIPE LINE IN HILLY COUNTRY 146 Weirs The Weir affords the most commonly used method of measuring water in moderately large quantities. The standard weir, or sharp-edged weir consists of a vertical partition across a channel with its top edge horizontal’ sharp cornered and narrow enough so that at the heads used the overflowing sheet jumps from the upstream edge clear of the downstream corner. Such weirs may be either with or without end contractions. A weir with end contractions is one whose crest extends only part way across the channel and is terminated by partitions in its plane, with their vertical edges rising above the level of the water on the upstream side. Such a weir may be compared to a rectangular orifice upon which the head has fallen below the top* A weir without end contractions is one which extends entirely across the channel. If a = height of crest of weir above bottom of channel of approach, A w = area of stream in the plane of the weir, H = height above the crest of the surface of still water upstream from the weir, &=head above crest as observed, v w = velocity in and perpendicular to the plane of the weir, then the formula for the discharge is similar to that for the orifice and is Q = A = % CL H */ 2 = % CL SinceLH=L ( h+hv ) =area of the stream above the crest level at the plane ot still water and CL H is the ar ea in the plane of the crest, the total head producing flow is% V2 g(h+hv). The Francis Formula. The coefficient C in this formula was de- termined experimentally by James B. Francis as about 0.62, and by com- bming this with, % V2^~ the well-known coefficient of the Francis Formula 3,33 is obtained. This formula was considered by its inventor to be reliable between heads of 0.5 foot and 2.00 feet. Later investigators have modified it into the form : Q = 3 33L(h-\-l Ahv) 3 /2 n* 1 this formula the process is as follows: Having measured the head h at a point above the surface curve to the weir, compute an approxi- mate value of the discharge by the equation Qi=3.33 Lh 3 / 2 . Find the approximate velocity at the plane where the head is observed by the equa- tion v = Qi -fa) and the velocity head by h = v 2 / 2 g. Then Q is obtained by substitution m the above formula, and should be within 3 to 4 percent of correctness if the head is not more than 30 percent of a and had been properly measured, and the sheet is fully aerated underneath. For weirs with end contractions Francis recommended reducing the length L in the above formula by 0.1 i/for each full end contraction. This correction is only an approximation and, for accurate gagings, weirs with end contractions should not be used. 147 Installation 148 Weirs The Bazin Formula is the most accurate one for wide ranges of head, and it may be safely applied between heads of 0.2 foot and 6 feet, and does not require a correction for velocity of approach, as it is based upon the observed head h. It applies only to weirs without end contractions and is «■(“+“) [ 1 +° J » Us )’]“’ B * 5 and the following tables give values of Q for a weir one foot long and for various values of h and a. The value of g used in computing these tables is 32.17 feet per second. Discharge in Cubic Feet per Second per Foot of Length over Sharp-edged Vertical Weirs without End Contractions Computed by Bazin’s Formula Head h Height in feet of crest of weir above bottom of channel of approach feet a =2 a = = 3 a = -4 a = = 5 a = -6 a = = 7 00 II e 0.2 0.33 0 33 0 33 0 . 33 0 33 0 . 33 0.33 0.3 0.58 0 58 0 58 0. .58 0 . ,58 0 . .58 0.58 0.4 0.88 0 88 0 88 0. .87 0 . .87 0 . .87 0.87 0.5 1.23 1 21 1 21 1. 21 1. 21 1 . 21 1.21 0.6 1.62 1 , ,59 1 .59 1 .58 1. .58 1 . .58 1.58 0.7 2.04 2. 01 1 .99 1 .98 1 . .98 1 .98 1.98 0.8 2.50 2, .45 2 .43 2, .42 2 .41 2 .41 2.41 0.9 3.00 2 .93 2 .90 2 .88 2 .88 2 .87 2.86 1 .0 3.53 3 .44 3. .40 3, .38 3 .36 3 .36 3.35 1.2 4.68 4 .55 4 .48 4 .47 4 .42 4 .41 4.40 1 .4 5.99 5 .78 5 .68 5 .62 5 .58 5 .56 5.54 1.5 6.68 6 .44 6 .30 6 .23 6 .20 6 .18 6.16 1.6 7.40 7, .12 6 .97 6 .89 6 .84 6 .80 6.78 1.8 8.93 8 .56 8 .37 8 .25 8 .18 8. .13 8.09 2.0 10.58 10 .12 9 .87 9 .72 9 .62 9 .55 9.51 2.2 12.34 11 .77 11 .46 11 .27 11 .14 11 .06 10.99 2.4 14.20 13 .53 13 .15 12 .91 12 .75 12 .64 12.56 2.5 15.17 14 .45 14 .03 13 .76 13 .59 13 .47 13.38 2.6 16.16 15 .38 14 .92 14 .63 14 .44 14 .30 14.20 2.8 18.23 17 .32 16 .79 16 .44 16 .21 16 .04 15.92 3.0 20.39 19 .36 18 .74 18 .33 18 .06 17 .86 17.71 3.2 22.64 21 .48 20 .77 20 .31 19 .98 19 .75 19.58 3.4 24.98 23 .70 22 .89 22 .36 21 .99 21 .72 21.52 3.5 26.20 24 .83 24 .00 23 .43 23 .01 22 .73 22.48 3.6 27.41 25 .99 25 .09 24 .49 24 .06 23 .75 23.52 3.8 29.94 28 .38 27 .38 26 .70 26 .22 25 .87 25.60 4.0 32.54 30 .84 29 .74 28 .99 28 .45 28 .05 27.74 4.2 35.22 33 .39 32 .18 31 .35 30 .75 30 .30 29.96 4.4 37.99 36 .01 34 .70 33 .78 33 .12 32 .62 32.24 4.6 40.83 38 .71 37 .29 36 .29 35 .56 35 .01 34.58 4.8 43.75 41 .49 39 .96 38 .87 38 .07 37 .46 37.00 5.0 46.71 44 .31 42 .67 41 .49 40 .62 39 .96 39.44 5.2 49.81 47 .27 45 .50 44 .23 43 .29 42 .57 42.01 5.4 52.94 50 .23 48 .38 47 .02 46 .00 45 .22 44.60 5.6 56.15 53 .33 51 .34 49 .88 48 .79 47 .94 47.28 5.8 59.42 56 .45 54 .34 52 .79 51 .62 50 .71 49.99 6.0 62.77 59 .65 56 .43 55 .78 54 .53 53 .55 52.78 149 Measurement of Water Discharge in Cubic Feet per Second per Foot of Length over Sharp-edged Vertical Weirs without End Contractions — Continued Computed by Bazin’s Formula Head h, feet Height in feet of crest of weir above bottom of channel of approach a =9 a = = 10 a = = 12 a = 16 a = 20 a =25 a = 30 0 2 0.33 0 .33 0 .33 0.33 0.33 0.33 0.33 o.3 0.58 0 .58 0 .58 0.58 0.58 0.58 0.58 0 4 0.87 0 .87 0 .87 0.87 0.87 0.87 0.87 0 5 1.21 1 .21 1 .21 1.21 1.20 1.20 1.20 0 6 1.57 1 .57 1 .57 1.57 1.57 1.57 1.57 0.7 1.97 1 .97 1 ,97 1.97 1.97 1.97 1.97 0.8 2.40 2 .40 2 .40 2.40 2.40 2.40 2.40 0 9 2.86 2 .86 2 .86 2.86 2.85 2.85 2.85 1.0 3.35 3 .34 3 .34 3.33 3.33 3.33 3.33 1.2 4.39 4 38 4 38 4.37 4.36 4.36 4.36 1 .4 5.53 5 52 5 51 5.49 5.49 5.48 5.48 1.5 6.14 6 13 6 12 6.11 6.10 6.09 6.09 1.6 6.76 6 74 6 73 6.71 6.69 6.69 6.69 1.8 8.07 8 05 8 02 7.99 7.98 7.97 7.96 2.0 9.47 9 44 9 40 9.36 9.34 9.33 9.32 2.2 10.95 10 91 10 86 10.81 10.78 10.76 10.75 2.4 12.50 12 45 12 39 12.32 12.28 12.25 12.24 2.5 13.31 13 26 13 18 13.10 13.06 13.03 13.01 2.6 14.13 14 07 13 99 13.90 13.85 13.82 13.80 2.8 15.83 15 76 15 66 15.54 15.48 15.44 15.42 3.0 17.60 17 .52 17 .39 17.25 17.18 17.13 17.10 3.2 19.45 19 .34 19 .19 19.02 18.93 18.87 18.83 3.4 21.36 21. .24 21. .06 20.86 20.75 20.68 20.63 3.5 22.38 22 .22 22 .00 21.83 21.69 21.62 21.60 3.6 23.34 23 .20 22. ,99 22.75 22.62 22.53 22.48 3.8 25.39 25. 23 24. .99 24.71 24.56 24.45 24.39 4.0 27.51 27. ,32 27. 05 26.72 26.55 26.42 26.35 4.2 29.69 29. .48 29. ,17 28.79 28.59 28.45 28.36 4.4 31.94 31. 70 31. 34 30.92 30.66 30.52 30.42 4.6 34.25 33. .98 33. 58 33.10 32.84 32.65 32.53 4.8 36.62 36. 33 35. 88 35.35 35.05 34.83 34.70 5.0 39.03 38. 70 38. 21 37.61 37.28 37.03 36.88 5.2 41.56 41. 20 40. 65 39.99 39.61 39.33 39.17 5.4 44.11 43. 71 43. 12 42.38 41.96 41.66 41.47 5.6 46.74 46. 31 45. 65 44.84 44.38 44.04 43.83 5.8 49.41 48. 94 48. 22 47.33 46.83 46.45 46.22 6.0 52.15 51. 64 50. 86 49.90 49.34 48.92 48.67 When the weir is so high that the velocity of the approaching water is practically zero Bazin’s formula reduces to / 0.00984 \ , Q= ^0.405+ ^ J Lh'l 2 gh At low heads, less than 0.2 of a foot, Bazin’s Formula gives discharges somewhat too high and the formula proposed by Fteley and Stearns is recommended, which is: Q = 3.33Lff 3/2 +0.0065 L. The results by this formula are within 4 to 6 percent of the experimental values for heads ranging from 0.2 to 0.007 ft., and the actual discharges were generally in excess of those given by the formula. It lolds only so long as the sheet jumps free of the crest and the space behind it is fully aerated. 150 Weirs The Flow over the Irregular Crests may be computed by multiplying the discharge of a standard weir of the same height and length and at the same head by a factor depending on the form of the crests. The fol- lowing tables give the multipliers for various forms of weirs (Fig. 71) as determined from experiments upon full-size mo- dels at the Hy- draulic Laborato- ry of Cornell Uni- versity: / 7 , Types of Weirs and Dams Multipliers for Flat-topped Weirs. Fig. 71A Head h, feet Width of flat crest in feet 6=0.48 6 =0.93 6=1.65 6=3.17 6=5.84 6=8.98 6 = 12.24 6 = 16.30 0.5 0.902 0.830 0.819 0.797 0.785 0.783 0.783 0.783 1.0 0.972 0.904 0.879 0.812 0.800 0.798 0.795 0.792 1.5 1.000 0.957 0.910 0.821 0.807 0.803 0.802 0.797 2.0 1.000 0.989 0.925 0.821 0.805 0.800 0.798 0.795 2.5 1.000 1.000 0.932 0.816 0.800 0.795 0.792 0.789 3.0 1.000 1.000 0.938 0.813 0.796 0.791 0.787 0.784 3.5 1.000 1.000 0.942 0.810 0.793 0.787 0.783 0.780 4.0 1.000 1.000 0.947 0.808 0.790 0.783 0.780 0.777 Multipliers (m) for Triangular Weirs. Fig. 71B Head h in feet, 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 For 6=6.65 ft, m = 1.060 1.079 1.091 1.086 1.076 1.067 1.060 1.054 For 6 = 11.25 ft, m = 1.060 1.079 1.092 1.097 1.096 1.095 1.094 1.093 Multipliers for Compound Weirs. Fig, 71 Head .... h, feet Type F Type G Type H Type I Type J Type K Type L 0.5 0.964 0.932 0.934 0.968 0.971 0.971 0.971 1.0 1.026 0.982 1.000 1.008 1.040 1.040 0.983 1.5 1.064 1.015 1.040 1.032 1.083 1.092 1.022 2.0 1.066 1.031 1.061 1.041 1.105 1.126 1.040 2.5 1.025 1.038 1.073 1.043 1.118 1.146 1.057 3.0 0.992 1.044 1.082 1.044 1.128 1.163 1.072 3.5 0.966 1.049 1.090 1.045 1.136 1.177 1.085 4.0 0.944 1.053 1.097 1.046 1.144 1.190 1,097 151 Water Power WATER POWER (From Kent’s Mechanical Engineers’ Pocket Book.) Power of a Fall of Water — Efficiency. The gross power of a fall of water is the product of the weight of water discharged in a unit of time into the total head, i. e., the difference of vertical elevation of the upper surface of the water at the points where the fall in question begins and ends. The term “head” used in connection with water-wheels is the difference in height from the surface of the water in the wheel-pit to the surface in the penstock when the wheel is running. If Q = cubic feet of water discharged per second, D= weight of a cubic foot of water = 62.36 pounds at 60° F., H = total head in feet; then DQH = gross power in foot-pounds per second, and DQH *t* 550 =0.1134 QH = gross horse-power. If Q' is taken in cubic feet per minute, H P ' -T— M® A water-wheel or motor of any kind cannot utilize the whole of the head H , since there are losses of head at both the entrance to and the exit from the wheel. There are also losses of energy due to friction of the water in its passage through the wheel. The ratio of the power developed by the wheel to the gross power of the fall is the efficiency of the wheel. For 75% efficiency, net horse-power =0.00142 Q'H = Q'H 706' A head of water can be made use of in one or other of the following ways, viz: First. By its weight, as in the water-balance and in the overshot wheel. Second. By its pressure, as in turbines and in the hydraulic engine, hydraulic press, crane, etc. Third. By its impulse, as in the undershot wheel, and in the Pel ton wheel. Fourth. By a combination of the above. Horse- power of a Running Stream. The gross horse-power is H.P. =QHX 62.36 4-550 = 0.1134 QH } in which Q is the discharge in cubic feet per second actually impinging on the float or bucket, and v 2 v 2 // = theoretical head due to fehe velocity of the stream = ^ in which v is the velocity in feet per second. If Q'be taken in cubic feet per minute H.P. =0.00189 Q'H. 152 Bernoulli’s Theorem Thus, if the floats of an undershot wheel driven by a current alone be 5 feet X 1 foot, and the velocity of stream = 210 feet per minute, or 3 feet per second, of which the theoretical head is 0.19 feet, Q = 5 square feet X 210 = 1050 cubic feet per minute; H.P. = 1050X0.19 X 0.00189 = 0.377 H.P. The wheels would realize only about 0.4 of this power, on account of friction and slip, or 0.151 H.P., or about 0.03 H.P. per square foot of float, which is equivalent to 33 square feet of float per H. P. Current Motors. A current motor could only utilize the whole power of a running stream if it could take all the velocity out of the water, so that it would leave the floats or buckets with no velocity at all; or in other words, it would require the backing up of the whole volume of the stream until the actual head was equivalent to the theoretical head due to the velocity of the stream. As but a small fraction of the velocity of the stream can be taken up by a current motor, its efficiency is very small. Current motors may be used to obtain small amounts of power from large streams, but for large powers they are not practicable. Bernoulli’s Theorem. Energy of Water Flowing in a Tube. v 2 / The head due to the velocity is ^ ~ the head due to the pressure is — ; the head due to actual height above the datum plane is h feet. The total head I v 2 f is the sum of these = 2~^+/i+~, in feet, in which v = velocity in feet per second, / = pressure in pounds per square foot, w — weight of 1 cubic foot / of water = 62. 36 pounds. If p = pressure in pounds per square inch— = 2.309p. If a constant quantity of water is flowing through a tube in a given time, the velocity varying at different points on account of changes in the diameter, the energy remains constant (loss by friction excepted) and the sum of the three heads is constant, the pressure head increasing as the velocity decreases, and vice versa. This principle is known as “Bernoulli’s Theorem.” In hydraulic transmission the velocity and the height above datum are usually small compared with the pressure-head. The work or energy of a given quantity of water under pressure = its volume in cubic feet Xits pressure in pounds per square foot; or if Q = quantity in cubic feet per second, and p = pressure in pounds per square inch, IF = 144 pQ and the H.P. =0.2618 pQ. 153 Water Power Tables Table for Calculating the Horse-power of Water Heads (Pelton Water Wheel Company.) The following table gives the horse-power of 1 cubic foot of water per minute under heads from 1 up to 2100 feet. Heads in feet Horse- power Heads in feet Horse- power Heads in feet Horse- power Heads in feet Horse- power 1 .0016098 220 .354156 430 .692214 1050 1.690290 20 .032196 230 .370254 440 .708312 1100 1.770780 30 .048294 240 .386352 450 .724410 1150 1.851270 40 .064392 250 .402450 460 .740508 1200 1.931760 50 .080490 260 .418548 470 .756606 1250 2.012250 60 .096588 270 .434646 480 .772704 1300 2.092740 70 .112686 280 .450744 490 .788802 1350 2.173230 80 .128784 290 .466842 500 .804900 1400 2.253720 90 .144882 300 .482940 520 .837096 1450 2.334210 100 . 160980 310 .499038 540 .869292 1500 2.414700 110 .177078 320 .515136 560 .901488 1550 2.495190 120 .193176 330 .531234 580 .933684 1600 2.575680 130 .209274 340 .547332 600 .965880 1650 2.656170 140 .225372 350 .563430 650 1.046370 1700 2.736660 150 .241470 360 .579528 700 1.126860 1750 2.817150 160 .257568 370 .595626 750 1.207350 1800 2.897640 170 .273666 380 .611724 800 1 .287840 1850 2.978130 180 .289764 390 .627822 850 1.368330 1900 3.058620 190 .305862 400 .643920 900 1.448820 1950 3.139110 200 .321960 410 .660018 950 1.529310 2000 3.219600 210 .338058 420 .676116 1000 1 .609800 2100 3.380580 When the Exact Head is Found in Above Table Example: Have 100-foot head and 50 cubic feet of water per minute. How many horse-power? By reference to the above table the horse-power of each cubic foot under 100-foot head will be found to be .16098. This amount multiplied by the number of cubic feet per minute, 50, will give 8.05 horse-power. ' When Exact Head is Not Found in Table Take the horse-power of 1 cubic foot per minute under 1-foot head, and multiply by the number of cubic feet available, and then by the number of feet head. The product will be the required horse-power. Note: The above table is based upon an efficiency of 85 per cent. 154 Gallons and Cubic Feet Gallons and Cubic Feet United States Gallons in a Given Number of Cubic Feet (1 cubic foot = 7.480519 U. S. gallons: 1 gallon = 231 cubic inches = 0.13368056 cubic foot.) Cubic feet Gallons Cubic feet Gallons Cubic feet Gallons 0.1 0.75 50 374.0 8 000 59 844.2 0.2 1.50 60 448.8 9 000 67 324.7 0.3 2.24 70 523.6 10 000 74 805.2 0.4 2.99 80 598.4 20 000 149 610.4 0.5 3.74 90 673.2 30 000 224415.6 0.6 4.49 100 748.1 40 000 299 220.8 0.7 5.24 200 1 496.1 50 000 374 025.9 0.8 5.98 300 2 244.2 60 000 448 831 . 1 0.9 6.73 400 2 992.2 70 000 523 636.3 1 7.48 500 3 740.3 80 000 598 441.5 2 14.96 600 4 488.3 90 000 673 246.7 3 22.44 700 5 236.4 100 000 748 051.9 4 29.92 800 5 984.4 200 000 1 496 103.8 5 37.40 900 6 732.5 300 000 2 244 155.7 6 44.88 1000 7 480.5 400 000 2 992 207.6 7 52.36 2000 14 961 . 0 500 000 3 740 259.5 8 59.84 3000 22 441.6 600 000 4 488 311.4 9 67.32 4000 29 922 . 1 700 000 5 236 363.3 10 74.81 5000 37 402.6 800 000 5 984 415.2 20 149.6 6000 44 883 . 1 900 000 6 732 467 . 1 30 224.4 7000 52 363.6 1 000 000 7 480 519.0 40 299.2 Cubic Feet in a Given Number of Gallons Gallons Cubic feet Gallons Cubic feet Gallons Cubic feet 1 .134 1 000 133.681 1 000 000 133 680.6 2 .267 2 000 267.361 2 000 000 267 361.1 3 .401 3 000 401.042 3 000 000 401 041.7 4 .535 4 000 534.722 4 000 000 534 722.2 5 .668 5 000 668.403 5 000 000 668 402.8 6 .802 6 000 802.083 6 000 000 802 083.4 7 .936 7 000 935.764 7 000 000 935 763.9 8 1.069 8 000 1 069.444 8 000 000 1 069 444.5 9 1.203 9 000 1 203 . 125 9 000 000 1 203 125.0 10 3.337 10 000 1 336.806 10 000 000 1 336 805.6 Cubic Feet per Second , Gallons in 24 Hours, etc. Cubic feet per second 760 1 1.5472 2.2280 Cubic feet per minute 1 60 92.834 133.681 U. S. gallons per minute . . 7.480519 448.83 694.444 1 000 U. S. gallons per 24 hours 10 771 . 95 646 317 1 000 000 1 440 000 Pounds of water (at 62°F.) per minute . . , 62.355 3741.3 5788.65 8335.65 155 Contents of Pipes and Cylinders Contents in Cubic Feet and United States Gallons of Pipes and Cylinders of Various Inside Diameters and One Foot in Length (1 gallon = 231 cubic inches. 