| yet ; j ss \ i - > Sf BRIDE'S PRESS PUBLICATIONS, No. 13. ‘GUSTAV E.STECHERTIBE 9 EAST 16. STREET NEW YORK “HKvery House Connection shall ventilate the Sewer.” Sykes Patent Interceptor. SYRES rATENS WE eat Se] PEEPS Ly Heurning and Labor. LIBRARY OF THE e t University of Hlinois. f CLASS. BOOK. VOLUME. ) a q he SOLA WDD cobs. Books are not to be taken from the Library. Accession No.2 fa 1a eae i Snceinscinaidii aia ain ain aie aie aie ie aoe ao A2itvu upyv ws newer es, The screw stoppers can be taken out of the Inspection Arms and the respective drains cleansed. The inlets A and B are made with a shoot into the Interceptor, there- by thoroughly flushing same by the roof-water during a storm. - By confining the liquid to the Interceptor no sewage can escape to permeate the surrounding subsoil. Concentration of all parts in the Chamber, where they are easily accessible, and where full control is obtained over the system. Price delivered to any pate of United Kingdom, 4in. 16/6, 6in. 22/6, 9in. 38/6, Side Inlets, 2/- each extra. ALBION CLAY CO., LIMITED. Albion Works, Woodville, Baki on-Trent, ok 18 NEW BRIDGE STREET, BLACKFRIARS, E.C. Me eg PUBLIC HEALTH. MAIN SEWERAGE AND HOUSE DRAINAGE. Patent Paragon Pipes. Gheapest in First Gost and Maintenance. TRADE PARAGON MARK. Sound Joints. ‘True alignment and Firm Bed. Made with varying Depths of Socket, A, B,and C. A—with Ordinary Depth of Socket for Ordinary Drainage. B—with Deep Sockets to make Sound Joints. Below is a section of C; with Extra Deep Sockets, to make reliable Gas and Watertight Joints to stand Pressure. PERSPECTIVE VIEW LONGITUDINAL ‘SECTION THROUGH C.D. SECTION THROUGH : AD. When specifying, the name should always be given in full, as PATENT PARAGON PIPES, A, B, or C, according to the kind required. Below is a section of the Ordinary Socket Pipes, showing their well-known defects and the existing state of the old System of Drainage. The Sockets being concentric with the Pipe, and of much greater diameter, the spigots drop, and the ledges formed stop the solids, and liquid sewage and sewer gas escape at the open joints. ORDINARY: PIPES SHOWING DEFECTIVE JOINTS The PATENT PARAGON PIPES remedy these defects by securing sure alignment of the invert at the Joints, thereby avoiding Silting and Stoppage of Drains. They are highly approved, and should be specified in all cases to ensure efficiency and safety in drainage at the Lowest Cost. The PATENT PARAGON PIPES are made of the best STONEWARE, and are of SUPERIOR QUALITY, true in line and section, and well glazed, and are being largely specified. —_——- For Prices, Samples, &c., apply to the ALBION GLAY GOMPANY, Limited, Albion Works, Woodville, BURTON-ON-TRENT. ‘Works Telegrams— ALBION, WOODVILLE.”’ LONDON DEPOT—MIDLAND RAILWAY, EUSTON ROAD. CHIEF LONDON OFFICE—18 NEW BRIDGE STREET, BLACKERIARS, E.C. Zelegrams—‘'‘ SEWERAGE, LONDON.”’ Telephone 2958. : A2 MULLER’S ALPHA PATENT Gras-MAKiNG MACHINE NO SKILLED LABOUR REQUIRED. With all latest improvements, including Patent Regulating Economiser. Gas Ewerywrhere.e Made Imnstantaneously. NO FIRE. NO SMOKE. NO ASHES. NO DIRT. MULLER & ADKINS eon] = = For Lighting Public and Private Buildings of every description in all parts of the country. Illustrated Price Lists, with Testimonials, obtained from H. L. MULLER, mary Ann St., fifninghited London Office—73 QUEEN VICTORIA ST. Win n’s PATENT ACME SYPHON CISTERN, FOR FLUSHING WATER CLOSETS, IN USE ALL OVER THE WORLD, BO,000O0 SOLD. STILL THE BEST IN THE MARKET. No. 1163. Price, as Drawn, 20s. Galvanized, 28s. Approved and authorised for use by all the London and Provincial Water Companies ; also now