1 cubic foot = 7.4805 gallons.) For 1 ft. in length For 1 ft. in length For 1 ft. in length S w <3 m "a; a> |.S| Cubic feet, also CD O) Cubic feet, also t> ® S.S’S os a Cubic feet, also Q area in U. S. Q ~ area in U. S. Q area in U. S. square gallons square gallons square gallons feet feet feet A .0003 .0025 6^4 .2485 1.859 19 1.969 14.73 ~h .0005 .0040 7 .2673 1.999 19 X 2.074 15.51 % .0008 .0057 7^4 .2867 2.145 20 2.182 16.32 TE .0010 .0078 734 .3068 2.295 20 X 2.292 17.15 V2 .0014 .0102 7Yi .3276 2.450 21 2.405 17.99 TE .0017 .0129 8 \ .3491 2.611 21X 2.521 18.86 5 A .0021 .0159 8H .3712 2.777 22 2.640 19.75 H .0026 .0193 834 .3941 2.948 22 X 2.761 20.66 % .0031 .0230 8% .4176 3.125 23 2.885 21.58 H .0036 .0269 9 .4418 3.305 23 X 3.012 22.53 X .0042 .0312 9H .4667 3.491 24 3.142 23.50 ff .0048 .0359 934 .4922 3.682 25 3.409 25.50 1 .0055 .0408 9% .5185 3.879 26 3.687 27.58 i X .0085 .0638 10 .5454 4.080 27 3.976 29.74 134 .0123 .0918 1034 .5730 4.286 28 4.276 31.99 IX .0167 .1249 1034 .6013 4.498 29 4.587 34.31 2 .0218 .1632 1034 .6303 4.715 30 4.909 36.72 234 .0276 .2066 11 .6600 4.937 31 5.241 39.21 234 .0341 .2550 1134 .6903 5.164 32 5.585 41.78 2% .0412 .3085 1134 .7213 5.396 33 5.940 44.43 3 .0491 .3672 11X .7530 5.633 34 6.305 47.16 334 .0576 .4309 12 .7854 5.875 35 6.681 49.98 3M .0668 .4998 12 34 .8522 6.375 36 7.069 52.88 3^4 .0767 .5738 13 .9218 6.895 37 7.467 55.86 4 .0873 .6528 1334 1.9940 7.436 38 7.876 58.92 434 .0985 .7369 14 1.069 7.997 39 8.296 62.06 434 .1104 .8263 14 34 1.147 8.578 40 8 . 727 65.28 4 X .1231 .9206 15 1.227 9.180 41 9.168 68.58 5 .1364 1.020 1534 1.310 9.801 42 9.621 71.97 534 .1503 1.125 16 1.396 10.44 43 10.085 75.44 534 .1650 1.234 16X 1.485 11.11 44 10 . 559 78.99 534 .1803 1.349 17 1.576 11.79 45 11.045 82.62 6 .1963 1.469 1734 1.670 12.49 46 11.541 86.33 634 .2131 1.594 18 1.767 13.22 47 12.048 90.13 634 .2304 .1724 18X 1.867 13.96 48 12.566 94.00 To find the capacity of pipes greater than the largest given in the table, look in the table for a pipe of one-half the given size, and multiply its capacity by 4; or one of one-third its size, and multiply its capacity by 9, etc. To find the weigth of water in any of the given sizes, multiply the capacity in cubic feet by 6234 or the capacity in gallons by 8%, or, if a more accurate result is required, by the weight of a cubic foot of water at the actual temperature in the pipe. Given the dimensions of a cylinder in inches, to find its capacity in U. S. gallons: Square the diameter, multiply by the length and by 0.0034. If d = diameter, l = length, gallons = ^ ^ ^231°^ ^ ^ = 0 • 0034 d^l. If D and L are in feet, gallons =5 .875 D-L. — — — 156 Cylindrical Vessels Cylindrical Vessels, Tanks and Cisterns Diameter in Ft. and Ins., Area in Sq. Ft. and Capacity in U. S. Gals, for 1 Ft. in Depth (1 gallon =231 cubic inches = 1 cubic foot/7.4805 =0.13368 cubic foot.) Diam- eter, ft. in. Area, square feet Gallons, 1 foot depth Diam- eter, ft. in. Area, square feet Gallons, 1 foot depth Diam- eter, ft. in. Area, square feet Gallons, 1 foot depth 1 0 .785 5.87 5 8 25.22 188.66 19 0 283 . 53 2120.9 1 1 .922 6.89 5 9 25.97 194.25 19 3 291.04 2177.1 1 2 1.069 8.00 5 10 26.73 199.92 19 6 298.65 2234.0 1 3 1.227 9.18 5 11 27.49 205.67 19 9 306.35 2291.7 1 4 1.396 10.44 6 0 28.27 211.51 20 0 314.16 2350 . 1 1 5 1.576 11.79 6 3 30.68 229.50 20 3 322.06 2409.2 1 6 1.767 13.22 6 6 33.18 248.23 20 6 330.06 2469 . 1 1 7 1.969 14.73 6 9 35.78 267.69 20 9 338.16 2529.6 1 8 2.182 16.32 7 0 38.48 287.88 21 0 346.36 2591.0 1 9 2.405 17.99 7 3 41.28 308.81 21 3 354.66 2653.0 1 10 2.640 19.75 7 6 44.18 330.48 21 6 363.05 2715.8 1 11 2.885 21.58 7 9 47.17 352.88 21 9 371.54 2779.3 2 0 3.142 23.50 8 0 50.27 376.01 22 0 380.13 2843.6 2 1 3.409 25.50 8 3 53.46 399.88 22 3 388.82 2908.6 2 2 3.687 27.58 8 6 56.75 424.48 22 6 397.61 2974.3 2 3 3.976 29.74 8 9 60.13 449.82 22 9 406.49 3040.8 2 4 4.276 31.99 9 0 63.62 475.89 23 0 415.48 3108.0 2 5 4.587 34.31 9 3 67.20 502.70 23 3 424.56 3175.9 2 6 4.909 36.72 9 6 70.88 530.24 23 6 433.74 3244.6 2 7 5.241 39.21 9 9 74.66 558.51 23 9 443.01 3314.0 2 8 5.585 41.78 10 0 78.54 587.52 24 0 452.39 3384.1 2 9 5.940 44.43 10 3 82.52 617.26 24 3 461.86 3455.0 2 10 6.305 47.16 10 6 86.59 647.74 24 6 471.44 3526.6 2 11 6.681 49.98 10 9 90.76 678.95 24 9 481.11 3598.9 3 0 7.069 52.88 11 0 95.03 710.90 25 0 490.87 3672.0 3 1 7.467 55.86 11 3 99.40 743.58 25 3 500.74 3745.8 3 2 7.876 58.92 11 6 103.87 776.99 25 6 510.71 3820.3 3 3 8.296 62.06 11 9 108.43 811.14 25 9 520.77 3895.6 3 4 8.727 65.28 12 0 113.10 846.03 26 0 530.93 3971.6 3 5 9.168 68.58 12 3 117.86 881 .65 . 26 3 541.19 4048.4 3 6 9.621 71.97 12 6 122.72 918.00 26 6 551.55 4125.9 3 7 10.085 75.44 12 9 127.68 955.09 26 9 562.00 4204 . 1 3 8 10.559 78.99 13 0 132.73 992.91 27 0 572.56 4283.0 3 9 11.045 82.62 13 3 137.89 1031.5 27 3 583.21 4362.7 3 10 11.541 86.33 13 6 143.14 1070.8 27 6 593.96 4443.1 3 11 12.048 90.13 13 9 148.49 1110.8 27 9 604.81 4524.3 4 0 12.566 94.00 14 0 153.94 1151.5 28 0 615.75 4606.2 4 1 13.095 97.96 14 3 159.48 1193.0 28 3 626.80 4688.8 4 2 13.635 102.00 14 6 165.13 1235.3 28 6 637.94 4772 . 1 4 3 14.186 106.12 14 9 170.87 1278.2 28 9 649 . 18 4856.2 4 4 14.748 110.32 15 0 176.71 1321.9 29 0 660.52 4941.0 4 5 15.321 114.61 15 3 182.65 1366.4 29 3 671.96 5026.6 4 6 15.90 118.97 15 6 188.69 1411.5 29 6 683.49 5112.9 4 7 16.50 123.42 15 9 194.83 1457.4 29 9 695.13 5199.9 4 8 17.10 127.95 16 0 201.06 1504 . 1 30 0 706.86 5287.7 4 9 17.72 132.56 16 3 207.39 1551.4 30 3 718.69 5376.2 4 10 18.35 137.25 16 6 213.82 1599.5 30 6 730.62 5465.4 4 11 18.99 142.02 16 9 220.35 1648.4 30 9 742.64 5555.4 5 0 19.63 146.88 17 0 226.98 1697.9 31 0 754.77 5646 . 1 5 1 20.29 151.82 17 3 233.71 1748.2 31 3 766.99 5737.5 5 2 20.97 156.83 17 6 240.53 1799.3 31 6 779.31 5829.7 5 3 21.65 161.93 17 9 247.45 1851.1 31 9 791.73 5922.6 5 4 22.34 167.12 18 0 254.47 1903.6 32 0 804.25 6016.2 5 5 23.04 172.38 18 3 261.59 1956.8 32 3 816.86 6110.6 5 6 23.76 177.72 18 6 268.80 2010.8 32 6 829.58 6205.7 5 7 24.48 183.15 18 9 276.12 2065 . 5 32 9 842 . 39 6301.5 157 Water Contents , in Barrels Number of Barrels (31 ^ Gallons) in Cylindrical Cisterns and Tanks (1 barrel =31 H gallons =31.5 X23 1/1728 =4.21094 cu. ft.; reciprocal =0.237477.) £ CD &«£ o Q.S 1 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Diameter in feet 5 6 7 8 9 10 11 12 13 4.663 6 .714 9.139 11.937 15.108 18.652 22.569 26.859 31.522 23.3 33 .6 45.7 59.7 75.5 93.3 112.8 134.3 157.6 28.0 40 .3 54.8 71.6 90.6 111.9 135.4 161.2 189.1 32.6 47 .0 64.0 83.6 105.8 130.6 158.0 188.0 220.7 37.3 53 .7 73.1 95.5 120.9 149.2 180.6 214.9 252.2 42.0 60 .4 82.3 107.4 136.0 167.9 203.1 241.7 283.7 46.6 67 .1 91.4 119.4 151.1 186.5 225.7 268.6 315.2 51.3 73 .9 100.5 131.3 166.2 205.2 248.3 295.4 346.7 56.0 80 .6 109.7 143.2 181.3 223.8 270.8 322.3 378.3 60.6 87 .3 118.8 155.2 196.4 242.5 293.4 349.2 409.8 65.3 94 .0 127.9 167.1 211.5 261.1 316.0 376.0 441.3 69.9 100 .7 137.1 179.1 226.6 279.8 338.5 402.9 472.8 74.6 107 .4 146.2 191.0 241.7 298.4 361.1 429.7 504.4 79.3 114 .1 155.4 202.9 256.8 317.1 383.7 456.6 535.9 83.9 120 .9 164.5 214.9 271.9 335.7 406.2 483.5 567.4 88.6 127 .6 173.6 226.8 287.1 354.4 428.8 510.3 598.9 93.3 134 .3 182.8 238.7 302.2 373.0 451.4 537.2 630.4 14 15 16 17 18 19 20 21 22 36.557 41 .966 47.748 53.903 60.431 67.332 74.606 82.253 90.273 182.8 209.8 238.7 269.5 302.2 336.7 373.0 411.3 451.4 219.3 251.8 286.5 323.4 362.6 404.0 447.6 493.5 541.6 255.9 293.8 334.2 377.3 423.0 471.3 522.2 575.8 631.9 292.5 335.7 382.0 431.2 483.4 538.7 596.8 658.0 722.2 329.0 377.7 429.7 485.1 543.9 606.0 671.5 740.3 812.5 365.6 419.7 477.5 539.0 604.3 673.3 746.1 822.5 902.7 402.1 461.6 525.2 .592.9 664.7 740.7 820.7 904.8 993.0 438.7 503.6 573.0 646.8 725.2 808.0 895.3 987.0 1083.3 475.2 545.6 620.7 700.7 785.6 875.3 969.9 1069.3 1173.5 511.8 587.5 668.5 754.6 846.0 942.6 1044.5 1151.5 1263.8 548.4 629.5 716.2 808.5 906.5 1010.0 1119.1 1233.8 1354.1 584.9 671.5 764.0 862.4 966.9 1077.3 1193.7 1316.0 1444.4 621.5 713.4 811.7 916.4 1027.3 1144.6 1268.3 1398.3 1534.5 658.0 755.4 859.5 970.3 1087.8 1212.0 1342.9 1480.6 1624.9 694.6 797.4 907.2 1024.2 1148.2 1279.3 1417.5 1562.8 1715.2 731.1 839.3 955.0 1078 . 1 1208.6 1346.6 1492 . 1 1645 . 1 1805 . 5 23 24 25 26 27 28 29 30 98.666 107.432 116.571 126.083 135.968 146.226 156.858 167.863 493.3 537.2 582.9 630.4 679.8 731.1 784.3 839.3 592.0 644.6 699.4 756.5 815.8 877.4 941.1 1007.2 690 . 1 7 752.0 816.0 882.6 951.8 1023.6 1098.0 1175.0 789.J 1 859.5 932.6 1008.7 1087.7 1169.8 1254.9 1342.9 888.0 966.9 1049 . 1 1134.7 1223.7 1316.0 1411.7 1510.8 986.^ 7 1074.3 1165.7 1260.8 1359.7 1462.2 1568.6 1678.6 1085.: 3 1181.8 1282.3 1386.9 1495.6 1608.5 1725.4 1846.5 1184.0 1289.2 1398.8 1513.0 1631.6 1754.7 1882.3 2014.4 1282.: 7 1396.6 1515.4 1639.1 1767.6 1900.9 2039.2 2182.2 1381.: 3 1504.0 1632.0 1765.2 1903.6 2047.2 2196.0 2350 . 1 1480.0 1611.5 1748.6 1891.2 2039.5 2193.4 2352.9 2517.9 1578.7 1718.9 1865.1 2017.3 2175.5 2339.6 2509.7 2685.8 1677.3 1826.3 1981.7 2143.4 2311.5 2485.8 2666.6 2853.7 1776. ( ) 1933.8 2098.3 2269.5 . 2447.4 2632.0 2823.4 3021.5 1874.7 2041.2 2214.8 2395.6 2583.4 2778.3 2980.3 3189.4 1973.3 2148.6 2321 .4 2521.7 2719.4 2924 . 5 3137.2 3357.3 158 Water Supply SOURCE A Waterworks System must secure its supply when and where it can be gotten, and must deliver it when and where required by its customers, or “ takers.” Waterworks structures are required to collect the water; to hold it from times when it is available until it is required ; to pump it to a higher elevation; to convey it from the point where it is available to the points where it is required, and to allow the water to be measured and controlled at all points. Water is required by the takers at very unequal rates, following the requirements and emergencies that arise in their busi- ness, and the fundamental requirement controlling the design of works is to secure the ability to supply water wherever and whenever required and in whatever reasonable amounts may be needed. COLLECTION OF WATER Intakes Intakes are structures built out into a body of water for the purpose of drawing water for use. The position of intakes is often affected by con- siderations of local pollution when sewage is allowed to flow into the same body of water from which the supply is taken. This is commonly the case in cities located upon rivers and great lakes. The depth of intake is fre- quently a matter of importance where water of different qualities is to be obtained at different levels. There are three types of intakes: (1) Un- protected intakes, (2) Submerged intakes, (3) Exposed or tower cribs. Unprotected intakes are used for small supplies. The pipe is allowed to terminate at the desired point, sometimes being protected by a coarse screen. A fine screen is not permissible because it will be clogged by matters carried by the water. A submerged Crib is a structure built on the bottom of the lake or river from the interior of which the water is taken. It serves the purpose of roughly screening the water and also of protecting the end of the intake pipe from damage. Exposed or TOWER CRIBS are structures built on the bottom of the river or lake and extending above high water. They are frequently provided at different levels with ports controlled by gates, and screens may be located in their interiors. Tower cribs have many advan- tages for large supplies. The ports may be closed and the water pumped out of the intake pipe and everything inspected for tightness and condition. Screens in them may be reached for cleaning and repairs. Tower cribs require excellent foundations and they must be built strong enough to withstand ice pressures. In cold climates they are only used for large supplies. In warmer climates where ice pressure is not effective they are also used for small supplies. Intake pipes or conduits are the connecting channels between the intakes and the shore. 159 Water Supply Steel Pipes for intakes are laid in much the same way as cast-iron pipes. Flexible joints are riveted to the ends of the steel pipes where required (Fig. 72), but the length of steel pipe between such joints may be greater, as steel pipe is stronger and more rigid than cast-iron pipe. Steel pipe is fre- quently designed to fit closely the contour of the bottom and it can then be put together with ordinary flange joints bolted up by a diver. Depth of Cover for Steel Pipe must not be excessive or the weight of the earth will flatten and deform it. A slight flattening is not objectionable as it does not cause the pipe to leak and does not great- ly reduce its carrying capacity. In bad trenches and where material is slippery the depth of cover should be kept some- what less than in solid ground. With firm material carefully placed around the pipe and well rammed on the sides the depth of cover for short distances may be greater than in loose caving material. If it is necessary to cover thin pipe to a great depth it may be stiffened by angle irons riveted to it at frequent intervals. A more substantial result is obtained by surrounding the pipe with con- crete. USEFUL INFORMATION. Cubic yards of earth in ditches with side slopes of one foot in ten. Bottom Width DEPTH IN FEET 4 5 6 7 8 9 10 12 14 16 18 20 2 ft .36 0.48 0.60 0.72 0.86 0.99 1.15 1.46 1.80 2.19 2.59 2.96 .44 0.57 0.71 0.85 1.01 1.16 1.33 1.68 2.06 2.48 2.92 3.33 2 ft .51 0.66 0.82 0.98 1.16 1.33 1.51 1.90 2.32 2.80 3.25 3.70 2U ft .65 0.76 0.93 1.11 1.30 1.49 1.70 2.12 2.58 3.10 3.58 4.07 4 ft .66 0.84 1.04 1.24 1.45 1.66 1.88 2.34 2.84 3.40 3.91 4.44 41% ft .74 0.94 1.15 1.37 l .60 1.83 2.07 2.57 3.10 3.70 4.24 4.81 5 ft .81 F04 1.26 1.50 1.75 2.00 2.25 2.80 3.36 4.00 4.57 5.18 Gates on Steel Pipes. There are two ways of connecting gates in steel pipes: (1) By flange connections, the flanges being riveted to the steel pipe and bolted to flange gates. The gates must have cases heavy enough and strong enough to withstand the temperature stresses in the steel pipe. This is essential. If flange gates of ordinary construction are used the cases are sure to be broken by the expansion and contraction of the pipe. (2) The 160 Gate Valves gates may be connected with the steel pipe through short pieces of cast-iron pipe and lead joints. In this case it is necessary to build anchorages on the steel pipe on either side of the gates. The two anchorages having equal and opposite temperature strains to hold may be conveniently connected by old steel rails laid in concrete. Connections and Accessories of Gates. Gates are furnished with either flange or bell ends at about the same cost. Bell ends are generally used in pipe lines in street work; flange connections are used in gatehouses, pumping stations, and about filter plants. GATE BOXES are metallic boxes covering the wrench connection and gate, extending to the surface of the ground, with an expansion joint to protect them from damage by frost and traffic and with a removable cover to allow the gate to be opened, ; from the surface with a suitable wrench after removing the cover. Manholes of masonry are often built about gates of special importance, large gates, and gates operated by gears, especially when located under pavements or in other places not easily accessible. It is not necessary to build such manholes about small gates because such gates can be readily and cheaply dug up in the infrequent cases of access to them being ne- cessary. Gears are used on large gates and gates under heavy pressure. In general 36-inch gates, 10 lb per sq. in. working pressure; 30-inch gates, 50 lb. per sq. in working pressure; and 20-inch gates, 150 lb. per sq. in.working pressure, are the smallest gates to be geared, spur gears are used on gates set vertically and opening upward, and beveled gears on gates set horizontally and opening sideways. The latter are to be used wherever the vertical space is not sufficient to put in the spur-geared gates. By-passes are provided in many cases on large gates operating under heavy pressures. These are built into and form part of the main gate. A small gate on the by-pass is opened to equalize the pressures in the pipe on either side of the gate before the main gate is opened. This allows the main gate to be opened with less effort than would otherwise be required. Hydraulically Operated Gates in which the screws of the ordinary gate are omitted, have hydraulic cylinders provided with plungers attached directly to the moving parts. A small control valve allows high-pressure water to act on one side of the other of the plunger, opening and closing the gate. The cost is about twice that of ordinary gates. Hydraulically operated gates with “rising screw” stems were first installed at Rochester, N. Y., at Cobbs Hill Reservoir. Surmounting the operating cylinder is a yoke upon which there is an adjustable clutch which engages the screw stem and allows the gate to be operated by hand cranks, whenever there is insufficient pressure in the Conduit for hydraulic operation. 161 162 Blow-off Boxes Z o H < A Eh > > O £ o h} PQ O I— ( H 163 Pipe Line Accessories Gates should not be placed where they cannot be inspected and tested and kept in good order. Electrically Operated Gates are furnished with electric motors geared to the screws that open and close them. Such gates are used occasionally in pumping stations and about filters where electric current is available. Sluice Gates are of simpler construction, arranged for being built into masonry of reservoirs and other structures, and for holding water against moderate heads only. There is great variety in the design of sluice gates. They are usually cheaper than standard gates, and for the services to which they are adapted are fully satisfactory. Auxiliaries Air Valves are small valves attached to pipes for the purpose of auto- matically letting out air. They are placed on summits only. Automatic air valves need only to be placed on summits of cast-iron pipe lines where the pressure is fight and variable, that is, on summits nearly up to the hydraulic grade fine. On all summits where the water is under considerable pressure it is sufficient to put on a petcock or a larger valve to be opened while the pipe is being filled and which can be closed at all other times. As air is more soluble in water under pressure there is no danger of the separa- tion of air at summits under considerable pressure, and should air be acci- dentally introduced to them it would be slowly dissolved and removed by the passing water. As a general rule air valves with a diameter of one inch for each foot in diameter of the water pipe are sufficient. The air valves must be protected from frost by specially constructed boxes to insure their being in readiness to act in winter. For Steel Pipe air valves are also required to let air into the pipe rapidly in case of need, as the pipe is not so constituted that it will support itself against outside pressure with a vacuum in the inside. A break in a pipe at a low point, allowing the water to run out rapidly, would cause a vacuum in higher parts of the pipe, which would cause the pipe to collapse. Consideration of this feature has led to placing air valves for automatically admitting air on summits of steel pipe. . Generally the air valve for this purpose should have a net area equal to a circle one-eighth of the diameter of the pipe. Air valves are to be insisted upon in all steel-pipe fines, but it must be remembered that they are called upon to act very rarely indeed, and for this reason a defective valve or arrangement may be used without the dis- covery being made that it is defective, and the fact that a simpler or cheaper type of air valve has been used in certain cases where there have been no breaks and consequently no demand that has taxed its capacity is not to be taken as an indication of the sufficiency of that particular design. 164 Conduits Blow-offs are small pipes attached at low points for the purpose of drawing off and wasting the water, contained in the pipe during times of inspection and repair. Blow-offs are usually much smaller in diameter than the main pipe. The necessity of blow-offs depends upon the character of the water and the service of the pipe. In general an air valve is placed on each summit and a blow-off at the bottom of each, sag in a pipe conduit line. They are generally unnecessary or very infrequent in distribution mains as there are so many connections, fire hydrants etc., which may be utilized. Manholes consisting of saddles attached to the pipe and removable covers capable Of being bolted securely to the frame are placed on steel pipes at distances ranging from 1000 to 2000 feet apart, to allow the pipe to be entered during construction and afterward for inspection and repair. In some cases manholes have been placed on cast-iron pipes, altho most lines have been built without them. Twin Lines of pipe are used in places of special danger. Either line will maintain at least a partial supply in case of break in the other. In case twin lines are long, there should be cross connections with gates so that in case of a break in either line a section only can be cut out, the flow at other points continuing through both lines. With this arrangement, the amount of water flowing through the system will be more than would flow through one line only. The Cost of 'Twin Lines with cross connections is from 30 to 50 percent greater than the cost of a single line of pipe of the same strength and capa- city. Where no other purpose than safety is secured by dividing the flow, it is generally better to spend the added money, or a part of it, in strength- ening one line and making it secure beyond question rather than dividing it between two smaller lines. River crossings, lines over coal fields, where there are sure to be settlements, and other points of special hazard are best crossed with twin lines, three lines of pipe cost from 60 to 80 percent more than one line of equal strength and capacity. Water Supply Conduits Leakage should be avoided as far as possible. All visible leaks should be stopped and the pipe examined in open trench under test pressure. Sand Cutting sometimes occurs where leaks occur in sharp sandy soil. A small jet from an imperfect lead joint has been known to wash sand in such a way as to cut entirely through the band of the pipe. Tubercles in Cast-iron Pipe. The carrying capacity of cast-iron pipe is Teduced in course of time by the growth of tubercles upon the interior of 165 Conduits the pipe. In a general way the capacity of the pipe, other things being equal, is reduced from this cause by as much as one percent per annum. In small pipes the deterioration is more rapid. Generally the deterioration is less rapid with clear lake waters and more rapid with turbid river waters, and especially waters carrying organic matter. Filtered river waters act more nearly like lake waters. Tubercles can be Removed by sending an instrument driven by the water pressure through the pipe. This instrument is called a “go-devil.” Scraping off the tubercles in this way increases the carrying capacity of the pipe. After the pipe has been scraped tubercles grow more rapidly than before, so that the remedy is a temporary and not a permanent one. When the pipe is once scraped it is usually necessary to scrape it again, and the process becomes an annual one, or the period may be even shorter. Organisms. A well coated steel plate pipe has a smooth surface upon which organisms do not adhere as readily as to the rougher surface of cast- iron pipes. These growths increase during warm weather and fall off to some extent as the water gets colder in the winter. Spring gaugings of long pipe lines which have been in use for some time show somewhat greater discharge than when the same conduits are gauged in the autumn. Effect of Cleaning upon the Quality of the Water. The corrosion and tuberculation of iron pipes always adds iron to the water, and this iron gives it a color, tends to deposit and is objectionable. Scraping the pipes frequently increases the rate of tuberculation and increases what- ever objection there may be to the iron in the water from this source. Pressure for Domestic Service Only. At the street line 20 lb. per sq. in. will raise water to the upper floor of three-story residences and allow a fair service, but generally 40 lb. per sq. in. is the least allowance for fair domestic service. For business blocks and higher buildings higher press- ures are needed; 60 or 70 lb. per sq. in. is not too much to give fair service in mills and business blocks that are not especially high. High steel build- ings generally pump their own water and no effort is made to supply them without such pumping. Pressure for Fire Service. If steam fire engines are used and depended upon as in many American cities, the only requirement for pressure is that during fires and with the heaviest draft the pipes shall have sufficient capa- city to supply water to the steam fire engines and at the. same time retain as much pressure as is needed for domestic service. If the pressure is higher, hose streams can be obtained from the hydrants without the use of the fire engines. The additional pressure to permit this to be done is very desirable. 70 lbs. during fires is the lowest pressure that permits effective hose streams 166 Reservoirs and Standpipes to be obtained for use on buildings of moderate size. If only residences are involved, 50 or 60 lbs. will give fair streams. In business districts with large buildings better hose streams are obtained with higher pressures, and in general the higher the pressure the better the fire service. 100 lbs. gives a good working service without steam fire engines. Higher pressures up to 150 lbs. and more are available in many cities. Reservoirs and Standpipes Distributing Reservoirs are connected immediately with the distri- bution system and as near as possible to the center of population supplied. Their function is to take water when it comes and to make it available when it is needed. They are especially to maintain the service at times of fire and on other occasions when water is drawn rapidly. Frequently they also serve the purpose of allowing the pumps supplying the service to be shut down during certain, hours of the day or at night, thereby economizing labor. This is especially the case in small plants. Open reservoirs with earth embankments or masonry walls have been frequently used and are most economical for the storage of large quantities of surface or lake waters. Ground waters and filtered waters always deteriorate in quality in such reservoirs, owing to the growth of certain organisms in the sunlight. covered reservoirs are always to be preferred for such waters. Roofs are sometimes used to exclude the light and keep the water from deteriorating. A light roof not necessarily water-tight serves this purpose. Masonry Covers for distributing reservoirs are often used. At Wash- ington, D. C., Springfield, Mass., and elsewhere, groined arch construction has been used. Floors to carry the weight of the roof and distribute it over the whole base are built as inverted groined arches. The piers are of con- crete, as thick as 12% of the span on centers, and not more than 12 times as high as thick. If the reservoir is deep, large piers will be required to meet this condition, and the span of the arches is increased to correspond. The roof is of groined arch vaulting without reinforcing. The outside walls, with a minimum thickness of about 12% of their height at top and 16% at bottom, are braced at the bottom by the floor blocks and at the top by the roof blocks, and are calculated as reinforced beams, with breaking moment at about 43% of the distance from the bottom to the top, equal to 4/i 3 , being the height of the wall in feet. In deep reservoirs economy is secured by carrying the floor on a slope of about 1 in 6 to the raised base of the walls, thereby reducing the height of the walls. The masonry is backed up by solid earth embankment, and two feet of soil is placed over the top to keep frost from the masonry. Ventilators are provided to allow the passage of air as water rises and falls in the reservoir. The top is covered with grass and shrubbery, but trees or any plants with strong heavy roots should not be planted. 167 Installation PIPE LINE TESTING Special precautions should be taken before placing hydraulic pressure tests on a steel pipe line after the same has been laid in a trench, prior to placing line in service. 1. See that all pipe line centers are properly backfilled and the line is thus weighted down to prevent floating. 2. All test heads or gate valves should be securely braced. 3. All blow-off valves should be closed. 4. All automatic air valves should be in position and in proper working order, with the control gate valves wide open. 5. No section of pipe should be tested without having at least one auto- matic air valve installed and in proper working order, even though the same may not be required for permanent operation. 168 Installation U INSTALLATION OF LARGE STEEL PIPES Transportation Pipe is unloaded from the cars by any convenient equipment such as a locomotive crane, derrick, yard gantry or other apparatus or it can be un- , oaded by hand by snubbing it with a preventer line and rolling it down iiclined skids or it can be hauled or lowered by the aid of teams. Distribution along the pipe line is governed largely by the topography of the country, the length of the line, the size of the pipe and the facilities coivenient. For a large amount of heavy pipe in a tolerably level country it }ays to construct a narrow gage service track and haul the pipe with diney locomotives. 7or short lines or very light pipe delivery can be made by automobile trrkks or trucks and trailers or the pipe can be loaded directly on timber sleds or on pole wagons according to topographical and weather conditions. It is distributed close to the line of the trench and securely blocked to pre- vent at from rolling down hill. Generally it is more convenient to handle when aid parallel with the trench but when the topography does not permit this arangement it may be placed at a skew or at right angles to the axis of the irench. In any case it can be slewed, rolled or snubbed into position for finally lowering into the trench, due care being given to protection of the coa ing. Trench Excavation The irench is usually made with a clear width of 12 to 18 in. more than the diameter of the pipe and deep enough to provide at least 2 ft. of cover over the op of the pipe. This amount of earth is considered necessary for adequate Drotection from loads and impact exclusive of protection required from fros . In ver rough or stony country it may be necessary to make the excava- tion by haid or with scrapers and teams, but the latter method necessitates sloping bulks. In shale, hardpan or rock, drilling with compressed air machines md blasting are generally necessary although soft or rotten rock and hard strata may sometimes be excavated by steam shovels without , blasting. 169 Installation When the amount of work, character of the soil and the topography ' permit, it is generally more rapid and economical to excavate with a trench machine or a light revolving steam shovel with a long boom and bucket. When the revolving steam shovel is used, it travels over the excavated trench supported on timber mats spanning the trench that are taken up ii the rear and laid down in advance by the shovel itself as it progresses. Tie use of the steam shovel for excavation is of advantage in that it permits tie separation of the spoil into waste and into suitable backfilling material. In order to accommodate or rivet and caulk the transverse field j oints30 ft. apart, bell holes 4 ft. long and 1 ft. deep are dug at the bottom of ;he trench and between then the bottom is carefully levelled to uniform gude to support the pipe continuously. Lowering and Assembling The pipe trench is spanned by transverse wooden skids on which the pipe is rolled in a position directly above the centre line .of the trenm and with the rear end of the section just over the forward end of the list as- sembled section. One or two stiff leg derricks are set opposite tie pipe section on the side of the trench or a pair of tripods with hand crate oper- ating manilla tackles are set up over the pipe, one near each end, manilla rope slings are placed around the pipe and engage the tackles, the pipe is hoisted slightly, skids removed, and the pipe lowered to appDximate position on the bottom of the trench. When the pipe is intended for riveted transverse circular fied joints, the rear end of the last section is entered in the forward end of the preceding section by means of steel spud bars flattened on one end and pointed on the other end. The flat end is used as a wedge for entering the pip and the , pointed end as a drift to engage the open rivet holes and pull then to regis- tration. The bars are made a few inches shorter than the pipe dameter so that they may have clearance for operation inside the pipe. Wha the rivet holes register they are service bolted and matched with a few idditional drift pins to prevent the possibility of displacement by creeping, expansion or contraction or by disturbances in assembling the next section. When necessary the entrance of one pipe into the next may be promoted by a longitudinal pull and hoist with the derrick. 170 Installation For a pipe of medium size, say 40 in. in diameter, the normal pipe laying gang consists of about 25 to 35 men who roll the pipe on the skids, bring up and set the derricks, enter the pipe sections, and bolt up the joints. i With field riveted joints, vertical and horizontal angles up to a deflec- tion of three degrees can be made with standard sections entered in tangent alignment and then forced into transverse positions corresponding to the spacing of the rivet holes carefully located to conform with the required deflection. Riveting The five-man riveting gang removes the temporary joint bolts, lays up the steel plate tightly with an iron maul, and bolts the pipe securely with sufficient bolts to hold the sheets tight for reaming and riveting. Riveting is usually done by pneumatic tools, operated on the outside except for the bottom half of the circumference where riveting is usually done from the inside. Rivets are heated in hand blast coal furnaces on the surface of the ground adjacent to the pipe joints and are delivered to the interior of the pipe through drop holes up to 2 in. in diameter that are provided for that purpose on the upper side of the pipe at every joint and are afterwards closed with screw plugs. On long lines or where the work is subject to delay or interruption at special points, the pipe is assembled sometimes in sections commenced at different points and eventually joined to each other by special closures. After the joints are riveted they are painted with a special preservative paint. Extended use is made of the patented high pressure flexible coup- lings for transverse field joints with lock-bar pipe for gas lines and on diameters of 24" and on under water lines where the pipe is too small to per^ mit working on the inside. After the field joints are completed the pipe is tested in convenient lengths of from 1 to 4 miles by pneumatic pressure for gas mains and in lengths of from 3^2 to 2 miles by hydraulic pressure for water mains to a required pressure, usually 50% in excess of the normal working pressure contemplated. 171 Installation Elevated and Submerged Pipes When it is desirable to elevate pipe concrete piers spaced about 30 ft. apart are generally used. On short trestles the pipe sections may often be most advantageously distributed on the surface of the ground and suc- cessively lifted to position by derricks or locomotive cranes. On long trestles it is generally desirable to provide a service track alongside for the delivery of the pipes. Usually one of the track stringers is laid directly on the pier tops alongside of the pipe and the opposite stringer is supported on a single vertical falsework post braced to the concrete pier. The saddle tops of the piers are spanned by skids on which the pipes are delivered. Afterwards the pipes are raised, skids removed and the pipes lowered to position on the piers where they are assembled and riveted in the same manner as in trenches. Submerged pipe is always laid in a protecting trench which when the conditions will permit, is generally most advantageously excavated by a hydraulic dredge. If the bottom is of rock or hard strata the excavation is usually done with a dipper dredge. Submerged pipe should be provided with flexible joints and can generally be floated to the site in 100 or 150 ft. lengths closed with temporary bulkheads. They are sunk to the bottom by admitting water and the successive sections are connected up by divers making the bolted joints. Sometimes the pipes are sunk between guide piles and sometimes special equipment for floating, sinking and connecting them is devised and installed to correspond with conditions and require- ments. Submerged pipe trenches are usually backfilled to a depth of about 2 ft. and when they are exposed to wave action, the covering is protected by rip rap. 172 Installation Fig. 75— LOCK-BAR PIPE LINE. SHOWING CLOSING IN PIECE. 