largely used in Barracks, Workhouses, and Her Majesty’s Prisons throughout the country, and adopted by the leading Railway Companies, while more than 80,000 have been sold in all. SPECIALLY SUITABLE FOR ALL PATTERNS OF PEDESTAL CLOSETS. WRITE FOR COMPLETE LISTS. CHARLES WINN & CQ.,, Manufacturers of Sanitary Appliances, BIRMINGEHADM. London Offices—41 HOLBORN VIADUCT, E.C. ~ HIGH-CLASS. Mu FOR a AND AGRICULTURALISTS.. Teiecr, @ Postan Anpress:- “WaROYPICK, SHEEFIE ADs Ga : Ld, ‘SHEFFIELD. is Engiand: aa ~.MaKERs oF THE “Univensaut AND Acme" Minune 4 AND Navvy packs: HAND & POWER BORING: MACHINES. FOR ROCK ae Colo. om PICKS, SHOVELS, SPADES, FORKS, HOES. AXES, ‘HAMMERS, WEDGES, CROWEARS, ANDALL Mininc mv Contractors, ‘AND’ Acai ‘SPECIAL Touen m°) ANSway ; : . S- iarontens ‘oF: ‘MicKkory MAwece x: 18 PaiseMevats AWARDED TOREXCELLENcE of Quatity & Onicinac Desicns. Established 1790. Telegrams: “ROWLEY, SWADLINCOTE.” J. WOODWARD & ROWLEY, ~SWADLINGCOTE, Near BURTON -ON-TRENT, ENGLAND: MANUFACTURERS OF ~. Gombination — | 25522 “ Wash-Down” RSV = Pedestal a Closets. SPECIALITIES IN Closets, Traps, Lavatories, Urinals, Sinks, And other Sanitary fittings. MANUFACTURERS OF THE “Wash-Out” a Patent BG SOLS + Glosets. | = _ Slaw See that the Registered Trade Mark, ‘ WASH- ‘G. eho a OUT,” is printed ‘inside @ On. , az the Basin. None are ik Fe genuine without this, STE DOWD lS O5 gee? THREE AWARDS AT THE INTERNATIONAL MEDICAL SANITARY EX/IIBITION, SOUTH KENSINGTON, 1887. MAKERS OF A LARGE VARIETY OF PEDESTAL CLOSETS. Price Lists and Full Particulars on Application. as Under the Patronage of H.R.H. the Department Prince of Wales. 4 = anti the ees) Lords of the —————— Admiralty. —————— CERTIFICATE OF MERIT (ONLY AWARD) SANITARY EXHIBITION. DUBLIN, 1984 CERTIFIGATE OF MERIT SANITARY EXHIBITION, BRIGHTON, 1890. CERTIFIGATE OF MERIT SANITARY EXHIBITION, NOTTINGHAM, 1899. FOR APPLYING THE SMOKE TEST TO DRAINS, FOR DISINFECTING PURPOSES, FOR THE DESTRUCTION OF VERMIN IN HOLES. The ‘‘ AspHyxtaror”’ is universally acknowledged to be the only reliab!e machine by which the smoke test can be applied to drains. It is used by Sanitary Authorities, Sanitary Associations, Unions, Medical Officers of Health, Architects, Plumbers and Builders throughout the United Kingdom and abroad. The “‘ ASPHYXIATOR ” is also applicable for disinfectant purposes. TESTIMONIALS. 66 & 68 CHESTNUT ROAD, TOTTENHAM, N. Dear Sirs, April 14th, 1893. We have pleasure in informing you that the ‘‘ AspHyxIAToR ” you sent has proved a most effective drain-testing machine, and having had it in use now some years, we con- sider it thoroughly reliable and far superior to rockets. It has also the advantage of being very easy to work. Yours truly, (Signed) HENRY KNIGHT & SON. SANITARY INSPECTOR’S OFFICE, TOWN HALL, GRIMSBY. Gentlemen, April 21st, 1893. Ihave much pleasure in testifying to the efficiency of the ‘‘ AspHyxr1aAToR” supplied by you for us in our Sanitary Department here. It is certainly the best drain-tester extant, and from my personal experience of the use of the machine I strongly recommend it to Sanitary Authorities as a reliable method of testing drainage.—Faithfully yours, (Signed) HENRY F. MOODY, Assoc. San. Inst., Sanitary Inspector. Descriptive Circular, with Testimonials, Price List of Machines, Fumigating Materials, and full instructions for use, Post Free on application to the Manufacturers, JOHN WATTS & CO., Broad Weir Works, BRISTOL. Telegraphic Address: ‘ ASPHYXIATOR,” Bristol. CauTion.