173 Distribution of Water Data for Steel Standpipes Required thickness Approximate relative costs Dia. Height Capa- city in of lowest Thick- Approx plate imate in in thou- with ness of weight Tank Founda- Total with feet feet sand stress not bottom, in net tion 5 feet 10% added for appurte- Per gallons exceed- inches tons at deep at thou- ing 5 cents $7.00 per nances and sand 10 000 lbs, in per lb cu yd connections gals 20 20 47 X X 9 $ 880 $540 $1560 $33 30 71 X X 12 1237 540 1960 28 40 94 X X 16 1590 540 2350 25 50 118 is X 20 2040 540 2840 24 25 20 74 X X 12 1155 800 2150 29 30 110 X X 16 1595 800 2640 24 40 147 is X 21 2090 800 3180 22 50 184 Vs X 26 2640 800 3780 21 60 221 is Vs 34 3390 800 4600 21 70 258 X. Vs 42 4210 800 5510 21 30 20 105 X X 15 1450 1110 2820 27 30 158 X X 20 1980 1110 3400 22 40 211 5 16 X 26 2640 1110 4130 20 50 264 T6 Vs 37 3700 1110 5300 20 60 316 X Vs 47 4680 1110 6370 20 70 369 is Vs 59 5870 1110 7680 21 80 422 % Vs 72 7200 1110 9150 22 90 475 X X 89 8920 1110 11350 24 100 528 ii X 105 10550 1110 12830 24 110 580 % y 2 124 12400 1110 14890 26 120 633 1A 16 X 144 14400 1110 17090 27 35 20 144 X X 18 1770 1480 3580 25 30 215 X 25 2470 1480 4350 20 40 287 Vs Vs 37 3680 1480 5670 20 50 359 X Vs 48 4830 1480 6950 19 60 431 is Vs 61 6130 1480 8380 19 70 502 k 80 8010 1480 10450 21 80 574 X X 98 9770 1480 12400 22 90 646 7 A X 118 11850 1480 14700 23 100 718 15. X 141 14100 1480 17100 24 110 790 iX X 166 16580 1480 19900 25 120 862 IX Vs 195 19530 1480 23100 27 130 934 1 is Vs 225 22500 1480 26400 28 40 20 188 X X 21 2150 1900 4450 24 30 282 is X 30 2990 1900 5490 19 40 376 is Vs 45 4500 1900 7040 19 50 470 is Vs 60 5980 1900 8670 19 60 564 % Vs 77 7750 1900 10620 19 70 658 X X 101 10120 1900 13220 20 80 751 Vs X 125 12500 1900 15850 21 90 846 H X 151 15140 1900 18750 22 100 941 1 is Vs 184 18400 1900 22350 24 110 1035 IX Vs 216 21600 1900 25850 25 120 1130 IX Vs 251 25100 1900 29700 26 174 Reservoirs and Standpipes Data for Steel Standpipes — Continued Dia. in feet Height in feet Capacity in thou- sand gallons Required thickness of lowest plate with stress not exceed- ing 10000 lbs, in Thick- ness of bottom, inches l Approx- imate weight in net tons Apr Tank at 5 cents per lb )roximate r( Founda- tion 5 feet deep at $7.00 per cu yd dative costs Total with 10% added for appurte- nances and connections Per thou- sand gals 45 20 238 X X 25 2 480 2350 $5 320 23 30 357 Vs Vs 40 4 020 2350 7 030 20 40 476 X Vs 55 5 500 2350 8 650 18 50 594 Vs Vs 74 7 380 2350 10 700 18 60 713 X y 2 101 10 100 2350 13 700 19 70 833 Vs- x 128 12 780 2350 16 640 20 80 951 TS V2 156 15 640 2350 19 800 21 90 1070 1* Vs 193 19 360 2350 23 900 22 100 1190 1 ~16 Vs 230 23 020 2350 27 900 23 50 20 293 T6 X 30 2 970 2870 6 430 22 30 440 7 1 6 Vs 50 4 950 2870 8 600 20 40 586 A Vs 68 6 820 2870 10 660 18 50 733 » x 97 9 680 2870 13 800 19 60 880 13 T6 V2 124 12 430 2870 16 820 19 70 1025 if y 2 156 15 620 2870 20 300 20 80 1170 ltf Vs 198 19 800 2870 24 900 21 90 1320 1 A Vs 238 23 870 2870 29 400 22 60 20 423 T6 x 38 3 830 4050 8 670 20 30 633 Vl Vs 66 6 600 4050 11 720 19 40 846 Vs Vs 91 9 120 4050 14 500 17 50 1060 tf y 2 132 13 200 4050 19 000 18 60 1270 15 T6 y 170 17 030 4050 23 200 18 70 1480 l H Vs 224 22 440 4050 29 200 20 80 1690 IX Vs 276 27 600 4050 33 700 20 70 20 574 Vs Vs 61 6 140 5400 12 700 22 30 861 T6 Vs 87 8 760 5400 15 600 18 40 1150 X y 133 13 370 5400 20 600 18 50 1438 15 y2 178 17 850 5400 25 600 18 60 1725 IVs Vs 241 24 160 5400 32 500 19 Overflows should invariably be provided for distributing reservoirs and should have sufficient capacity to discharge all the water that the pipes or pumps are capable of bringing to them. Many reservoirs have been lost and great damage done by failure to provide sufficient overflow capacity. Standpipes are elevated reservoirs built of sheet steel entirely above the surface of the ground, and are commonly used where the desired water level is a considerable distance above the surface of the ground. The limita- tions of steel construction do not in general allow standpipes to be used in large works. Roofs should be provided on all standpipes holding waters deteriorating in the sunshine, that is, in general, for ground waters and filtered waters. 175 Distribution System Reinforced concrete standpipes have been used with satisfactory results. It does not appear that any very large financial saving has been made by their use. Towers of masonry are frequently built about standpipes for ornamental purposes, and to protect them from wind pressure, and to make very tall standpipes small in diameter safe. fr lElevated Steel Tanks supported on steel trestles are used in place of standpipes where the quantities of water to be stored are not large and the elevation above the surface of the ground is considerable. The East Providence tank holding 1 000 000 gallons, from 135 to 205 feet above the ground, was erected in 1904 at a cost of about $100 000. (N. E. W. W. A. vol. 19, p. 55). Wooden tanks are frequently used in railway supplies and in industrial operations, but are seldom to be recommended for public water supply. The Distribution System includes all the main pipes and lateral pipes, the standpipes and distributing reservoirs, gates, meters, all services and connections as far as owned by the water department within and near the area that is actually served with water. The piping in a distribution system must be designed so that water can be supplied to any point at any time at the greatest rate at which water may be fairly demanded at that place. Gridiron System. This is a system in which all pipes are connected with all other pipes at street intersections, so that in case of a fire at any point water comes to that point through pipes from all directions. This ar- rangement is more advantageous in supplying water for fire protection than the branching system, which would be sufficient and often best for supplying water for all purposes except fire service. The gridiron system is practically universal in American cities. An economical system for the distribution of water for routine uses only would consist of a system of branching pipes, each branch being made sufficiently large to supply the water to the territory served by it at the time of day when use is greatest. The Gridiron System avoids “dead ends” and insures circulation. Pipes are however laid below frost in the North Eastern States, with 4 to 5 feet of cover. 17G Gates and Gate Valves Gate Valves are placed at intervals on all pipe lines of considerable length. In city streets they are generally placed near intersections and so arranged, in the gridiron system, that any section may be shut out without interfering with the remainder while at the same time but a limited number of fire hydrants are affected. Outside the city valves are placed less fre- quently, and are best placed on summits where the pressure is least. The gates serve the purpose of facilitating tests of the pipe and shutting off portions of it for repairs in case of emergency. Gates Smaller than the Pipe are often used on pipes 30 inches in diameter and over, connection being made by reducers on either side. The cost is less and the smaller gates are operated more quickly and easily. There is a little head lost, and the smaller the gate the more head is lost. This is controlling in determining how much smaller than the pipe it is best to make the gates. Loss of Head in Gates with Taper Cone Connections The figures given are in velocity heads (or in feet, when the velocity in the main pipe is 8.03 ft. per sec.) They may also be taken as tenths of feet when the velo- city in the main pipe is 2.54 ft. per sec. Basis. Loss of head in a gate, 0.15, velocity head. Loss of head in cones, 0.20 of the amount that the velocity head at the throat is greater than the velocity head in the pipe. The actual amount of head lost in a gate depends upon the form of gate, and considerable variations are to be anticipated with gates of different designs. The amount lost in the cones depends upon the taper design and smoothness of the surfaces, and considerable variations either way are to be anticipated. Generally 24-inch gates may be used on 30 and 36 inch pipes, 30-inch gates on 42 and 48 inch pipes, and 36-inch gates on 60 and 72 inch pipes; but if head or elevation is very valuable the gate should be one size larger than above indicated. The usual form of valve consists of a “Body” casting connected in the line of the pipe surmounted by a “Bonnet” a “Dome” connected to the body by flanges. The “Disc” rises into the dome when the gate is opened and is actuated by a screw stem of either “rising” or “non-rising” type. The Disc is either wedge shaped fitting into corresponding grooves in the body or is made of two parallel plates which are forced apart by fold ing wedges, often the disc is seated in closing and vice versa in opening. Diam. of gate, inches Diameter of pipe in inches 30 36 42 48 54 60 72 20 1.57 3.47 6.59 24 0.65 1.57 3.07 5 !4o S.72 30 0.15 0.52 1.14 2.09 3.47 5^40 11.45 36 0.15 0.44 0.91 1.57 2.51 5.40 42 0.15 0.40 0.75 1.25 2.83 48 0.15 0.35 0.65 1.57 177 Water Consumption Water Consumption Per Capita Consumption is the amount of water used per day for each person living in the city of area supplied on the basis of the annual average figures. In other words, it is the whole quantity of water supplied in gallons in one year, divided by 365 and divided by the total population of the district supplied with water. Maximum Monthly Rate of Consumption. During that month in the year when the consumption is highest, from 15 to 25% more water is used than the average for the year. In some cases 40% more water is used High monthly rates of consumption are usually associated with either a very dry period, with more than the usual sprinkling of streets and lawns or an exceptionally cold month, with a continued draft of water through many services to keep exposed and imperfectly protected pipes from freezing. Where services are metered the excess consumption in cold weather largely disappears. It is cheaper to cover the pipes or otherwise to protect them from freezing than to pay for the water that it is necessary to allow to run in order to protect them. ( ! * Meters and Consumption w ^ 1 1 r- - — - - — - — - y-’S The general effect, of meters is to reduce consumption generally by elim- inating waste. It appears that the tendency is for an unmetered city to consume more than twice as much water as one which is metered. One of the accompanying tables gives the percentage of consumption metered and the per capita consumption in each of the 155 cities of more than 30,000 population. These figures are compiled from statistics for the year 1915 published by the Census Board. Another table combines these - figures showing the number of cities which meter all their water, and the average per capita consumption per day of the group: the same for those which meter between 90% and 99%, inclusive; and so on for all cities, grouped by 10 units of percentage of water metered. Of the 26 cities reporting all water metered, only one had a per capita consumption greater than the average for all cities; of the 70 having more than % of the water metered, only 10 had a per capita consumption greater than the average for all cities. The average consumption for these 70 cities was 103 gallons, while that for the 47 cities showing less than Y metered, was 161 gallons. There are a few cities with fairly low consumption; also a few very com- pletely metered ones with a rather high rate. But these averages all of the larger cities of the country (not a number of “hand picked” ones) show a most decided tendency of consumption rates to fall as meters are intro- duced. The more rapid drop for the first 25 to 30 percent of water metered apparently shows that metering persuades the large consumer to economize on water to a greater extent that it does the small ones. * Municipal Journal, June 1, 1916. 178 Meterage & Consumption in Larger Cities CITY Percent of Water Metered rer uapita Consump- tion (a) CITY Percent of Water Metered Jr'er Uapita Consump- tion (a) Akron . 30 156 Fall River 57 48 Albany . 33 230 . Fitchburg 100 104 Allentown 1 120 Flint 60 120 Altoona 6 108 Fort Wayne 100 64 Amsterdam 14 224 Fort Worth 100 79 Atlanta . 100 113 Galveston 99 95 Atlantic City .... . 98 156 Grand Rapids 60 123 Auburn 21 177 Hamilton 85 84 Augusta 9 196 Flarrisburg 90 111 Aurora 75 99 Hartford 100 64 Austin 75 122 Haverhill 27 172 Baltimore 27 131 Hoboken 70 93 Bay City 30 172 Holyoke 29 112 Bayonne 100 120 Houston . . 58 86 Bellingham 25 162 Jackson 100 93 Binghamton 59 127 Jacksonville 95 89 Birmingham ..... 100 b Jamestown 65 77 Boston 46 111 Jersey City 24 149 Brockton 100 42 Joliet 90 201 Buffalo 32 342 Kalamazoo 100 64 Cambridge . 33 86 Kansas City, Kan. . 52 157 Camden 6 127 Kansas City, Mo. . 71 149 Canton . 35 124 Knoxville 47 220 Cedar Rapids . . . . . 100 90 La Crosse 56 125 Charlotte . 100 63 Lancaster 29 133 Chelsea . 67 90 Lansing 80 106 Chicago 22 226 Lawrence 93 43 Cincinnati 61 130 Lima 80 147 Cleveland 99 118 Lincoln 100 78 Colorado Springs . . 2 180 Lorain 37 119 Columbia . 100 141 Los Angeles 80 141 Columbus 95 92 Louisville 45 129 Council Bluffs 75 146 Lowell 56 99 Covington 100 46 Lynchburg 15 223 Dallas 50 115 Lynn 50 64 Dayton 100 117 McKeesport ...... 66 113 Decatur 95 121 Macon 50 150 Denver 7 b • Malden 100 46 Detroit 42 189 Manchester 25 64 Dubuque 100 110 Memphis 60 87 Duluth 73 102 Milwaukee 72 110 E. Orange 44 68 Minneapolis 92 81 El Paso 90 69 Mobile 32 146 Erie 36 231 Montgomery 75 80 Evansville 18 164 Muskogee 88 92 Everett 46 72 Nashville 75 106 179 Meterage & Consumption in Larger Cities Percent Per Capita Percent Per Capita CITY of Water Consump- CITY os Water Consump- Metered tion (a) Metered tion (a) Newark ... 46 107 San Diego . 100 137 New Bedford. . . . . 96 72 San Francisco 7 b New Britain. . ... 99 85 Savannah 2 140 New Orleans. . ... 100 74 Schenectady 11 130 Newport ... 66 60 Seattle 94 160 Newton ... 61 70 Sioux City . 100 78 New York. . . . ... 26 102 Somerville . 65 74 Niagara Falls . ... 40 283 Spokane 65 246 Norfolk ... 80 94 South Bend . 33 85 Oklahoma City . . . . 98 116 Springfield, 111. . . . 99 150 Omaha ... 96 118 Springfield, O . . . . . 48 155 Orange ... 100 72 Springfield, Mass. . 60 103 Oshkosh ... 38 130 St. Louis 30 128 Pasadena ... 96 120 St. Paul 61 70 Pawtucket ... 90 62 Syracuse . 99 147 Perth Amboy . ... 55 193 Tacoma 8 430c Philadelphia. . 8 182 Taunton . 58 65 Pittsburgh .... 15 252 Toledo 90 118 Pittsfield 15 152 Topeka . 100 89 Portland, Ore. ... 21 141 Trenton . 22 153 Portland, Me. ... 20 130 Troy. 12 314 Providence. . . . ... 70 65 Waco . 33 141 Pueblo 7 295 Washington 59 161 Quincy ... 90 73 Waterbury 50 100 Reading ... 20 139 Waterloo . 62 54 Richmond ... 70 105 Wheeling 6 309 Rochester. . . . . 70 106 Wilmington, Del. . . 100 105 Rockford ... 100 58 Worcester . 74 78 Sacramento. . . . 366 Woonsocket . 98 34 Saginaw ... is 330 Yonkers . 100 91 Salem ... 25 89 Youngstown . 33 134 Salt Lake City . . . . 33 203 Average 40 139 Metering Water and Average Consumption Water Water supplied, supplied, Percent of Water Number gallons Percent of Water Number gallons Metered of Cities per capita Metered of Cities per capita per day per day 100 26 85 40 to 49 9 138 90 to 99 . . . 23 109 30 to 39 15 184 80 to 89 6 128 20 to 29 15 142 70 to 79 . . . 13 103 10 to 19 8 235 60 to 69 14 113 0 to 9 13 195 50 to 59 13 117 a — average amount of water supplied to distribution system daily, divided by population served. b — not reported c — about half this amount overflows from a low service reservoir and is allowed to run to waste. 180 Water Consumption Water Consumption Maximum Weekly and Daily Rates. There will be some weeks and some days when the quantities will considerably exceed the average for the maximum month. Generally a maximum daily consumption of 10 or 15 gallons per capita in excess of the average for the maximum month must be expected. Hourly Fluctuations in Flow. Water is required primarily for domes- tic and manufacturing purposes, and for these purposes is required in quan- tities that are fairly well determined and at times that do not vary very much from day to day. The greatest normal use of water is in the morning hours. The afternoon use is a little less. The night use of water is compara- tively small. Amount of Growth to be Anticipated. In designing pipe lines, it is necessary to anticipate growth to a certain extent in order to avoid the necessity of duplicating the lines at an early date. On the other hand, anticipating future growth to an unreasonable extent results in burdening present takers with the cost of facilities provided for the future to an un- reasonable extent. In general, all new pipe lines should be designed to serve a population 50% greater than the present population, and in cases of special difficulty, where an additional line would be specially difficult or expensive, a greater growth than this should be anticipated. Increasing the diameter of the pipe, 1 % increases the carrying capacity 2.63%, and increases the cost of the pipe from 1% to 1.5%, according to the size and class of pipe and the conditions under which it is laid. On this basis adding 1% to the investment adds from 1.75% to 2.63% to the carry- ing capacity, $100 invested now in increasing the size of the pipe adds as much to the capacity as from $175 to $263 invested in a new pipe line at some time in the future if the new line is of the same size as the present one. $100 invested now at 5% will amount to $175 in 11 years and $263 in 20 years; at 4% the increase will be reached in 14 years and 25 years respec- tively. In general these represent economical limits of time to be antici- pated. As a general rule design should be made for ten or fifteen years only where the growth is over 3% per annum or where money is hard to get, and design for twenty or twenty-five years where growth is under 2% per annum or where money is obtainable at a low rate, and also in all cases where pipe is less than 12 inches in diameter or where pressure is light. There are many exceptions to this rule under peculiar conditions and it must be applied with caution. 181 Water Consumption Population that can be Supplied by Pipes of Various Sizes Based on an average use of one hundred gallons per capita daily Diameter of one pipe line, inches For two or more pipes, sum of areas in sq. ins. Sectional area of pipe sq. ins. With an average amount of fire service * With no fire service. Max- imum draft 170 gallons per capita daily Flat slopes and long lines V =2 Average condition V=3 Steep slopes and short lines V =4 Flat slopes and long lines V =2 Average conditions V=3 Steep slopes and short lines V =4 4 13 12 27 48 660 990 1 330 6 28 61 132 228 1490 2 240 2 950 8 50 182 392 666 2 650 3 980 5 320 10 79 425 900 1 500 4 150 6 190 8 280 12 113 835 1 720 2 850 5 950 8 950 12 000 16 201 2 320 4 620 7 400 10 600 15 900 21 300 20 314 4 940 9 520 14 900 16 500 24 800 33 200 24 452 8 900 16 700 25 500 23 900 35 800 47 800 30 707 17 200 32 000 48 000 37 400 56 100 74 800 36 1018 30 300 53 300 78 200 53 800 80 500 108 000 42 1385 46 600 80 400 117 000 73 200 110 000 146 000 48 1810 67 100 114 000 163 000 95 300 142 000 190 000 54 2290 91 600 153000 219 000 121 000 181 000 242 000 60 2827 120 000 200 000 282 000 148 000 224 000 299 000 •Gallons daily = 120 pop. +1 000 000 Pop. in thousands. Fire Protection The Requirements of Fire Service vary greatly. In European cities, with fire-proof buildings, but little water is required for the extinguishment of fire. In tropical countries, where buildings are widely separated and represent but small value, and often in wet climates, it does not pay to furnish fire service. It is better to let buildings burn now and then than to provide long and larger pi,pes and other equipment that would be required for fire service. In American cities wooden construction is common and wooden floors are used in many buildings having brick walls. A large pipe capacity is required to provide the water which is required for extinguishing fires in such buildings. 182 Water Consumption The Amount of Water required for extinguishing fires is not very large in the aggregate, but when fires occur it is wanted at a high rate, and pipes must therefore be provided of large capacity to meet this demand. Pipe sizes required for fire protection in American cities are always larger than those required for other uses, and the size of pipe to be selected within the area of the distribution system, and between it and the distributing reservoir or pumping station where direct pumping is used, is mainly con- trolled by questions of fire protection. Water Required for Fire Service. The amount of water to be pro- vided for fire service depends upon the size and number of fire steams required in a given area. For Average American Conditions, take the square root of the popu- lation in thousands and this indicates the rate in millions of gallons of water per day at which water should be provided for fire service. For example : If the population is 9 thousand allow water at a rate of 3 million gallons per day for fire service. If the population is 25 thousand allow 5 million gallons per day, and if 100 thousand allow 10 million gallons of water per day. The pipes must be designed large enough so that the quantity of water for fire service will be available even though the fire occurs at a time when water is being used at a high rate for other purposes. It is not necessary to assume the extreme maximum rate of draft for other purposes; some chances can be taken. To find the required capacity add, first, the average annual rate of consumption; second, 20 gallons per capita to cover ordinary fluctua- tions; third, the amount of water allowed for fire protection. If the fluctua- tions are unusually great, take 30 or 40 gallons per capita in place of 20. Concentration of Water for Fire Service. In the case of cities up to 100 000 inhabitants it is generally necessary to provide pipe capacity so that the whole amount of water provided for fire protection can be delivered with some loss of pressure in the neighborhood of the closest, largest, highest and most valuable buildings, and at each of such points if there are several; elsewhere piping capable of delivering smaller quantities varying with the kind and value of construction and the proximity of the various buildings. This table may be used as a very general guide. With high per capita consumption and bad fire conditions the sizes should be increased. Under opposite conditions they may be reduced. It will often pay to make pipe sizes a little smaller in the distribution and larger in the supply mains with- out changing the total capacity of the system. 183 Water Consumption A Standard Fire Stream is one flowing 250 gallons per minute through a smooth nozzle 1 }/$ inches in diameter, with a pressure at the base of the tip of r 45 pounds. Such a stream is effective to a height of 70 feet above the ground or with a horizontal carry not exceeding 63 feet. When fed through the *best quality 23 ^-inch rubber-lined hose the hydrant pressure required to throw such a stream taken while the stream is running is as follows: Feet of hose = 50 100 200 400 600 Lb. per sq. in = 56 63 77 106 135 The hydrant pressure is less during the fire than at other times, because more head is lost in friction in the pipes, and the ordinary pressure must be greater to insure standard conditions during fire. The best hydrant pressure for general use is considered to be from 80 to 100 lbs., but as other conditions are frequently controlling, fire service must be largely adapted to what is available. The best statement of the hydraulics of fire streams and nozzles is in a paper by John R. Freeman, Trans. Am. Soc. C. E., 1889, vol. 21, P, 303. Slope Reduction Tables Data Useful in Steel Conduit Design TABLES FOR THE REDUCTION OF SLOPE MEASUREMENTS TO HORIZONTAL DISTANCES FROM 10 TO 100 FEET, WITH DIFFERENCE OF LEVEL FROM 0.0 TO 20.0 FEET SLOPE DISTANCES IN FEET AT TOP OF PAGE. DIFFERENCES OF ELEVATION, IN FEET IN TENTHS, IN SIDE COLUMNS. TABLE OF CORRECTIONS IN BODY OF SHEET, CARRIED TO FEET, TENTHS, HUNDREDS AND THOUSANDTHS OF A FOOT. EXAMPLE: GIVEN A SLOPE MEASUREMENT OF 80 FEET, WITH A DIFFERENCE OF LEVEL C'F 2.1 FEET, TO ASCERTAIN THE HORIZONTAL DISTANCE— FROM THE TA.BLE, UNDER 80 AND OPPOSITE 2.1, FIND .028 FEET, THE CORRECTION TO BE DEDUCTED: THEN 80.00— .028— 79.972 FEET, THE CORRECT HORIZONTAL DISTANCE. 185 Slope Reduction Tables 10 20 30 40 50 60 70 80 90 100 0.0 0.0 .1 .001 .1 .2 .002 .001 .001 .001 *2 .3 .005 .002 .002 .001 .001 .001 .001 .001 .001 .001 .3 .4 .008 .004 .003 .002 .001 .001 .001 .001 .001 .001 .4 0.5 .013 .006 .004 .003 .003 .002 .002 .002 .001 .001 0.5 .6 .018 .009 .006 .005 .004 .003 .003 .002 .002 .002 .6 .7 .025 .012 .008 .006 .005 .004 .004 .003 .003 .003 .7 .8 .032 .016 .011 .008 .006 .005 .005 .004 .004 .003 .8 .9 .041 .020 .014 .010 .008 .007 • .006 .005 .005 .004 .9 1.0 .050 .025 .017 .013 .010 .008 .007 .006 .006 .005 l.f .1 .061 .030 .020 .015 .012 .010 .008 .008 .007 .006 1 .2 .072 .036 .024 .018 .014 .012 .010 .009 .008 .007 2 .3 .085 .042 .028 .021 .017 .014 .012 .011 .009 .009 .3 .4 .099 .049 .033 .025 .020 .016 .014 .012 .011 .010 .4 1.5 .113 .056 .038 .028 .023 .019 .016 .014 .013 .011 1.5 .6 .129 .064 .043 .032 .026 .021 .018 .016 .014 .013 .6 .7 .146 .072 .048 .036 .029 .024 .021 .018 .016 .015 .7 .8 .163 .081 .054 .041 .032 .027 .023 .020 .018 .016 .8 .9 .182 .090 .060 .045 .036 .030 .026 .023 .020 .018 .9 2.0 .202 .100 .067 .050 .040 .033 .029 .025 .022 .02C 2.0 .1 .223 .111 .074 .055 .044 .037 .032 .028 .025 .022 .1 .2 .245 .121 .081 .061 .048 .040 .035 .030 .027 .0 r A .2 .3 .268 .133 .088 .066 .053 .044 .038 .033 .029 .0:7 .3 .4 .292 .145 .096 .072 .058 .048 .041 .036 .032 .029 .4 *2.5 .317 .157 .104 .078 .063 .052 .045 .039 .035 .<31 2.5 .6 .344 .170 .113 .085 .068 .056 .048 .042 .038 034 .6 .7 .371 .183 .122 .091 .073 .061 .052 .046 .041 037 .7 .8 .400 .197 .131 .098 .079 .065 .056 .049 .044 .039 .8 .9 .429 .211 .141 .105 .086 .070 .060 .053 .047 .042 .9 3.0 .460 .226 .150 .113 .090 .075 .064 .056 .050 .045 3.0 .1 .493 .242 .161 .120 .096 .080 .069 .060 .053 .048 .1 .2 .526 .258 .171 .128 .103 .085 .073 .064 .057 .051 .2 .3 .560 .274 .182 .136 .109 .091 '.078 .068 .061 .055 .3 .4 .596 .291 .193 .145 .116 .096 .083 .072 .064 .058 .4 3.5 .633 .309 .205 .153 .123 .102 .088 .077 .061 .061 3.5 .6 .671 .327 .217 .162 .130 .108 .093 .081 .072 .065 .6 .7 .710 .345 .229 .172 .137 .114 .098 .085 .076 .069 .7 .8 .750 .364 .242 .181 .145 .120 .103 .090 .010 .072 .8 .9 .792 .384 .255 .191 .152 .127 .109 .095 .0*5 .076 .9 4.0 .835 .404 .268 i .201 .160 .133 .114 .100 .*89 .080 | 4.0 186 Slope Reduction Tables 10 20 30 40 50 60 70 80 90 100 4.1 .879 .425 .282 .211 .168 .140 .120 .105 .093 .084 4.1 .2 .925 .446 .295 .221 .177 .147 .126 .110 .098 .088 .2 .3 .972 .468 .310 .232 .185 .154 .132 .116 .103 .092 .3 .4 1.020 .490 .324 .243 .194 .162 .138 .121 .108 .097 .4 4.5 1.070 .513 .339 .254 .203 .169 .145 .127 .113 .101 4.5 .6 1.121 .536 .355 .265 .212 .176 .151 .132 .118 .106 .6 .7 1.173 .560 .370 .277 .222 .184 .158 .138 .123 .111 .7 .8 1.227 .584 .387 .289 .231 .192 .165 .144 .128 .115 .8 .9 1.283 .609 .403 .301 .241 .200 .172 .150 .134 .120 .9 5.0 1.340 .635 .420 .314 .251 .209 .179 .157 .139 .125 5.0 .1 1.398 .661 .437 .326 .261 .217 .186 .163 .145 .130 .1 .2 1.458 .688 .454 .339 .271 .226 .193 .169 .150 .135 .2 .3 1.520 .715 .472 .353 .282 .235 .201 .176 .156 .141 .3 .4 1.583 .743 .490 .366 .293 .244 .209 .183 .162 .146 .4 5.5 1.648 .771 .508 .380 .303 .253 .216 .189 .168 .151 5.5 .6 1.715 .800 .527 .394 .314 .262 .224 .196 .174 .157 .6 .7 1.784 .829 .546 .408 .326 .271 .233 .203 .181 .163 .7 .8 1.854 .859 .566 .423 .338 .281 .241 .211 .187 .168 .8 .9 1.926 .890 .586 .438 .349 .291 .249 .218 .194 .174 .9 6.0 2.000 .921 .606 .453 .361 .301 .258 .225 .200 .180 6.0 .1 2.076 .953 .627 .468 .374 .311 .266 .233 .207 .186 .1 .2 2.154 .985 .648 .483 .386 .321 .275 .241 .214 .192 .2 .3 2.234 1.018 .669 .499 .399 .332 .284 .249 .221 .199 .3 .4 2.316 1.052 .690 .515 .411 .342 .293 .256 .228 .205 .4 6.5 2.400 1.086 .?13 .532 .424 .353 .303 .265 .235 .212 6.5 .6 2.487 1.120 .735 .548 .438 .364 .312 .273 .242 .218 .6 .7 2.576 1.155 .758 .565 .451 .375 .321 .281 .250 .225 .7 .8 2.668 1.191 .781 '.582 .465 .386 .331 .290 .257 .232 .8 .9 2.762 1.228 .806 .600 .478 .398 .341 .298 .265 .238 .9 7.0 2.869 1.265 828 .617 .492 .410 .351 .307 .273 .245 7.0 .1 2.968 1.302 .852 .635 .507 .422 .361 .316 .281 .252 .1 .2 3.060 1.341 .877 .653 .521 .434 .371 .325 .289 .260 .2 .3 3.166 1.380 .902 .672 .536 .446 .382 .334 .297 .267 .3 .4 3.274 1.419 .927 .690 .551 .458 .392 .343 .305 .274 .4 7.5 3.386 1.459 .953 .709 .566 .471 .403 .352 .313 .282 7.5 .6 3.511 1.500 .979 .729 .581 .483 .414 .362 .322 .289 .6 .7 3.620 1.542 7.005 .748 .596 .496 .425 .372 .330 .297 .7 .8 3.742 1.584 :.032 .768 .612 .509 .436 .381 .339 .305 .8 .9 3.869 1.626 L .059 .788 .628 .522 .447 .391 .347 .313 .9 8.0 4.000 1.670 1.086 .808 .644 .536 .459 .401 .356 .321 8.0 187 Slope Reduction Tables 10 20 30 40 50 60 70 80 90 100 8.1 4.136 1.714 1.114 .829 .660 .549 .470 .411 .365 .329 .1 .2 4.276 1.758 1.142 .850 .677 .563 .482 .421 .374 .337 .2 .3 4.422 1.803 1.171 .871 .694 .577 .494 .432 .384 .345 .3 .4 4.574 1.849 1.200 .892 .711 .591 .506 .442 .393 .353 .4 8.5 4.732 1.896 1.229 .913 .728 .605 .518 .453 .402 .362 8.5 .6 4.897 1.943 1.259 .935 .745 .620 .530 .464 .412 .371 .6 .7 5.069 1.991 1.289 .958 .763 .634 .543 .475 .422 .379 .7 .8 5 . 250 2.040 1.320 .980 .780 .649 .555 .486 .431 .388 .8 .9 5.440 2.089 1.351 1.003 .798 .664 .568 .497 .441 .397 .9 9.0 5.641 2.139 1.382 1.026 .817 .679 .581 .508 .451 .406 9.0 .1 5.854 2.190 1.413 1.049 .835 .694 .594 .519 .461 .415 .1 .2 6.081 2.242 1.445 1.072 .854 .710 .607 .531 .471 .424 .2 .3 6.324 2.294 1.478 1.096 .872 .725 .621 .542 .482 .433 .3 .4 6.588 2.347 1.511 1.120 .891 .741 .634 .554 .492 .443 .4 9.5 6.877 2.400 1.544 1.144 .911 .757 .648 .566 .503 .452 9.5 .6 7.200 2.455 1.577 1.169 .930 .773 .661 .578 .514 .462 .6 .7 7.569 2.510 1.611 1.194 .950 .789 .675 .590 .524 .472 .7 .8 8.010 2.565 1.646 1.219 .970 .806 .689 .603 .535 .481 .8 .9 8.589 2.622 1.681 1.244 .990 .822 .704 .615 .546 .491 .9 10.0 10.000 2.679 1.716 1.270 1.010 .839 . 718 j .627 .557 .501 10.0 .1 1.751 1.296 1.031 .856 .733 .640 .569 .511 .1 .2 1.787 1.322 1.051 .873 .747 .653 .580 .521 .2 .3 1.823 1.349 1.072 .891 .762 .666 .591 .532 .3 .4 1.860 1.375 1.094 .908 .777 .679 .602 .542 .4 ! 10.5 1.897 1.402 1.115 .926 .792 .692 .614 .553 I0..I .6 1.935 1.430 1.136 .944 .807 .705 .626 .563 .. .7 1.973 1.458 1.158 .962 .823 .719 .638 .574 .7| .8 2.012 1.486 1.180 .980 .838 .732 .650 .585 .8 .9 2.051 1.514 1.202 .998 .854 .746 .663 .596 • 9 f 11.0 2.089 1.542 1.225 1.017 870 .760 .675 .607 11.0 1 .1 2.129 1.571 1.248 1.036 .886 .774 .687 .618 .r .2 2.169 1.600 1.271 1.055 .902 .788 .700 .629 .2[ .3 2.209 1.629 1.294 1.074 .918 .802 .712 .640 .3\ .4 2.250 1.659 1.317 1.093 .935 .816 .725 .652 A 11.5 2.292 1.689 1.340 1.112 .951 .831 .738 .663 11.5 .6 2.333 1.719 1.364 1.132 .968 .845 .751 .675 .6 .7 2.375 1.749 1.388 1.152 .985 ,860 .764 .687 .7 .8 2.418 1.780 1.412 1.172 1.002 .875 .777 .699 .8 .9 2.461 1.811 1.437 1.192 1.019 .890 .790 .711 .9 12.0 2.505 1.842 1.461 1.212 1.036 .905 .804 .723 12.0 188 Slope Reduction Tables 10 20 30 40 50 60 70 80 90 100 12.1 2.548 1.874 1 .486 1.232 1 .054 .920 .817 .735 12.1 .2 2.593 1.906 1.511 1.253 1.071 .936 .831 .747 .2 .3 2.637 1.938 1.536 1.274 1 .089 .951 .844 .759 .3 .4 2.683 1.971 1.562 1.295 1.107 .967 .858 .772 .4 12.5 2.728 2.003 1.588 1.316 1.125 .983 .872 .784 12.5 .6 2.774 2.036 1.614 1.338 1.143 .999 .886 .797 .6 .7 2.821 2.070 1.640 1.359 1.162 1.015 .901 .810 .7 .8 2.867 2.103 1.666 1.381 1.180 1.031 .915 .823 .8 .9 2.915 2.137 1.693 1.403 1.199 1.047 .929 .836 .9 13.0 2.963 2.171 1.720 1.425 1.218 1.063 .944 .849 13.0 .1 3.011 2.206 1.747 1 .448 1.237 1 .080 .959 .862 .1 .2 3.060 2.241 1.774 1.470 1.256 1 .097 .973 .875 .2 .3 3.109 2.276 1.801 1.492 1 .275 1.113 .988 .888 .3 .4 3.159 2.311 1.829 1.515 1.294 1.130 1.003 .902 .4 13.5 3.209 2.347 1.857 1.538 1.314 1.147 1.018 .915 13.5 .6 3.260 2.383 1.885 1.561 1.334 1.164 1.034 .929 .6 .7 3.311 2.419 1 .914 1.585 1.354 1.182 1 .049 .943 .7 .8 3.362 2.456 1 .942 1.608 1.374 1.199 1.064 .957 .8 .9 3.414 2.493 1.971 1 . 632 1.394 1.217 1.080 .971 .9 14.0 3.467 2.530 2.000 1.656 1 .414 1.235 1 .096 .985 14.0 .1 3.520 2.567 2.029 1.680 1.435 1.252 1.111 .999 .1 .2 3.573 2.605 2.059 1.704 1 .455 1.270 1.127 1.013 .2 .3 3.627 2.643 2.089 1.729 1.476 1.288 1.143 1.028 .3 .4 3.682 2.682 2.119 1.754 1.497 1.307 1 . 159 1.042 .4 14.5 3.737 2.721 2.149 1.778 1.518 1.325 1.176 1.057 14.5 .6 3.792 2.760 2.179 1 .803 1.539 1.344 1.192 1.072 .6 .7 3.848 2.799 2.210 1 .829 1.561 1.362 1.209 1.086 .7 .8 3.904 2.839 2.241 1 .854 1.592 1.381 1.225 1.101 .8 .9 3.961 2.879 2.272 1.879 1.604 1 .400 1.242 1.116 .9 15.0 4.019 2.919 2.303 1.905 1.626 1 .419 1.259 1.131 15.0 .1 2.960 2.335 1 .931 1.648 1 .438 1 .276 1.147 .1 .2 3.001 2.366 1 .957 1.670 1 .457 1.293 1.162 .2 .3 3.042 2.398 1 .983 1.692 1 .477 1.310 1.177 .3 .4 3.083 2.431 2.010 1 .715 1 .496 1.327 1.193 .4 15.5 3.124 2.463 2.037 1.738 1 .516 1.345 1.208 15.5 .6 3.167 2.496 2.063 1.760 1.536 1.362 1.224 .6 .7 3.210 2.529 2 090 1.783 1.556 1.380 1.240 .7 .8 * 3.253 2.562 2.117 1 .806 1.576 1.398 1.256 .8 .9 3.296 2.596 2.145 1.830 1.596 1 .416 1.272 .9 16 0 3.339 2.629 2.173 1.853 1.616 1.434 1.288 16.0 189 Slope Reduction Tables 10 20 30 16.1 .2 .3 .4 16.5 .6 .7 .8 .9 17.0 .1 .2 .3 .4 17.5 .6 .7 .8 .9 18.0 .1 .2 .3 .4 18.5 .6 .7 .8 .9 19.0 .1 .2 .3 .4 19.5 .6 .7 .8 .9 20.0 40 50 3.383 2.663 3.427 2.697 3.472 2.732 3.517 2.766 3.562 2.801 3.608 2.836 3.653 2.871 3.699 2.907 3.746 2.943 3.792 2.979 3.839 3.015 3.887 3.051 3.935 3.088 3.982 3.125 4.031 3.162 4.080 3.200 4.129 3.238 4.179 3.276 4.229 3.314 4.279 3.352 4.329 3.391 4.380 3.430 4.432 3.469 4.483 3.509 4.535 3.548 4.588 3.588 4.640 3.628 4.693 3.669 4.747 3.710 4.801 3.751 4 .855 3.792 4.909 3.833 4.964 3.875 5.019 3.917 5.075 3.959 5.131 4.002 5.187 4.045 5.244 4.088 5.301 4.131 5.359 4.174 60 70 * 80 90 100 2.200 1.877 1.637 1.452 1.305 16.1 2.228 1.900 1.657 1.470 1.321 .2 2.256 1.924 1.678 1.488 1.337 .3 2.285 1.948 1.899 1.507 1.354 .4 2.313 1.972 1.720 1.526 1.371 16.5 2.342 1.997 1.741 1.544 1.387 .6 2.371 2.021 1.762 1.563 1.404 .7 2.400 2.046 1.784 1.582 1.421 .8 2.429 2.071 1.805 1.601 1.438 .9 2.459 2.096 1.827 1.620 1.456 17.0 2.488 2.121 1.849 1.639 1.473 .1 2.518 2.146 1.871 1.659 1.490 .2 2.548 2.171 1.893 1.678 1.508 .3 2.578 2.197 1.915 1.698 1.525 .4 2.609 2.223 1.937 1.718 1.543 17.5 2.639 2.249 1.960 1.738 1.561 .6 2.670 2.275 1.983 1.758 1.579 .7 2.701 2.301 2.005 1.778 1.597 • 8 2.732 2.327 2.028 1.798 1.615 • 9 2.764 2.354 2.051 1.818 1.633 18.0 2.795 2.381 2.074 1.839 1.652 .1 2.827 2.407 2.098 1.859 1.670 .2 2.859 2.434 2 . 122 1.880 1.689 .3 2.891 2.461 2.145 1.901 1.707 .4 2.923 2.489 2.168 1.922 1.726 18.5 2.956 2.516 2.192 1.943 1.745 .6 2.988 2.544 2.216 1.964 1.764 .7 3.021 2.572 2.240 1.985 1.783 .8 3.054 2.600 2.265 2.007 1.802 • 9 3.088 2.628 2.289 2.028 1.822 19.0 3.121 2 .656 2.314 2.050 1.841 .1 3.155 2.685 2.338 2.072 1.861 .2 3.189 2.713 2.363 2.094 1.880 .3 3.223 2.742 2.388 2.116 1.900 .4 3.257 2.771 2.413 2.138 1.920 19.5 3.291 2.800 2.438 2.160 1.940 .6 3.326 2.829 2 . 