—In consequence of spurious imitations by unprincipled firms, Buyers should observe that every genuine Machine bears our Registered Trade Mark “ ASPHYXIATOR.” AGENTS WANTED FOR THE UNITED STATES, CANADA. AND PRINCIPAL CITIES IN EUROPE, (HE BRITISH WORKMAN’S AND GENERAL ASSURANCE COMPANY. MILLER PATENT AUTOMATIC FLUSHING HIGHEST AND ONLY AWARD CHICAGO, 1893, WHICH READS: ‘‘FOR SIMPLICITY — EFFICIENCY — RELIABILITY.’: Starts under smallest Drop-by-Drop Supply. Ld VD. vi ry Se --—_—- - ——— —- . _ KG S\\ oF PENSE se piers be ES “ Standard” Design. Patent. PAY bailed) ” 2S. Ie —- AB 9 Pe es te eld he, EVERY SYPHON GUARANTEED. No small pipes, no joints, no internal obstructions whatever. Instantaneous full-bore discharge of enormous rapidity. Starts under smallest drop-by-drop supply. Absolutely reliable under all conditions, Simplest in existence. For further Particulars and Prices, address ALBERT WOLLHEIM, C.E., 4gzneer, MiLLER SYPHON SYNDICATE, LEADENHALL House, 101 LEADENHALL STREET, LONDON, E.C MILLER PATENT AUTOMATIC FLUSHING Specified and used by Leading Sanitary and Municipal Fingineers in England, United States, Canada and other Countries and British Colonies. «“ SPECIAL” DESIGN. PATENT. QV WL QV WAgVgs a WS SS Wy CORRESPONDENCE INVITED. Once Tried, Always Used. Low Cost. Discharges about, 50 % faster than any other syphon. Notr.—To Municipal Engineers, etc.- We will -gladly forward a trial syphon on approval. CORRESPONDENCE INVITED. Address: ALBERT WOLLHEIM, C.E, Zngineer, Miller Syphon Syndicate, Leadennall House, 101 Leadenhall Street, London, E.C. THE BRITISH WORKMAN’S AND GENERAL ASSURANCE COMPANY. THE YEAR’S OPERATIONS (1895). The premium income was £380,088—an increase of upwards of £44,000 —this increase being much in excess of anything previously recorded by the — Company. THE HISTORY OF THE INSTITUTION. The history of this institution, and especially its recent history, is marvellous. Everyone who is concerned in it is justly proud. And there is something sub- stantial of which to be proud, as is shown in the following figures, illustrating the Company’s progress during the last twelve years :— PREMIUM INCOME. 1884 eet : ~ £118,017 1885 Ss Raa gS Ue anit ta roe Ree 130,057 1886 ae 3 a a See Seale 142,864 1887 Seen EGY Sey inp eres fo 153,384 1888 is Gakbeg a, Pepe 6 Wel BO ae 173,543 1889 NEN stg aee PA Dale ares Seana 207,575 1890 ote UVa Pee i Barres baat = oor Ss 243,889 1891 a tel) Sy ee UME te pace er 274,969 1892 See, Ee Sac ar SS eae 289,406 1893 AE hia ste RS Fas eestor ae ae 306,234 1894 Se RC srs REO pg eee ae 335,282 1895 a tao: eae: aioe et 380,088 The premium income ofa Life! Office is the measure of its popularity and progress, and in the period under review the income of the BRITISH WORKMAN’S AND GENERAL ASSURANCE COMPANY has been more than quadrupled. STANDING IN THE FRONT RANK. This Company is comparatively young, but there are not eight Life offices in the United Kingdom which have so large an income. The progress has been marvellous, and this is to be explained by the liberality of the management towards the policy-holders. No other company has distributed an equal amount of benefits for the same amount of premiums paid. No other Industrial Life Office has treated its members with equal consideration in the matter of surrender values. The BRITISH WORKMAN’S is an ideal Industrial Office. THE ORDINARY DEPARTMENT. The business in this department is highly satisfactory; 2,923 new policies have been issued, assuring the sum of £232,766 at an annual premium of £12,330. In this branch, apart from the Industrial, the nett premium income for the last year reached the solid figure of £42,790, and the accumulated funds increased from £92,000 to £113,711. The Ordinary Department is growing in importance at a rapid rate, and its development—which is well assured—will contribute largely to the future success of the Company. 