463 * 2.182 1.960 .7 3.361 2.858 2.489 2.205 1.980 .8 3.396 2.888 2.514 2 .227 2.000 .9 3.431 2.918 2.540 2.250 2.020 20.0 190 Cut Constants Constants for Cut of 1 deg. for Different Diams. Diam. A" PI- K" Pi. A" PI. Vs" PI. A" PI. W PI. Inches Inches Inches Inches Inches Inches Inches 20 .3555 .3577 .3599 .3621 .3643 .3665 21 .37295 .37515 .37735 .37955 .38175 .38395 22 .3904 .3926 .3948 .3970 .3992 .4014 23 .40785 .41005 .41225 .41445 .41665 .41885 24 .4253 .4275 .4297 .4319 .4341 .4363 25 .44275 .44495 .44715 .44935 .45155 .45375 26 .46020 .46240 .46460 .46680 .46900* .47120 27 .47765 .47985 .48205 .48425 .48645 .48860 28 .4951 .4973 .4995 .5017 .5039 .5061 29 .51255 .51475 .51695 .51915 .52135 .52355 30 .5300 .5322 .5344 .5366 .5388 .5410 31 .54745 .54965 .55185 .55405 .55625 .55845 32 .56490 .56710 .56930 .57150 .57370 .57590 33 .5824 .5846 .5868 .5890 .5912 .5934 34 .59985 .60205 .60425 .60645 .60865 . .61085 35 .61730 .61950 .62170 .62390 .62610 .62830 36 .6347 .6369 .6391 .6413 .6435 .6457 37 .65215 .65435 .65455 .65875 .66095 .66315 38 .66960 .67180 .67400 .67620 .67840 .68060 39 .6870 .6892 .6914 .6936 .6958 .6980 40 .70445 .70665 .70885 .71105 .71325 .71545 41 .72190 .72415 .72630 .72840 .73070 .73290 42 .7394 .7416 .7438 .7460 .7482 .7504 43 .75685 .75905 .76125 .76345 .76565 .76785 44 .77430 .77650 .77870 .78090 .78310 .78530 45 .7919 .7941 .7963 .7985 .8007 .8029 46 .80935 .81155 .81375 .81595 .81815 .82035 47 .82680 .82900 .83120 .83340 .83560 .83780 48 .8442 .8464 .8486 .8508 .8530 .8552 49 .86165 .86385 .86605 .86825 .87045 .87265 50 .87910 .88130 .88350 .88570 .88790 .89010 51 .8965 .8982 .9004 .9026 .9050 .9072 52 .91395 .91565 .91785 .92005 .92245 .92405 53 .93140 .93310 .93530 .93750 .93990 .94150 54 .9489 .9511 .9533 .9555 .9577 .9599 55 .96635 .96855 .97075 .97295 .97315 .97735 56 .98380 .98600 .98820 .99040 .99260 .99480 57 1.0012 1.0034 1 .0056 1.0078 1.0100 1.0122 58 1.01865 1.02085 1.02305 1.02525 1.02745 1.02965 59 1.03610 1.03830 1.04050 1.04270 1.04490 1.04710 60 1 .0536 1.0558 1.0580 1.0602 1.0624 1.0646 61 1.07105 1.07325 1.07545 1.07765 1.07985 1.08205 62 1.08850 1.09070 1.09290 1.09510 1.09730 1.09950 63 1 . 1059 1.1081 1.1103 1.1125 1.1147 1.1169 64 1.12335 1 . 12555 1.12775 1.12995 1.13215 1 . 13435 65 1 . 14080 1 . 14300 1 . 14520 1 . 14740 1 . 14960 1.15180 66 1.1583 1 . 1605 1.1627 v 1.1649 1.1671 1.1693 67 1 . 17575 1.17795 1.18015 1.18235 1 . 18455 1.18675 68 1.19320 1 . 19540 1.19760 1 . 19980 1.20200 1.20420 69 1.2106 1.2128 1.2150 1.2172 1.2194 1.2216 70 1.22805 1.23025 1.23245 1.23465 1.23685 1.23905 71 1.24550 1.24770 1.24990 1.25210 1.25430 1.25650 72 1 . 2629 1.2651 1.2673 1.2695 1.2717 1.2739 191 Circumferences and Areas of Circles Diam. Circum. Area Diam. Circum. Area Diam. Circum. Area 23 . 30 . 16 . 50.265 201.06 A 72.649 420.00 X 95 033 718.69 A 50.658 204.22 X 73.042 424 . 56 A 95.426 724 . 64 X 51.051 207.39 A 73.435 429.13 A 95.819 730 . 62 A 51.444 210.60 A 73.827 433.74 A 96.211 736 . 62 A 51.836 213.82 A 74.220 438.36 A 96.604 742 . 64 A 52.229 217.08 X 74.613 443.01 A 96.997 748.69 A 52.622 220.35 A 75.006 447 . 69 31 . 97.389 754.77 7 A 53.014 223.65 24 . 75.398 452.39 A 97.782 760.87 17 . 53.407 226.98 A 75.791 457.11 A 98.175 766.99 Vs 53.800 230.33 X 76.184 461.86 A 98.567 773 . 14 X 54 . 192 233.71 A 76.576 466.64 A 98.960 779.31 Vs 54 . 585 237 . 10 A 76.969 471.44 A 99.353 785.51 A 54.978 240 . 53 A 77.362 476.26 A 99.746 791.73 A 55.371 243.98 A 77.754 481.11 A 100.138 797.98 A 55.763 247.45 A 78 . 147 485.98 32 . 100.531 804 . 25 A 56.156 250.95 25 . 78.540 490.87 A 100.924 810.54 18 . 56.549 254.47 A 78.933 495.79 A 101.316 816.86 • Vs 56.941 258.02 X 79.325 500.74 A 101.709 823.21 A 57.334 261.59 A 79.718 505.71 A 102 . 102 829 . 58 A 57.727 265.18 A 80.111 510.71 A 102.494 835.97 A 58.119 268.80 A 80 . 503 515.72 A 102.887 842.39 Ai 58.512 272.45 A 80.896 520.77 A 103.280 848.83 A 58.905 276.12 A 81.289 525.84 33 . 103.673 855.30 A 59 . 298 279.81 26 . 81.681 530.93 3 ^ 104.065 861.79 19 . 59.690 283.53 A 82.074 536.05 X 104.458 868.31 A 60.083 287.27 X 82.467 541.19 A 104.851 874 . 85 X 60.476 291.04 A 82 . 860 546.35 A 105.243 881.41 A 60.868 294.83 A 83 . 252 551.55 A 105.636 888.00 A 61.261 298.65 A 83 . 645 556.76 A 106.029 894 . 62 x 61.654 302.49 A 84.038 562.00 A 106.421 901.26 62.046 306.35 A 84.430 567.27 34 . 106.814 907.92 A 62.439 310.24 27 . 84.823 572 . 56 3 ^ 107.207 914.61 20 . 62.832 314.16 A 85.216 577 . 87 A 107.600 921.32 A 63.225 318.10 X 85.608 583.21 A 107.992 928.06 X 63.617 322.06 A 86.001 588 . 57 A 108.385 934.82 A 64.010 326.05 A 86 . 394 593.96 A 108.778 941.61 A 64.403 330.06 A 86.786 599 . 37 A 109 . 170 948.42 A 64.795 334 . 10 A 87 . 179 604.81 A 109.563 955.25 A 65 . 188 338.16 A 87.572 610.27 35 . 109.956 962.11 A 65.581 342.25 28 . 87.965 615.75 A 110.348 969.00 21 . 65.973 346.36 * A 88.357 621.26 A 110.741 975.91 A 66.366 350 . 50 A 88.750 626 . 80 A 111.134 982.84 X • 66.759 354 . 66 A 89 . 143 632.36 A 111.527 989.80 A 67.152 358.84 A 89 . 535 637.94 A 111.919 996.78 A 67.544 363.05 A 89.928 643.55 A 112.312 1003.8 A 67.937 367.28 A 90.321 649.18 A 112.705 1010.8 A 68.330 371.54 A 90.713 654 . 84 36 . 113.097 1017.9 A 68.722 375.83 29 . 91.106 660 . 52 A 113.490 1025.0 22 . 69.115 380 . 13 A 91.499 666.23 A 113.883 1032.1 A 69 . 508 384.46 A 91.892 671.96 A 114.275 1039 2 X 69.900 388.82 A 92.284 677.71 A 114.668 1046.3 A 70 . 293 393.20 A 92 . 677 683.49 A 115.061 1053.5 A 70.686 397.61 A 93.070 689.30 A 115.454 1060.7 A 71.079 402.04 A 93.462 695.13 A 115.846 1068.0 X 71.471 406.49 A 93.855 700.98 37 . 116.239 1075.2 A 71.864 410.97 30 . 94 . 248 706.86 A 116.632 1082.5 23 . 72.257 415.48 A 94 . 640 712.76 A 117.024 1089.8 192 Circumferences and Areas of Circles — -Continued Diam. Circum. Area Diam. Circum. Area Diam. Circum. Area 37. 44 . 51 . H 117.417 1097 . 1 139.801 1555.3 *A- 162.185 2093.2 l A 117.810 1104.5 Vs 140 . 194 1564.0 X 162.577 2103.3 Vs 118.202 1111.8 X 140.586 1572.8 Vs 162.970 2113.5 X 118.596 1119.2 Vs 140.979 1581.6 52 . 163.363 2123.7 % 118.988 1126.7 45 . 141 .372 1590.4 Vs 163.756 2133.9 38 . 119.381 1134.1 Vs 141.764 1599.3 X 164.148 2144.2 Vs 119.773 1141.6 X 142.157 1608.2 Vs 164.541 2154.5 X 120.166 1149.1 Vs 142.550 1617.0 V. 164.934 2164.8 Vs 120.559 1156.6 V 2 142.942 1626.0 Vs 165.326 2175.1 H 120.951 1164.2 Vs 143.335 1634.9 X 165.719 2185.4 Vs 121.344 1171.7 X 143.728 1643.9 Vs 166.112 2195.8 X 121.737 1179.3 Vs 144.121 1652.9 53 . 166.504 2206.2 Vs 122.129 1186.9 46 . 144.513 1661.9 Vs 166.897 2216.6 39 . 122.522 1194.6 Vs 144.906 1670.9 X 167.290 2227.0 3^ 122.915 1202.3 X 145.299 1680.0 Vs 167.683 2237.5 X 123.308 1210.6 Vs 145.691 1689.1 V. 168.075 2248.0 Vs 123.700 1217.7 V 2 146.084 1698.2 Vs 168.468 2258.5 H 124.093 1225.4 Vs 146.477 1707.4 Vi 168.861 2269 . 1 Vs 124.486 1233.2 X 146.869 1716.5 Vs 169.253 2279.6 X 124.878 1241 .0 Vs 147.262 1725.7 54 . 169.646 2290.2 Vs 125.271 1248.8 47. 147.655 1734.9 Vs 170.039 2300.8 40 . 125.664 1256.6 ■ Vs ' 148.048 1744.2 X 170.431 2311.5 Vs 126.056 1264.5 X 148.440 1753.5 Vs 170.824 2322 . 1 X 126.449 1272.4 Vs 148.833 1762.7 V, 171 .217 2332.8 Vs 126.842 1280.3 Vi 149.226 1772.1 Vs 171.609 2343.5 V* 127.235 1288.2 Vs 149.618 1781.4 Vi 172.002 2354.3 Vs 127.627 1296.2 Vi 150.011 1790.8 Vs 172.395 2365.0 Vi 128.020 1304.2 Vs 150.404 1800 . 1 55 . 172.788 2375.8 Vs 128.413 1312.2 48 . 150.796 1809.6 Vs 173.180 2386.6 41 . 128.805 1320.3 Vs 151.189 1819.0 X 173.573 2397.5 Vs 129 . 198 1328.3 X 151.582 1828.5 Vs 173.966 2408.3 X 129.591 1336.4 Vs 151.975 1837.9 V 2 174.358 2419.2 Vs 129.983 1344.5 V 2 152.367 1847.5 Vs 174.751 2430 . 1 Vi 130.376 1352.7 Vs 152.760 1857.0 X 175.144 2441 . 1 Vs 130.769 1360.8 % 153.153 1866.5 Vs 175.536 2452.0 X 131.161 1369.0 Vs 153.545 1876.1 56 . 175.929 2463.0 Vs 131.554 1377.2 49 . 153.938 1885.7 Vs 176.322 2474.0 42 . 131.947 1385.4 Vs 154.331 1895.4 X 176.715 2485.0 Vs 132.340 1393.7 X 154.723 1905.0 Vs 177.107 2496.1 X 132.732 1402.0 Vs 155.116 1914.7 V 2 177 . 500 2507.2 Vs 133 . 125 1410.3 V 2 155.509 1924.4 Vs 177.893 2518.3 X 133.518 1418.6 Vs 155.902 1934.2 X 178.285 2529.4 Vs 133.910 1427.0 Vi 156.294 1943.9 Vs 178.678 2540.6 X 134.303 1435.4 Vs 156.687 1953.7 57 . 179.071 2551.8 Vs 134.696 1443.8 50 . 157.080 1963.5 Vs 179.463 2563.0 43 . 135.088 1452.2 157.472 1973 . 3 X 179.856 2574.2 Vs 135.481 1460.7 157.865 1983.2 Vs 180.249 2585.4 X 135.874 1469 . 1 3 /6 158.258 1993.1 V 2 180.642 2596.7 Vs 136.267 1477.6 158.650 2003.0 Vs 181.034 2608.0 V 2 136.659 1486.2 A 159.043 2012.9 X 181.427 2619.4 Vs 137.052 1494.7 X 159.436 2022.8 Vs 181.820 2630.7 X 137.445 1503.3 Vs 159.829 2032.8 58 . 182.212 2642 . 1 Vs 137.837 1511.9 51 . 160.221 2042.8 Vs 182.605 2653.5 44 . 138.230 1520.5 Vs 160.614 2052.8 X 182.998 2664.9 Vs. 138.623 1529.2 X 161.007 2062.9 Vs 183-390 2676.4 X 139.015 1537.9 Vs 161.399 2073.0 Vi 183.783 2687.8 Vs 139.408 1546.6 V 2 161.792 2083 . 1 Vs 184.176 2699.3 193 Circumferences and Areas of Circles — Continued Diam . Circum. Area Diam. Circum. Area Diam. Circum. Area 5 8.X 184.569 2710.9 65.J4 206.952 3408.2 73 . 229.336 4185.4 a 184.961 2722.4 66 . 207.345 3421.2 Vs 229.729 4199.7 59 . 185.354 2734.0 Vs 207.738 3434.2 A 230.122 4214.1 Vs 185.747 2745.6 A 208.131 3447.2 Vs 230.514 4228.5 A 186.139 2757.2 X 208.523 3460.2 A 230.907 4242.9 Vs 186.532 2768.8 A 208.916 3473.2 Vs 231.300 4257.4 A 186.925 2780.5 Vs 209.309 3486.3 X 231.692 4271.8 Vs 187.317 2792.2 X 209.701 3499.4 Vs 232.085 4286.3 X 187.710 2803.9 Vs 210.094 3512.5 74 . 232.478 4300.8 % 188.103 2815.7 67 . 210.487 3525.7 Vs 232.871 4315.4 60 . 188.496 2827.4 A 210.879 3538.8 A 233.263 4329.9 Vs 188.888 2839.2 X 211.272 3552.0 Vs 233.656 4344.5 A 189.281 2851.0 Vs 211.665 3565.2 A 234.049 4359.2 Vs 189.674 2862.9 A 212.058 3578.5 Vs 234.441 4373.8 A 190.066 2874.8 Vs 212.450 3591.7 X 234.834 4388.5 Vs X 190.459 2886 . 6 V 212.843 3605.0 Vs 235.227 4403 . 1 190.852 2898.6 Vs 213.236 3618.3 75 . 235.619 4417.9 % 191.244 2910.5 68 . 213.628 3631.7 Vs 236.012 4432.6 61 . 191.637 2922.5 Vs 214.021 3645.0 A 236.405 4447.4 Vs 192.030 2934.5 X 214.414 3658.4 Vs 236.798 4462.2 A 192.423 2946.5 Vs 214.806 3671.8 A 237 . 190 4477.0 192.815 2958.5 A 215.199 3685.3 Vs 237.583 4491.8 H 193.208 2970.6 Vs 215.592 3698.7 X 237.976 4506.7 193.601 2982.7 X 215.984 3712.2 Vs 238.368 4521.5 % 193.993 2994.8 Vs 216.377 3725.7 76 . 238.761 4536.5 7 A 194.386 3006.9 69 . 216.770 3739.3 Vs 239.154 4551.4 62 . 194.779 3019.1 Vs 217.163 3752.8 A 239.546 4566.4 3 ^ 195.171 3031.3 . X 217.555 3766.4 Vs 239.939 4581.3 M 195.564 3043.5 Vs 217.948 3780.0 A 240.332 4596.3 % 195.957 3055.7 A 218.341 3793.7 Vs 240.725 4611.4 A 196.350 3068 0 Vs X 218.733 3807.3 X 241.117 4626.4 % 196.742 3080.3 219.126 3821.0 Vs 241.510 4641.5 X 197.135 3092.6 Vs 219.519 3834.7 77 . 241.903 4656.6 % 197.528 3104.9 70 . 219.911 3848.5 Vs 242.295 4671.8 63 . 197.920 3117.2 Vs 220.304 3862.2 A 242.688 4686.9 3 ^ 198.313 3129.6 X 220.697 3876.0 Vs 243.081 4702.1 198.706 3142.0 Vs 221.090 3889.8 M 243.473 4717.3 % 199.098 3154.5 A 221.482 3903.6 Vs 243.866 4732.5 3 ^ 199.491 3166.9 Vs 221.875 3917.5 X 244.259 4747.8 199.884 3179.4 x 222.268 3931.4 Vs 244.652 4763 . 1 % 200.277 3191.9 Vs 222.660 3945.3 78 . 245.044 4778.4 % 200.669 3204.4 71 . 223.053 3959.2 Vs 245.437 4793.7 64 . 201.062 3217.0 Vs 223.446 3973.1 A 245.830 4809.0 M 201.455 3229.6 X 223.838 3987.1 Vs 246.222 4824.4 A 201.847 3242.2 Vs 224.231 4001.1 A 246.615 4839.8 Vs 202.240 3254.8 A 224.624 4015.2 Vs 247.008 4855.2 A 202.633 3267.5 Vs 225.017 4029.2 X 247.400 4870.7 Vs 203.025 3280.1 % 225.409 4043.3 Vs 247.793 4886.2 X 203.418 3292.8 Vs 225.802 4057.4 79 . 248.186 4901.7 Vs 203.811 3305.6 72 . 226.195 4071.5 Vs 248 . 579 4917.2 65 . 204.204 3318.3 Vs 226.587 4085.7 A 248.971 4932.7 A 204.596 3331.1 A 226.980 4099.8 Vs 249.364 4948.3 A 204.989 3343.9 Vs 227.373 4114.0 A 249.757 4963.9 Vs 205.382 3356.7 A 227.765 4128.2 Vs 250 . 149 4979.5 A 205.774 3369.6 Vs 228.158 4142.5 X 250.542 4995.2 Vs 206.167 3382.4 X 228.551 4156.8 Vs 250.935 5010.9 X 206.560 3395.3 i Vs i 228.944 4171.1 80 . 251.327 5026.5 194 Circumferences and Areas of Circles — Continued Diam. Circum. Area Diam. Circum. Area Diam. Circum. Area 80. 87. 94. A 251.720 5042.3 K 274.104 5978.9 As 296 . 488 6995.3 A 252.113 5058.0 As 274.497 5996.0 A 296.881 7013.4 A 252 . 506 •f)73 . 8 A 274.889 6013.2 A 297.273 7032.5 A 252 . 898 5089 . 6 A 275.282 6030.4 A 297.666 7051.0 A 253.291 5105.4 A 275.675 6047.6 A 298.059 7069.6 A 253.684 5121.2 A 276.067 6064.9 95. 298.451 7088.2 Vs 254.076 5137.1 88. 276.460 6082.1 As 298.844 7106.9 81. 254.469 5153.0 As 276.853 6099.4 A 299 . 237 7125.6 A 254.862 5168.9 A 277.246 6116.7 A ■ 299.629 7144.3 A 255.254 5184.9 A 277.638 6134.1 A. 300.022 7163.0 A 255.647 5200.8 A 278.031 6151.4 Vs 300.415 7181.8 A. 256.040 5216.8 A 278.424 6168.8 A 300.807 7200.6 A 256.433 5232.8 A 278.816 6186.2 A 301.200 7219.4 A 256.825 5248.9 A 279.209 6203.7 96. 301.593 7238.2 A 257.218 5264.9 89. 279.602 6221.1 As 301.986 7257.1 82 257.611 5281.0 As 279.994 6238.6 A, 302.378 7276.0 A 258.003 5297 . 1 A 280.387 6256 . 1 A 302.771 7294.9 A 258.396 5313.3 A 280.780 6273.7 A. 303.164 7313.8 A 258.789 5329.4 A. 281.173 6291.2 A 303.556 7332.8 A 259 . 181 5345.6 Vs 281.565 6308.8 A 303.949 7351.8 A 259.574 5361.8 A 281.958 6326.4 A 304.342 7370.8 A 259.967 5378 . 1 As 282.351 6344.1 97. 304.734 7389.8 A 260.359 5394.3 90. 282.743 6361.7 As 305 . 127 7408.9 83. 260.752 5410.6 As 283.136 6379.4 A 305.520 7428.0 A 261.145 5426.9 A 283.529 6397.1 A 305.913 7447.1 A 261.538 5443.3 A 283.921 6414.9 A 306.305 7466.2 A 261.930 5459.6 A 284.314 6432.6 A 306.698 7485.3 A 262.323 5476.0 A 284.707 6450.4 A 307.091 7504.5 A 262.716 5492.4 A 285.100 6468.2 A 307.483 7523.7 A 263.108 5508.8 A 285.492 6486.0 98. 307.876 7543.0 A 263.501 5525.3 91. 285 . 885 6503.9 As 308.269 7562.2 84. 263.894 5541.8 A 286.278 6521.8 A 308.661 7581.5 A 264.286 5558.3 A 286.670 6539.7 A 309.054 7600.8 A 264.679 5574.8 A 287.063 6567.6 A 309.447 7620.1 A 265.072 5591.4 A 287.456 6575.5 A 309.840 7639.5 A 265.465 5607.9 A 287.848 6593.5 A 310.232 7658.9 A 265.857 5624.5 A 288.241 6611.5 A 310.625 7678.3 A 266.250 5641.2 A 288.634 6629.6 99. 311.018 7697.7 A 266.643 5657.8 92. 289.027 6647.6 A 311.410 7717.1 85. 267.035 5674.5 A 289.419 6665.7 A 311.803 7736.6 A 267.428 5691.2 A 289.812 6683.8 A 312.196 7756.1 A 267.821 5707.9 A 290.205 6701.9 A 312.588 7775.6 A •268.213 5724.7 A 290.597 6720 . 1 A 312.981 7795.2 A 268.606 5741.5 A 290.990 6738.2 A 313.374 7814.8 A 268.999 5758.3 A 291.383 6756.4 A 313.767 7834.4 A 269.392 5775.1 A 291.775 6774.7 100. 314.159 7854.0 A 269.784 5791.9 93. 292.168 6792.9 86. 270 . 177 5808.8 As 292.561 6811.2 A 270.570 5825.7 A 292.954 6829.5 A 270.962 5842.6 Vs 293.346 6847.8 A 271.355 5859.6 A. 293.739 6866.1 A 271.748 5876.5 Vs 294 . 132 6884.5 A 272 . 140 5893.5 A 294.524 6902.9 A 272.533 5910.6 A 294.917 6921.3 A 272.926 5927.6 94. 295.310 6939.8 87. 273.319 5944.7 As 295.702 6958.2 A 273.711 5961.8 A 296.095 6976.7 195 196 Lengths of Circular Arcs Lengths of the Arcs of Circles to the Radius 1. Degrees 0 i0. 00000 1 0.01745 2 0.03490 3 i0. 05235 00000 60 32925! 61 65850! 62 98776 63 31701 64 64626! 65 97551 66 30476! 67 63402 ! 68 96327 69 Minutes Seconds 0.06981 0.08726 0.10471 0.12217 _ 0.13962 9 0.15707 1.04719 75512 120 1.06465 08437 121 1.08210 41362 122 1.09955 74288 123 1.11701 07213 124 1.13446 40138 125 1.15191 73063 126 1.16937 05988 127 1.18682 38914 128 1.20427 71839 129 2.09439 2.11184 2.12930 2.14675 2.16420 2.18166 2.19911 2.21656 2.23402 2.25147 51024 83949 16874 49800 82725 15650 48575 81500 14426 47351 0.00000 0.00029 0.00058 0.00087 0.00116 0.00145 0.00174 0.00203 0.00232 0.00261 00000 08882 17764 26646 35528 44410 53293 62175 71057 79939 o.ooooo ooooo 0.00000 48481 0.00000 96963 0.00001 45444 0.00001 93925 0.00002 42407 0.00002 90888 0.00003 39370 0.00003 87851 0.00004 36332 10 0.17453 : 1 .22173 04764 130 2.26892 80276 10 0.00290 88821 0.00004 84814 11 0.19198 12 0.20943 13 0.22689 0.24434 0*. 26179 0.27925 0.29670 0.31415 0 33161 62177 95102 28028 60953 93878 26803! 59728! 92654 25579! 1.23918 1.25663 27409 29154 30899 1.32645 34390 1.36135 1.37881 376891131 70614 03540 36465 69390 02315 35240 68166 138 010911139 2.28638 2.30383 2.32128 2.33874 2.35619 2.37364 2.39110 2.40855 2.42600 13201 11 46126 12 79052 11977 44902 77827 10752 17 43678 18 76603 19 0.00319 0 . 00349 0.00378 0.00407 0.00436 0.00465 0.00494 0.00523 59878 0.00552 97703 06585 15467 24349 33231 42113 0.00005 0.00005 0.00006 0 . 00006 0.00007 0.00007 0 . 00008 0 . 00008 0.00009 33295 81776 30258 78739 27221 75702 24183 72665 21146 20 0.34906 585041 80 1.39626 34016 140 2.44346 09528 20 0.00581 77642 20 0.00009 69627 36651 91429 1 3839? 24354 40142 57280 41887 90205 43633 23130 45378 56055 j 47123 88980 48869 21906 50614 54831 1.41371 1.43116 1.44862 1.46607 1.48352 1.50098 1.51843 1.53588 .55334 669411141 99866 142 32792! 143 65717 |144 986421145 315671146 64492 '147 97418 1148 303431149 2.46091 2.47836 2.49582 2.51328 2.53072 2.54818 2.56563 2.58308 2 . 60054 42453 75378 08304 41229 74154 07079 40004 72930 05855 0.00610 0.00639 0.00669 0.00698 0.00727 0.00756 0.00785 0.00814 0.00843 86524 21 95406 22 04288 23 1317024 22052 30934 26 3981627 48698 28 5758129 0.00010 0.00010 0.00011 0.00011 0.00012 0.00012 0.00013 0.00013 0.00014 18109 66590 15071 63553 12034 60516 08997 57478 05960 30 0.52359 87756 90 1.57079 63268 150 2.61799 38780 0.00872 66463 30 0.00014 54441 31 32 33 34 0 35 ;0 36 10 37 ;0 38 0 39 0 54105 55850 57595 59341 61086 62831 64577 66322 68067 20681 91 53606 92 86532 93 19457 94 52382 95 85307! 96 18232 ! 97 51158! 98 84083 99 1 . 58824 1.60570 1.62315 1 . 64060 1.65806 1.67551 1.69296 1.71042 1.72787 96193 |151 29118 152 62044 153 94969[j 154 27894! 155 608191156 93744 157 26670 158 59595! 159 2.63544 2.65290 2.67035 2.68780 2.70526 2.72271 2.74016 2.75762 2.77507 3510739 04630 37556 70481 03406 36331 69256 02182 0.00901 0.00930 0.00959 0.00989 0.01018 0.01047 0.01076 28637 0.01105 3751938 0.01134 4640139 01991 10873 0.00015 0.00015 0.00015 0.00016 0.00016 0.00017 0.00017 0.00018 0.00018 02922 51404 99885 48367 96848 45329 93811 42292 90773 40 0.69813 17008 100 1.74532 925201 160 2.79252 68032 40 0.01163 55283 40 0.00019 39255 49933)101 82858 102 15784 103 48709*! 104 816341105 14559 106 47484,107 80410!!l08 13335109 , \t — 0.87266 462601110 71558 73303 75049 76794 78539 80285 82030 83775 85521 1.76278 1 . 78023 1.79768 1.81514 1.83259 1 . 85004 1.86750 1.88495 1.90240 25445 58370 91296 24221 57146! 90071 22996! 55922| 88847* 2.80998 2.82743 2 . 84488 2.86233 2.87979 2.89724 2.91469 2.93215 2.94960 00957 33882 66808 43 99733 44 32658 45 65583 46 98508 47 31434 48 64359 49 0.01192 0.01221 0.01250 0.01279 0.01308 0.01338 0.01367 0.01396 0.01425 64166 < 73048 ^ 81930 { 90812 99694 < 08576 ^ 17458 47 26340 48 35222 49 0.00019 0.00020 0.00020 0.00021 0.00021 0.00022 0.00022 0.00023 0.00023 87736 36217 84699 33180 81662 30143 '78624 27106 75587 50 1.91986 21772 170 2.96705 97284 50 0.01454 44104 50 0.00024 24068 0.89011 0.90757 0.92502 0.94247 0.95993 0.97738 0.99483 1.01229 1.02974 79185! Ill 12110 112 45036 113 77961 114 10886 115 43811 116 76736117 096621118 42587119 1.93731 1.95476 1.97222 1.98967 2.00712 2.02458 2.04203 2.05948 2.07694 54697* 171 87622 172 20548 173 53473 174 86398 175 19323 176 52248)177 85174 178 18099 179 2.98451 3.00196 3.01941 3.03687 3.05432 3.07177 3.08923 3.10668 3.12413 30209 63134 96060 28985 6191055 94835 56 27760 57 60685 58 9361159 0.01483 0.01512 0.01541 0.01570 0.01599 0.01628 0.01658 0.01687 0.01716 52986 61869 70751 79633 88515 97397 06279 15161 24043 59 0.00024 0.00025 0.00025 0.00026 0.00026 0.00027 0.00027 0.00028 0.00028 72550 21031 69513 17994 66475 14958 63437 11919 60401 60 1 .04719 75512*120 2.09439 51024180 3.14159 2653660 0.01745 3292560 0.00029 08882 197 1 Length Corrections LENGTH CORRECTION FOR 100.00 FT. FROM 0 TO 5.9 RISE Rise Angle Cor. Rise Angle Cor. Rise Angle Cor. .0 2.0 l°-09' .02014 4.0 2°-18' .08056 .1 2.1 1°-13' .02255 4.1 2°-21' .08410 .2 2.2 1°-16' .02444 4.2 2°-25' .08894 .3 0°-ll' .00051 2.3 l°-20' .02708 4.3 2°-28' .09266 .4 0°-14' .00083 2.4 l°-23' .02914 4.4 2°-32' .09773 .5 0°-18' .00137 2.5 l°-26' .03129 4.5 2°-35' .10163 .6 0°-21' .00187 2.6 l°-30' .03427 4.6 2°-39' . 10694 .7 0°-25' .00264 2.7 l°-33' .03659 4.7 2°-42' .11101 .8 0°-28' .00332 2.8 l°-37' .03980 4.8 2°-46' .11656 .9 0°-31' .00407 2.9 l°-40' .04231 4.9 2°-49' .12081 1.0 0°-35' .00518 3.0 l°-44' .04576 5.0 2°-52' .12514 1.1 0°-38' .00611 3.1 l°-47' .04843 5.1 2°-56' .13102 1.2 0°-42' .00746 3.2 l°-50' .05119 5.2 2°-59' .13553 1.3 0°-45' .00857 3.3 l°-54' .05498 5.3 3°-03' .14165 1.4 0°-49' .01016 3.4 l°-57' .05791 5.4 3°-06' .14633 1.5 0°-52' .01144 3.5 2°-01' .06194 5.5 3°-09' .15109 1.6 0°-55' .01280 3.6 2°-04' .06505 5.6 3°-12' .15592 1.7 0°-59' .01473 3.7 2°-08' .06931 5.7 3°-16' .16249 1.8 l°-02' .01626 3.8 2°-ll' .07260 5.8 3°-20' .16918 1.9 l°-06' .01843 3.9 2°-15' .07716 5.9 3°-23' .17430 FROM 6.0 TO 11.9 RISE Rise Angle Cor. Rise Angle Cor. Rise Angle Cor. 6.0 3°-27' .18123 8.0 4°-35' .32085 10.0 5°-43' .49982 6.1 3°-30' .18652 8.1 4°-38' .32786 10.1 5°-47' .51159 6.2 3°-33' .19189 8.2 4°-42' .33739 10.2 5°-50' .52052 6.3 3°-36' .19733 8.3 4°-45' .34463 10.3 5°-53' .52952 6.4 3°-40' .20470 8.4 4°-49' .35442 10.4 5°-57' .54165 6.5 3°-44' .21221 8.5 4°-52' .36182 10.5 6°-00' .55083 6.6 3°-47' .21793 8.6 4°-55' .36932 10.6 6°-04' .56319 6.7 3°-50' .22373 8.7 4°-59' .37943 10.7 6°-07' .57256 6.8 3°-54' .23157 8.8 5°-02' .38711 10.8 6°-10' .58201 6.9 3°-57' .23812 8.9 5°-06' .39746 10.9 6°-14' .59472 7.0 4°-01' .24563 9.0 5°-09' .40532 11.0 6°-17' .60435 7.1 4°-04' .25178 9.1 5°-12' .41325 11.1 6°-21' .61731 7.2 4°-07' .25801 9.2 5°-16' .42396 11.2 6°-24' .62712 7.3 4°-ll' .26643 9.3 5°-19' .43207 11.3 6°-27' .63700 7.4 4°-14' .27283 9.4 5°-23' .44303 11.4 6°-31' .65031 7.5 4°-18' .28149 9.5 5°-26' .45133 11.5 6°-34' .66038 7.6 4°-21' .28807 9.6 5°-29' .45970 11.6 6°-38' .67394 7.7 4°-25' .29696 9.7 5°-33' .47098 11.7 6°-41' .68419 7.8 4°-28' .30372 9.8 5°-36' .47955 11.8 6°-44' .69453 7.9 4°-32' .31383 9.9 5°-40' .49107 11.9 6°-48' .70843 198 Conversion Table Conversion Table Basis: I cubic foot of water at 39.1°F. = = 62 . 425 pounds. 1 U. S. gallon = 231 cubic inches. 1 imperial gallon = 277.274 cubic inches.* U. S. gallon 231.000000 cubic inches. U. S. gallon = 0.133681 cubic foot. U. S. gallon = 0.833111 imperial gallon. U. S. gallon = 3.785434 liters. U. S. gallon of water at 39.1 °F . . . = 8 . 345009 pounds. Imperial gallon 277.274000 cubic inches. Imperial gallon . = 0 . 160459 cubic foot. Imperial gallon . . . = 1.200320 U. S. gallons. Imperial gallon . . . = 4.543734 liters. Imperial gallon of water at 39. 1°F. . . . . . . = 10.016684 pounds.* Cubic foot — 7.480519 U. S. gallons. Cubic foot = 6.232103 imperial gallons. Cubic foot = 28.317016 liters. Cubic foot of water at 39.1 °F = 62 . 425000 pounds. Cubic foot of water at 39.1 °F . . . = 0.031212 ton. Cubic inch — 0.004329 U. S. gallon. Cubic inch = 0 . 003607 imperial gallon. Cubic inch = 0.016387 liter. Cubic inch of water at 39 . 1°F = 0.036126 pound. Cubic inch of water at 39 . 1°F ........ . . . = 0 . 578009 ounce. Pound of water at 39 . 1°F = 27.681217 cubic inches. Pound of water at 39 . 1°F = 0.016019 cubic foot. Pound of water at 39 . 1°F = 0.119832 U. S. gallon. Pound of water at39.1°F = 0 . 099833 imperial gallon. Pound of water at 39 . 1°F . . . = 0.453617 liter. Liter 0.264170 U. S. gallon. Liter . . . = 0 . 220083 imperial gallon. Liter = 61.023378 cubic inches. Liter = 0.035314 cubic foot. Liter of water at 39 . 1°F . . . = 2 . 204505 pounds. *The British imperial gallon is usually defined as being equal to 277 . 274 cubic inches, or 10 pounds of pure water at the temperature of 62°F. when the barometer is at 30 inches. 199 Equivalents CONVENIENT EQUIVALENTS 1 second-foot equals 40 California miner’s inches. (Law of March 23, 1901.) 1 second-foot equals 38.4 Colorado miner’s inches. 1 second-foot equals 7.48 United States gallons per second; equals 448.8 gallons per mintue; equals 646 317 gallons per day. 1 second-loot equals 6.23 British imperial gallons per second. 1 second-foot for one year covers one square mile 1,131 feet deep; 13.57 inches deep. 1 second-foot for one year equals 31 536 000 cubic feet. 1 second-foot equals about one acre-inch per hour. 1 second-foot falling 10 feet equals 1 . 136 horse-power. 100 California miner’s inches equal 18 . 7 United States gallons per second. 100 California miner’s inches equal 96.0 Colorado miner’s inches. 100 California miner’s inches for one day equal 4.96 acre-feet. 100 Colorado miner’s inches equal 2.60 second-feet. 100 Colorado miner’s inches equal 19.5 United States gallons per second. 100 Colorado miner’s inches equal 104 California miner’s inches. 100 Colorado miner’s inches for one day equal 5 . 17 acre-feet. 100 United States gallons per minute equal 0 . 223 second-foot. 100 United States gallons per minute for one day equal 0.442 acre- foot. 1 000 000 United States gallons per day equal 1.55 second-feet. 1 000 000 United States gallons equal 3.07 acre-feet. 1 000 000 cubic feet equal 22 . 96 acre-feet. 1 acre-foot equals 325 851 gallons. 1 inch deep on 1 square mile equals 2 323 200 cubic feet. 1 inch deep on 1 square mile equals . 0737 second-foot per year. 200 Installation Fig. 77— -66" LOCK-BAR PIPE LINE— BROOKLYN, N. Y. THROUGH CITY STREETS 201 Weights of Steel Plates Weights of Steel Plates Per Square Foot u. s. Standard July 1, 1893 American English Decimals Inches Steel Brown & Sharpe Stubbs or Birming- ham . 187 5 3/16 7.655 7 .188 6 6 .203 8.288 . 203 125 13/64 8.293 4 . 204 31 8.342 ,218 7s 7/32 8.931 5 .219 5 .22 8.982 3 . 229 42 9.367 4 .234 234375 15/64 9.569 4 .238 9.717 24491 s 10.000 3 .250 1/4 10.207 2 . 257 ™ 10 519 3 .259 10.575 . 265 625 17/64 10.845 2 .266 1 .281 .281 25 9/32 11.483 2 .284' 11.595 1 ,289 s 11 812 . 296 875 19/64 12 121 1 .300 12.249 ,312 s 5/16 12.759 0 .313 0 . 324 86 13.264 . 328 125 21/64 13.397 0 .34 13.882 . 343 75 11/32 14.035 00 .344 . 359 S7S 23/64 14.673 00 ,364 8 14.894 ,367 s 14.996 000 .375 3/8 15.311 00 .38 15 515 . 390 625 25/64 15 949 0000 .406 . 406 25 13/32 16.587 000 . 409 M 16.725 Weights of Steel Plates Weights of Steel Plates— Continued Per Square Foot u. s. Standard July 1, 1893 American English Brown & Sharpe Stubbs 0 ] Birming- r Decimals Inches Steel ham 000 .421875 27/64 17.225 .425 17.352 00000 .437 5 .438 7/16 17.863 0000 . 453 125 29/64 18.501 0000 .454 .46 18 . 536 18.781 000000 . 468 75 .469 15/32 19.139 0000000 00000 .484875 .500 31/64 1/2 19.777 20.415 ,515 623 33/64 21.053 .531 25 17/32 21.691 . 546 876 35/64 22.329 .562 5 9/16 22.966 . 578 125 37/64 23.604 . 593 75 19/32 24.242 . 609 375 39/64 24.880 .625 5/8 25.518 . 640 623 41/64 26.156 . 656 23 , .671 873 21/32 26.794 43/64 27.432 .687 3 11/16 28.070 . 703 123 45/64 28 . 708 .718 75 23/32 .29.346 . 734 375 47/64 29.984 .750 3/4 30.622 . 765 625 49/64 31.260 .781 25 25/32 31.898 ,796 873 51/64 32.536 .812 5 13/16 33.174 . 828 123 53/64 33.812 . 843 75 27/32 34.450 ,859 873 55/64 35.088 .875 7/8 35.726 .890 625 57/64 36.364 . 906 23 29/32 37.002 203 Weights of Steel Plates Weights of Steel Plates — Continued Per Square Foot Decimals Inches Steel Decimals Inches Steel .921 875 59/64 37.640 1 . 218 7S 1 . 7/32 49.761 ,937 s 15/16 38.278 1.234 37 1 . 15/64 50.399 .953 125 61/64 38.916 1.25 1.1/4 51.037 .968 75 31/32 39 . 554 1.281 25 1.9/32 52.313 .984 375 63/64 40 . 192 1.312 s 1.5/16 53.589 1. 1 40.83 1.343 75 1.11/32 54.865 1.015 62 1 . 1/64 41.467 1.375 1 . 3/8 56.141 1.031 26 1.1/32 42 106 1.406 25 1 13/32 57.417 1.046 87 1.3/64 42 744 1.437 s 1 7/16 58.693 1.062 s 1.1/16 43.381 1.468 75 1 . 15/32 59.969 1.078 12 1 . 5/64 44.019 1.5 1 1/2 61.245 1.093 75 1 . 3/32 44 657 1.531 25 1 . 17/32 62.521 1.109 37 1 . 7/64 45.295 1.562 s 1 . 9/16 63.796 1.125 1.1/8 45.933 1.593 75 1 19/32 65.072 1 . 140 62 1.9/64 46.571 1.625 1.5/8 66.348 1 . 156 25 1.5/32 47 209 1 . 656 2S 1.21/32 67.624 1.171 87 1.11/64 47.847 1.687 s 1 11/16 68.900 1.187 s 1.3/16 48.485 1 . 718 7S 1.23/32 70.176 1.203 12 1 . 13/64 49.123 1.75 1.3/4 71.452 Note. — This table is based upon the average weight of 1 cubic foot of Steel, as given by — Haswell, 490.12 Nystrom, 489.80 In calculating total weights of Plates, a percentage must be added to the weight given in this table to allow for spring of Rolls, according to width and gauge of Plates. See Standard Specifica- tions, table of allowance for overweight, pages 26 and 27. 204 Size in Inches 8 x8 x3^ x6 x4 x3 H x5 x4 x3^ x3 4^x3 4 x4 4 x3}4 3^x3^ 3 H 3 3Hx2J4 3Mx334 3Mx2 3 x3 3 x2 K 3 x2 2Mx2^ 2Hx234 2^x2 2 3^x1^ 2Hxl^ 2 34x2 34 2Mxi3^ 2 x2 2 xiy 2 2 xlH l^xl % iy 2 xiy 2 iy 8 xi iy 8 x h lXxlX iy 8 xiy 8 1 xl 1 X X 1 X y 8 y 8 x y 8 %X % Weights of Steel Angles WEIGHTS OF STEEL ANGLES Thickness in Inches Vs 3 16 M 5 16 % 7 16 9 16 % n 16 M 13 16 Vs 15 16 1 26.4 29.6 32.7 35.8 38.9 42.0 45.0 48.1 51 .0 15.0 17.0 19.1 21.0 23.0 24.9 26 ! 8 28.7 30.5 32 ! 3 14.9 17.2 19.6 21 .9 24.2 26.5 28 7 31.0 33.1 35.3 37 .4 12.3 14.3 16.2 18.1 20.0 21.8 23.6 25.4 27.2 28.9 30.6 11.7 13.5 15.3 17.1 18.9 20.6 22.4 24 0 25.7 27.3 28 ! 9 12.3 14.3 16.2 18.1 20.0 21.8 23.6 25.4 27.2 28.9 30 ! 6 11.0 12.8 14.5 16.2 17.8 19.5 21.1 22 7 24.2 8.7 10.4 12.0 13.6 15.2 16.8 18.3 19.8 21.3 22.7 8.2 9.8 11.3 12.8 14.3 15.7 17.1 18.5 19.9 7.7 9.1 10.6 11.9 13.3 14.7 16.0 17.3 18 5 5.2 6.6 8.2 9.8 11.3 12.8 14.3 15.7 17.1 18.5 19.9 7.7 9.1 10.6 11.9 13.3 14.7 16.0 17.3 7.2 8.5 9.8 11.1 12.4 13.6 14.8 16.0 17 1 5.8 7.2 8.5 9.8 11.1 12.4 13.6 14.8 16.0 17.1 6.6 7.9 9.1 10.2 11 .4 12.5 13.6 14 7 15 8 4.9 6.1 7.2 8.3 9.4 10.4 11.5 12.5 7.85 4.3 5.3 6.3 7.2 8.1 9.0 2.5 3.7 4.9 6.1 7.2 8.3 9.4 10.4 11.5 3.4 4.5 5.6 6.6 7.6 8.5 9.5 3.1 4.1 5.0 5.9 6.8 7.7 2.3 3.4 4.5 5.6 6.6 7.6 8.5 2.1 3.1 4.1 5.0 5.9 6.8 7.7 2.8 3.7 4.5 5.3 6.1 6.8 2.6 3.4 2.4 3.2 3.9 1.9 2.8 3.7 4.5 5.3 6.1 6.8 2.3 3.0 3.7 4.4 5.0 5.6 i .7 2.5 3.2 4.0 4.7 5.3 2.1 2.8 3.4 4.0 2.1 2.7 i .4 2.2 2.8 3.4 4.0 4.6 1.3 1.8 2.4 2.9 3.4 1.0 1.9 0.9 i .3 1.1 1.48 2.0 2.4 0.9 1.3 0.8 1.2 1.5 0.7 1.0 0.6 0.9 0.7 1.0 0.6 0.9 0.5 The above weights are given in pounds per foot 205 Estimated Weights per Hundred Rivets CONE-HEAD BOILER RIVETS OF SCANT DIAMETER L’gth Inches 34 A ** tt % 13. 16 Vs 1 IK* K 8.75 13.7 16.20 Vs 9.35 14.4 17.22 1 10.00 15.2 18.25 21.70 26.55 37.0 46 60 1 Ys 10.70 16.0 19.28 23.10 28.00 38.6 48 63 95 IK 11.40 16.8 20.31 24.50 29.45 40.2 50 65 98 133 1 Vs 12.10 17.6 21.34 25.90 30.90 41.9 52 67 101 137 IV 12.80 18.4 22.37 27.30 32.35 43.5 54 69 104 141 1 Vs 13 .50 19.2 23.40 28.70 33.80 45.2 56 71 107 145 1 % . 14.20 20.0 24.43 30.10 35.25 IVs 14.90 20.8 25.46 31.50 36.70 2 15.60 21.6 26.49 32.90 38.15 47. 58 74 110 149 2 Vs 16.30 22.4 27.52 34.30 39.60 48.7 60 77 114 153 ^K 17.00 23.2 28.55 35.70 41.05 50.3 62 80 118 157 2% 17.70 24.0 29.58 37.10 42.50 51.9 64 83 121 161 2K 18.40 24.8 30.61 38.50 43.95 53.5 66 86 124 165 2% 19.10 25.6 31.64 39.90 45.40 55.1 68 89 127 169 2/4 19.80 26.4 32.67 41.30 46.85 56.8 70 92 130 173 2 7 /s 20.50 27.2 33.70 42.70 48.30 58.4 72 95 133 177 3 21.20 28.0 34.73 44.10 49.75 60. 74 98 137 181 3 J4 22.60 29.7 36.79 46.90 52.65 63.3 78 103 144 189 3 3 4 24.00 31.5 38.85 49.70 55.55 66.5 82 108 151 197 3 34 25.40 33.3 40.91 52.50 58.45 69.8 86 113 158 205 4 26.80 35.2 42.97 55.30 61.35 73. 90 118 165 213 434 28.20 36.9 45.00 58.10 64.25 76.3 94 124 172 221 ± l /2 29.60 38.6 47.09 60.90 67.15 79.5 98 130 179 229 31.00 40.3 49.15 63.70 70.05 82.8 102 136 186 237 5 32.40 42.0 51.21 66.50 72.95 86. 106 142 193 245 534 33.80 43.7 53.27 69.20 75.85 89.3 110 148 200 254 53i 35.20 45.4 55.33 72.00 78.75 92.5 114 154 206 263 5?4 36.60 47.1 57.39 74.80 81.65 95.7 118 160 212 272 6 38.00 48.8 59.45 77.60 84.55 99. 122 166 218 281 634 40.80 52.0 63.57 83.30 90.35 105.5 130 177 231 297 7 43.60 55 . 2 67.69 88.90 96.15 112. 138 188 245 314 Heads. 5.50 8.40 11.50 13.20 18.00 23.0 29.0 38.0 56.0 77.5 *These two sizes are calculated for exact diameter. tt Button-Heads weigh approximately the same as Cone- Head Rivets. ft ft tt tt Steeple. Round. Cone. Countersunk The measure of Countersunk Head Rivets is over all. All other styles are measured from under the head. Boiler Rivets less than one inch long are one-half cent per pound extra. Tank Rivets inch in diameter and less are sold at a list price and subject to discount. 206 Metric Conversion Table Metric Conversion Table Arranged by C. W. Hunt, New York. Millimeters X .03937 = inches. Millimeters -=-25.4= inches. Centimeters X . 393 = inches. Centimeters 4-2.54 = inches. Meters X 39. 37= in. (Act Cong.) Meters X 3 . 28 = feet. Meters X 1 . 094 = yards. Kilometers X . 621 = miles. Kilometres 1 . 6093 = miles. Kilometers X 3280 . 7 = feet. Sq. Millimeters X . 055 = sq. in. Sq . Millimeters 4- 645 = sq. in . Sq. Centimeters X . 155 = sq. in. Sq. Centimeters 4- 6. 45 =sq. in. Sq. Meters X 10. 764 =sq. ft. Sq. Kilometers X 247 . 1 = acres. Hectars X 2 . 47 = acres. Cu. Centimeters 4-16. 387 = cu. in. Cu. Centimeters 4-3 . 69 =fl. drs. (U. S. P.) Cu. Centimeters-r-29.57=fl. ozs. (U. S. P.) Cu. Meters X 35. 314 = cu. ft. Cu. Meters XI .308 = cu. yds. Cu. Meters X 264. 2= gals. (231 cubic inches.) Litres X 61 .023 = cu. in. (Act Cong.) Litres X 33. 84 = fl. oz. (U. S. P.) Litres X 2642 = gals. (231 cu. in.) Litres 4- 3. 78 = gals. (231 cu. in.) Litres 4- 28. 31 7 = cubic feet. Hectolitres X 3 . 53 = cubic feet. Hectolitres 4- 2. 84 =bu. (2150.42 cu. inches.) Hectolitres X . 131 =cu, yds. Hectolitres 4-26.42 = gals. (231 cubic inches.) Grammes X 15 . 432 = grains (Act Congress.) Grammes 4- 981 = dynes. Grammes (water) 4-29 . 57 = fl. oz Grammes 4- 28. 35 = oz. av’pois. Grammes per cu. cent 4- 27. 7 = lbs. per cu. in. Joule X .7373= ft. pounds. Kilo-grammes X 2 . 2046 = lbs. Kilo-grammes X 35 . 3 = oz . avoir- dupois. Kilo-grammes 4-1102.3 = tons. (2,000 lbs.) Kilo-grammes per sq. cent. X 14.223= lbs. per sq. in. Kilo-gram metres X 7.233 = ft. lbs. Kilo per metre X .672 = lbs. per foot. Kilo per cubic metre X . 026 = lbs. per cubic foot. Kilo per ChevalX2.235 =lbs. per horsepower. Kilo-Watts XI. 35 =H. P. Watts 4- 746 = Horse Power. Watts 4- 737 =ft. lbs. per second. Calorie X 3. 968 = B. T. U. Cheval vapeurX98.3 = H. P. (Centigrade) X 18 +32 = deg. F. Franc X 193 = dollars. Gravity Paris = 980 . 94 centime- ters per second. 207 Useful Factors Inches X 0.08333 = feet Inches X 0.02778 = yards Inches X 0.00001578 = miles Square inches X 0.00695 = square feet Square inches X 0.0007716 = square yards Cubic inches X 0.00058 = cubic feet Cubic inches X 0.0000214 = cubic yards Cubic inches X 0.004329 = U. S. gallons Feet X 0.334 = yards Feet X 0.00019 = miles Square feet X 144.00 = square inches. Square feet X 0.1112 = square yards Cubic feet X 1728.00 = cubic inches Cubic feet X 0.03704 = cubic yards Cubic feet X 7.48 = U. S. gallons Yards X 36.000 = inches Yards X 3.000 = feet Yards X 0.0005681 = miles Square yards X 1296.000 = square inches Square yards X 9.000 = square feet Cubic yards X 46656.000 = cubic inches Cubic yards X 27.000 = cubic feet Miles X 63360.000 = inches Miles X 5280.000 = feet Miles X 1760.000 = yards Avoirdupois ounces X 0.0625 = pounds Avoirdupois ounces X 0.00003125 = tons Avoirdupois pounds X 16.000 = ounces Avoirdupois pounds X .01 = hundredweight Avoirdupois pounds X 0.0005 = tons Avoirdupois pounds X 27.681 = cu. in wat. at 39.2°F. Avoirdupois tons X 32000.00 = ounces Avoirdupois tons X 2000.00 = pounds Horsepower X 746.00 = Watts Watts X 0.00134 = horsepower 208 Useful Factors Cubic feet (of water) (39.1°) X 62.425 = pounds Cubic feet (of water) (39 . 1°) X 7.48 = U. S. gallons Cubic feet (of water) (39.1°) X 6.232 = English gallons Cubic feet (of water) (39 . 1°) X 0.028 = tons Cubic foot of ice X 57.2 = pounds Cubic inches of water (39 .1°) X 0.036024 = pounds Cubic inches of water (39 .1°) X 0.004329 = U. S. gallons Cubic inches of water (39 . 1°) X 0.003607 = English gallons Cubic inches of water (39.1°) X 0.576384 = ounces Pounds of water X 27.72 = cubic inches Pounds of water X 0.01602 = cubic feet Pounds of water X 0.083 = U. S. gallons Pounds of water X 0.10 = English gallons Tons of water X 268.80 = U. S. gallons Tons of water X 224.00 = English gallons Tons of water X 35.90 = cubic feet Ounces of water X 1.735 = cubic inches A column of water 1 inch square by 1 foot high weighs 0.434 pounds. A column of water 1 inch square by 2.31 feet high weighs 1 pound. Water is at its greatest density at 39.2° F. Sea water is 1 .6 to 1 .9 heavier than fresh. One cubic inch of water makes approximately 1 cubic foot of steam at atmospheric pressure. 27222 cubic feet of steam at atmospheric pressure weighs 1 pound. Weight of round iron per foot = square of diameter in quarter inches - 5 - 6 Weight of flat iron per foot = width X thickness X 10-3. Weight of flat plates per square foot = 5 pounds for each^-inch thick ness. Weight of chain = diameter squared XI 0.7 (approximately.) Safe load (in pounds) for chains = square of quarter inches in diameter of bar. U. S. gallons U. S. gallons U. S. gallons U. S. gallons U. S. gallons English gallons (Imperial) English gallons (Imperial) English gallons (Imperial) English gallons (Imperial) English gallons (Imperial) Water Factors X 8 X 0 X 231 X 0 X 3 X 10 X 0 X 277 X 1 X 4 .33 = pounds . 13368 = cubic feet 00 = cubic inches 83 = English gallons 78 = litres = pounds 16 = cubic feet 274 = cubic inches 2 = U. S. gallons 537 = litres 209 Useful Information To find circumference of a circle multiply diameter by 3.1416. To find diameter of a circle multiply circumference by .3183. To find area of a circle multiply square of diameter by .7854. To find surface of a ball multiply square of diameter by 3.1416. To find side of an equal square multiply diameter by .8862. To find cubic inches in a ball multiply cube of diameter by .5236. Doubling the diameter of a pipe increases its capacity four times. A gallon of water (U. S. standard) weighs 8}£ lbs. and contains 231 cubic inches. A cubic foot of water contains 7.48 gallons, 1728 cubic inches, and weighs 62.4 lbs. To find the pressure in pounds per square inch of a column of water multiply the height of the column in feet by .434. A standard horse power: The evaporation of 30 lbs. of water per hour from a feed-water temperature of 100° F. into steam at 70 lbs. gauge pressure. One horse power is the power required to raise 33,000 lbs. one foot in one minute. Equals 33,000 foot-pounds per minute “ 1,980,000 “ “ hour To find the horse-power of an engine multiply the piston speed in feet per minute by the area of the piston in square inches and by the mean effective pressure, then divide by 33,000. Each nominal horse power in boilers requires one cubic foot of water per hour. In calculating horse power of tubular boilers, consider 12 square feet of heating surface equal to one nominal horse power.) To find capacity of tanks any size; given dimensions of a cylinder in inches, to find its capacity in U. S. gallons: 210 Useful Information Square the diameter, multiply by the length and by ,0034. To approximately ascertain heating surface in tubular boilers multiply % the circumference of boiler by length of boiler in inches and add to it the area of all the tubes. When designing boilers the T. S. is specified, the factor of safety, diameter and pressure per square inch are decided upon, and the only quantities . remaining unknown are the thickness and the efficiency of the joint. Let P= pressure of steam in pounds per square inch. T = thickness of plate in shell. E= efficiency of joints in shell. D = diameter of shell. Si = ultimate strength of material. F= factor of safety. Solving the equation ^ ^ = TXE XPXF 2 Si XE Pressure allowable for concaved heads of boilers: Multiply the pressure per square inch allowable for bumped heads attached to boilers or drums convexly by the constant .6, and the product will give the pressure per square inch allowable in concaved heads. — U. S. Gov. Rule II, Par. 12. To find the amount of air that can be produced by different size air cylin- ders : Find the area of the cylinder and multiply that by the stroke; then multiply result by 2 if it is a Straight Line Compressor; by 4 if a Duplex Compressor; or by 2 if Compound Duplex Compressor. Divide this result by 1728, which will give amount of air per stroke and then multi- j ply by number of strokes per minute. 211 CROSS INDEX Air-Bound Pipes 130 Valves 164 Anchorages 65 Angles, Steel, Weights of, Table 205 Approximate Formula, Trautwine. .. 124 Areas and Circumferences of Circles, Table 192 Arcs, Circular, Lengths of, Table .... 197 Assembling and Lowering Pipe 170 Lock Bar-Pipe 19 Cast-Iron, Failure 87-94, 96 Values of “C” in Chezy Formula, for 131 Values of “f” in Fanning’s Formula, for 132 Cast-Iron Vs. Steel Pipe 75-77 Cause of corrosion 74-78 Chemical and Physical Properties of Materials 13 Chezy Formula 131 Values of “C” for Cast-Iron Pipes . .. . 131 Circular Arcs, Lengths of, Table .... 197 Circular Seams, Rivets in, Table. ... 62 Circumferences and Areas of Circles, Barrels, contents of, Table 158 Table 192-195 Bazin Formula .144, 149 Coating Pipe 21 Bearing and Shearing Value of Rivets, Coating, specifications for 17 Table .. .63, 64 Cast-Iron Pipe, Table 84 Bending Tests 13 Collection of Water .. 156 Bends in Steel Pipe ' 68 Compressibility of Water .. 119 Bernoulli’s Theorem 153 Conduits, Water Supply 165, 166 Beveling, Truing and Punching of Cone-Head Boiler Rivets Table . . . .. 206 Lock-Bar Pipe 17 Connections and Accessories of Blow-Offs 165 Gates .. 161 Boxes 163 Connections, Standard Blow-Off . . 44 Blow-Off Connections, Standard. . 44 Constants, Cut, Table .. 191 Box, Measuring, Miners’ Inch. . . 143 Consumption, Water 178-184 Boxes, Blow-Off 163 Contents, in Barrels, Table .. 158 Butt Joints, Double Riveted Table. . 59 of Cylindrical Vessels Tanks and Triple Riveted Strength of, Cisterns, Table .. 157 Table 60 of Pipes and Cylinders, Table. .. 156 Quadruple Riveted, Strength of, Contraction in Pipe .. 137 Table 61 Convenient Equivalents .. 200 Butt Strap Joint 37 Conversion Table .. 199 By-Passes 161 Metric .. 207 Corrections, Length, Table .. 198 Corrosion . . 74-78 C Cause of . . 74-78 Capacity of Steel Pipe, Carrying . , 73 of Iron and Steel .. 78 Carrying Capacity of Steel Pipe. . 73 of Wrought Iron and Steel, Cast-Iron, Pipe Coatings, Table. . 84 Relative ..77, 78 Electrolysis in 79 Cost of Steel Pipes .. 86 212 CROSS INDEX Continued Coupling, Flexible High Pressure. ... 38 Covers, Masonry 167 Crib, Submerged 159 Crimping and Rolling of Lock-Bar Pipes 19 Cubic Feet and Gallons, Table 155 Current Motors, 153 Cut constants, Table 191 Curvature in Pipe 136 Cylinders and Pipes, Contents of . . . . 156 Cylindrical Vessels, Tanks and Cis- terns, Contents of, Table 157 D Darcy’s Formula 126, 127, 131, 132 Values of “C” 127 Data for Steel Pipe, Table 65 Steel Standpipes 174, 175 Destruction of a Pipe 79, 80 Diameter, Variations in 136 Discharges and Velocities for Pipe. . . 133 Distribution System 176 Double Riveted Butt Joints, Table. . 59 Lap Joints, Table ! 57 E Electrically Operated Gates 164 Electrolysis 79-81 in Cast-Iron Pipes 79 of Steel Pipe 80 Elevated Steel Tanks 176 Elongation Tests 13 Equivalents, convenient 200 Evacuation, Trench 169, 170 Expansions in Pipe 136 Expansion Joint, East Jersey. ...... 39 Exponential Formula for Pipes .... 134, 135 Williams & Hazen’s 127 F Fabricating of Lock-Bar Pipe 17 Factors, Useful 208,209 Water 209 Failure, Cast-Iron Pipe 87, 88, 89, 90, 91, 92, 93, 94, 96 Fall of Water, Power of, 152 Fanning’s Formula 132 Fanning’s Formula Values of “f” for Cast-Iron Pipes 132 Field Test Head 49 Fire, Protection 182, 183 Service Pressure 166 Stream, Standard 184 Flange Joint 37 Flexible Coupling, High Pressure. ... 38 Flexible Submarine Joint 41 Flow, mean velocity of 124 of Water in Pipes 119, 120, 123 Flowing Water, Measurement of . . . . 138 Formula Bazin 144, 149 Chezy 131 Chezy, Values of “C” for Cast- Iron Pipe 131 Chezy, Values of “C” for Steel Riveted Pipes 132 Darcy’s 126, 127, 131, 132 Darcy’s Values of “C” 127 Exponential for Pipes 134, 135 Exponential, Williams and Ha- zen’s 127 Fanning’s 132 Francis 144,147 Fteley and Stearns 144 Hamilton Smith 144 Kutter’s 125 approximate, Trautwine 124 Four, for Discharge of Wiers, . . . 144 of Long Pipe Lines 131 Weirs, Table 149, 150 Four Formulas for Discharge of Wiers. . . 144 Francis Formula 144, 147 Fteley and Stearns Formula 144 G Gallons and Cubic Feet, Table 155 Gate Valves 161 Vaults 162 Gates, Accessories and Connections of 161 Electrically operated 164 Hydraulically operated 161 on Steel Pipes 160 Sluice 164 213 CROSS INDEX Continued Gates and Gate Valves 177 Gears 161 Girth Joints, Lap, Single Riveted, Table 56 Grade — Line, Hydraulic 130 Gridiron System 176 H | Hamilton Smith Formula 144 Hammer, Water .... 130 Haasen’s and Williams Exponential Formula 127 Heads, Pressure Equivalent to, Table 118 j of water different, for Pressure, Table 118 Water, Table for Calculating Horsepower of, 154 Heat of Water, Specific, Table 119 j High Pressure Flexible Coupling, .... 38 j Horse-Power of Running Stream 152, 153 i Hydraulically Operated Gates 161 | Hydraulic Grade-Line 130 Hydraulics — Water 116 I j Ice and Snow, weights of, Inch, Miner’s Inspection of Materials Installation of Large Steel Pipes Intakes . Iron and Steel, Corrosion of . . . Insulation Joints Insulating Wrappings J Joint, Butt, Strap 37 Butt, Double Riveted, Table. . . 59 Butt, Triple Riveted Strength of Table 60 Butt, Quadruple Riveted, Strength of, Table 61 East Jersey Expansion, 39 Flange 37 Flexible Submarine 41 Riveted Taper 36 Joint, Submarine 40 Insulation 80 Leaded, Leakage of 87 Lap, Double Riveted, Table. ... 57 Lap Girth Single Riveted, Table . 56 Lap, Single Riveted 56 Lap, Triple Riveted, Table 58 K Kutter’s Formula 125 L Lap Girth Joints, Single Riveted, Table 56 Lap Joints, Double Riveted, Table. . . 57 Single Riveted 56 Triple Riveted, Table 58 Leaded Joints, Leakage of, 87 Leakage 165 Leakage of Leaded Joints 87 Length Corrections, Table 198 Lengths of Circular Arcs, Table 197 Lock-Bar Pipe, Assembling 19 Crimping and Rolling of, 19 Fabricating of, 17 Planing and Upsetting 17 Safe working Pressure, Table. . .50, 52 Strength of, 68 Testing 19 Truing, Punching and Beveling. 17 Weight of, Table 30 Long Pipe Line Formulas 131 M Manholes 161 , 165 : Manholes, Standard 42 Masonry Covers 167 Materials, Inspection of 15 Specification 13 Mean Velocity of Flow 124 Measurement by Venturi Tubes 140 of Flowing Water 138 Miner’s Inch, Table 143 Measuring Box, Miner’s Inch 143 Meter, Venturi, 139, 140 118 . ..141,142 15 . . . 169-173 159 78 80 82,83 214 GROSS INDEX Continued Meterage and Water Consumption in Larger Cities, Table 179,180 Metric Conversion, Table 207 Miner’s Inch 141, 142 Measuring Box 143 Measurements, Table 143 Motors, Current 153 Multipliers for Flat-topped Weirs. . . 151 for Triangular Weirs 151 N Notes on Weights 25 O Obstructions in Pipe 137 Organisms 166 Overflows 175 P Permissible Variations in weight of materials 15 Physical Tests and Pressure 69-71 Physical and Chemical Properties of materials 13 Piezometer 138 Pipe, Air Bound 130 and Cylinders, Contents of 156 Cast-Iron, Failure of 87, 88, 89, 90, 91, 92, 93, 94, 96 Coating of 21 Contraction in 137 Curvature in 136 Destruction of a 79, 80 Electrolysis in Cast-Iron 79 Exponential Formula for 134, 135 Expansions in 136 Line Formulas, Long 131 Large Steel, Installation of . . . 169-173 Lock-Bar, Weight of, Table .... 30 Maximum and mean Velocities in 139 Obstructions in 137 Riveted 55 Riveted, Weight of, Table 31 Roughness in 136 Steel Lines, Manufactured by East Jersey Pipe Company. . 112 , 113 Steel 55 Pipe, Steel Bends in 68 Steel, Electrolysis of 80 Steel, Cost of, 86 Transportation of 169 Testing 168 Thickness of Steel 54 , 55 Twin Lines 165 Valves in 137 Weight of Steel 55 Pitot Tube 138, 139 Plates, Steel, Weights of, Table . . . 202-204 Power of Water Fall 152 Water 152 Pressure and Physical Tests 69-71 Pressure for Domestic Service. ..... 166 for Different Heads of Water, Table ns for Fire Service 166 Heads equivalent to, Table 118 Water 117, 118 Water Due to its Weight 117 Protection, Fire 183, 184 Q Quadruple Riveted Butt Joints, Strength of, Table 61 Quantity of Water Discharged 121 R Reducers, Riveted Steel Plate 48 Reduction of Slope Measurements, Tables 185-190 Relative Corrosion of Wrought Iron and Steel 77, 78 Reservoirs and Standpipes 167 Distributing 167 Riveted Butt Joints, Double, Table . . 59 Triple Strength of, Table 60 Riveted Lap Joints, Double, Table . . 57 Single 56 Riveted Lap Girth Joints, Single, Table 56 Riveted Lap Joints Triple, Table .... 58 Riveted Pipe 55 Safe Working Pressure, Table. . .51, 53 Weight of, Table. . 31 215 CROSS INDEX Continued Riveted Steel Plate Reducers 48 Riveted Taper Joint 36 Riveting Pipe 171,172 Rivets, Cone-Head Boiler, Table. . . . 206 in Circular Seams, Table 63 Shearing and Bearing Value of, Table 63,64 Rolling and Crimping of Lock-Bar Pipe 19 Roughness in Pipe 136 S Saddles Standard Socket, Table 45 Straight, Table 43 Sand Cutting 165 Safe Working Pressure for Lock-Bar Pipe, Table.... 50,52 for Riveted Pipe, Table 51, 53 Sharp-Edged Wier 142, 143 Shearing and Bearing Value of Rivets, Table 63,64 Sheared Plates, Permissible Varia- tions in, when ordered to Thickness 26 Sheared Plates, Permissible Varia- tions in Weight of, when ordered to weight 27 Single Riveted Lap Girth Joints, Table 56 Single Riveted Lap Joints 56 Slope Reduction Tables 185-190 Sluice Gates 164 Smith, Hamilton Formula 144 Snow and Ice, Weights of 118 Socket Saddles, Standard, Table. ... 45 Source of Water Supply 159 Specific Heat of Water, Table 119 Specification of materials 13 Specifications for coating 17 Specimens for Testing 15 Standpipes and Reservoirs 167 Standpipes, Steel Data for 174, 175 Stearns and Fteley Formula 144 Steel Angles, Weights of, Table 205 Steel and Iron, Corrosion of 78 Steel and Wrought Iron Pipe Coat- tings, Table 84 Steel and Wrought Iron, Relative Corrosion of, 77, 78 Steel Pipe 55 Bends, in 68 Carrying Capacity 73 Data, Table 65 Electrolysis of 80 Lines Manufactured by East Jersey Pipe Co 112,113 Thickness of 54, 55 Steel Plate Reducers, Riveted 48 Weight of 55 Steel Plates, Weights of, Table .... 202-204 Steel Riveted Pipes, Values of “C” in Chezy Formula 132 Steel Vs. Cast-Iron Pipe 75-77 Steel Pipes, Cost of 86 Straight Saddles, Table 43 Strap Joint, Butt. 37 Stream, Fire, Standard 184 Running, Horsepower of 152, 153 Strength of Lock-Bar Pipe 68 Triple Riveted Butt Joints, Table Quadruple Riveted Butt Joints . . Stresses, Temperature Supply, Water, Source of Submarine Joint Flexible Submerged Crib Submerged Weirs System, Gridiron T Table, Coatings Cast-Iron Pipe Cone-Head Boiler Rivets Data for Steel Pipe Double Riveted Butt Joints .... Contents in Barrels Contents of Pipes and Cylinders . Calculating Power of Water Heads Circumferences and Areas of Circles 192-195 Coefficient “C” 126 Contents of Cylindrical Vessels, Tanks and Cisterns 157 61 65 159 40 41 159 145 176 84 206 65 59 158 156 154 216 GROSS INDEX Continued Table, Conversion 1" Double Riveted Lap Joints 57 Gallons and Cubic Feet 155 Length Corrections 198 Lengths of Circular Arcs 197 Metric Conversion 207 Miner’s Inch Measurements .... 143 Pressure for Different Heads of Water 118 Pressure Heads equivalent to. . . . 118 Rivets in Circular Seams 62 • Safe Working Pressure for Lock- Bar Pipe 50-52 Safe Working Pressure for Riveted Pipe 61 Shearing and Bearing Value of Rivets 63, 64 Single Riveted Lap Girth J oints 56 Specific Heat of Water 119 Standard Socket Saddles 45 Steel and Wrought Iron Pipe Coatings 84 Straight Saddles 43 Strength of Triple Riveted Butt Joints Strength of Quadruple Riveted Butt Joints 61 Triple Riveted Lap Joints 58 Weight of Lock-Bar Pipe 30 Weight of Riveted Pipe 31 Weights of Steel Angles 205 Weights of Steel Plates Table. . 202-205 Weight of Water per Cubic Foot at Different Temperatures .... 116 Weir Formulas 150 Tables, Slope Reduction 185-190 Tanks, Cisterns and Cylindrical Vessels, Contents of, Table. .. . 57 Elevated Steel 176 Taper Joint, Riveted 36 Tees and Y’s 46 Temperature Stresses 65 Test Head, Field 49 Test Specimens 15 Testing of Lock-Bar Pipe 19 Pipe Line 168 Testimonial Letters 97, 99, 101-110 Tests, Bending 13 Tests, Elongation of materials 13 Physical and Pressure 69-71 Theorem, Bernoulli’s 153 Thickness of Steel Pipe 54, 55 Transportation of Pipes 169 Trautwine Approximate Formula . .. . 124 Trench, Evacuation 169, 170 Triangular or V-shaped Weir. 144 Triple Riveted Butt Joints Strength of, Table 60 Lap Joints, Table 58 Tube, Pitot 138, 139 Tubes, Venturi Measurement by . . . . 140 Tubercles in Cast-Iron Pipe 165 Twin Pipe Lines 165 V V-shaped or Triangular Weir 144 Valves, Air 164 Gate 161 Gate and Gates 177 in Pipe 137 Values of “C” in Darcy’s Formula. . . . 127 Values of “C” in Chezy Formula for Cast-Iron Pipes, Table 131 Values of “C” in Chezy Formula for for Steel Riveted Pipes ....... 132 Values of Coefficient “M” Table 124 Values of “F” in Fanning’s Formula for Cast-Iron Pipes 132 V ariations in Diameter 136 Variations Permissible, in Gauge of Sheared Plates when ordered, to Thickness 26 Variations Permissible in Weight of Sheared Plates when ordered, to weight 27 Vaults, Gate Valve 162 Velocities and Discharges for Pipe. . . 133 Velocities in Pipes, Maximum and mean 139 Venturi Meter, 139, 140 Venturi Tubes, Measurement by 140 W Water, Collection of 159 Compressibility of 119 217 CROSS INDEX Continued Water Consumption 178-184 Consumption and Meterage in Larger Cities, Table 179, 180 Discharged, Quantity of 121 Factors 209 Flow, of, in Pipes 119, 120, 123 Flowing, Measurement of 138 Hammer 130 Heads, Table for Calculating Horsepower of, 154 Hydraulics . 116 Power. . 152 Pressure 117, 118 Pressure of, Due to its Weight. . 117 Supply Conduits 165, 166 Supply, Source of 159 Volume of 116 Weight of per cubic foot at differ- ent temperatures, Table 116 Weight of Lock-Bar Pipe, Table 30 Material, Permissible Variations 15 Riveted Pipe, Table 31 Steel Pipe 55 Water per Cubic Foot at Differ- ent Temperatures, Table 116 General Notes on 25 Weight of Snow and Ice 118 Steel Angles . . 205 Weights of Steel Plates, Table. . . .202-204 Weir, Sharp-Edged 142 Triangular or V-shaped 144 Weirs 142, 144, 145, 147, 149, 150, 151 Compound, Multipliers for 151 Flat-topped Multipliers for 151 Four Formulas for Discharge of 144 Formulas, Table 149, 150 Submerged 145 Williams & Hazen’s Exponential Formula 127 Working Pressure Safe, for Lock-Bar Pipe, Table 50,52 Safe for Riveted Pipe, Table 51, 53 Wrappings, Insulating 82, 83 Wrought Iron and Steel Pipe Coat- ings, Table 84 Wrought Iron and Steel, Relative Corrosion of 77, 78 Y’s and Tees. 46 218 Written and Designed by Charles Austin Hirschberg , Inc, Advertising Counselors New York