2 -Patentees and Manufacturers of Automatic Flushing Syphons OP acct \ TT “Ss W. H. BODIN & CO.., onsulting Sanitary Specialists & Engineers, “ACME” SANITARY ENGINEERING WO2KS, WEDNESBURY, BOAe LEVEL IS Ete ts IRONS, DIRT BOX __RELIA BLE mis ACTION _ = SS SS ee aX typ La iy Le ji tin Ye a mere 4 | TWO GOLD i: MEDALS AWARDED PERFECT AcTion AND POWERFUL i (ee STAFES. | ZZ bs | = i i and Tanks, and Sanitary Ironwork generally. LATRINES, TROUGH TEE eet LAVATORIES AND VERTIS PLIANGES. Tamk Makers, Galwanizerss &wCe THE N. A. P. ARTIZANS’ WINDOW. J BY AVOIDING ENTAL STRAINS. by Z Re f 4 HER MAESTYS Ap Si & USED EXTENSIVELy ‘ ee OVERNMENT, vail | fe IMPERIAL 7 INSTITUTE. dopted b =« THE LONDON School. BOARD, *= THE MANCHESTER CORPORATION, I 7] Wy 200 in Queen AnnesMansions Westmingier — |}. & SUPPORTED By A LARGE NUMBER OF Gold Medals, Manchester & Sunderland. THE SEWERAGE ENGINEER’S NOTE-BOOK. BEING STANDARD NOTES ON SEWER FORMULH AND SEWERAGE CALCULATIONS. BY ALBERT WOLLHEIM, Assoc.M.Inst.0.H, Reprinted from “THE SURVEYOR AND MUNICIPAL AND County ENGINEER,” With numerous additional Tables and twenty-seven Diagrams. ALL RIGHTS RESERVED. LONDON : Tut St. Bripn’s Press, Limiten, 24 BripE LANE, FLEET St., H.C. Lonpdon;: PRINTED AND PUBLISHED BY Tuer St. Bripe’s Press, LIMITED, 24 BripE Lanet, H.C. PREFACK. Evolved from notes and data originally collected and compiled by the author for his own use, and printed last year in serial form in THe SuRvVEYOR AND Municrpan AND County Enaintrr, this little volume is now issued as a vade mecuwm for the sewerage engineer, the assistant and the student. Though more particularly designed to be kept on the office desk, its size will admit of its being carried in the pocket when giving evidence before Committees, as well as at Local Inquiries into Applications for Loans for Sewerage Works, where prompt answers always add greatly to the value of the evidence. It is hoped that readers will come forward freely with additional tables, memoranda, diagrams and suggestions likely to improve the book. Such com- ~ munications, addressed to the author (care of the publishers), will be appreciated and acknowledged in due course. If “ The Sewerage Engineer’s Note-Book”’ in any way proves useful to that section of the profession for which it is intended, its razson d’étre will be justified and the author’s object will have been attained. ALBERT WOLLHEIM LEADENHALL Hovusgs, Lonpon, E.C., March, 1896. NG ; - « > y CO NAP EANCT Si. Parr I. GENERAL FORMULZ at F é ‘ ; ' é Part II. STANDARD SECTIONS OF SEWERS . A ; . A Part III. SEWER DISCHARGE FORMULE 2 : ;: : é Part LV. DIAGRAMS OF SEWER DISCHARGE AND VELOCITY . * Part V. THe RELATION BETWEEN RAINFALL AND SEWER Dis- CHARGE . : Z APPENDIX. TABLE V. Pipr Sewers.—A (Sectional Area), R (Hydraulic Mean Depth), “BR, and NN for Velocity and Discharge ° ° . Tasue VI. Circutar Srewers.—A (Sectional Areas), R (Hydraulic Mean Depth), “RB, and Maleniens for Velocity and Discharge. ; : : 4 : ; Taste VII. SranpaRpD Eaa-SHare Sewers.—A, Rand WR Taste VIII. New Eee-SHare Spewers.—A, R and JR TaBLE IX. STanpaRD Hee-Suare Szewers.—Multipliers for Ve- locity and Discharge . . ; : . PAGE 37 51 65 81 82 85 87 89 TABLE X. New KHee-SHarE SeweErs.—Maultipliers for Velocity and Discharge. : : : : . ° . TaBle XI. V/s (/Sine of Angle of Inclination) for Inclination up to 1 in 2000 TasLe XII. QUANTITY OF BRICKWORK FOR CIRCULAR SEWERS e TapLe XIII. QUANTITY OF BRickKworRK FoR Eea-SHAPE SEWERS . TaBLe XIV. EXCAVATION IN TRENCHES.—Cubic Yards per Lineal Yard of Trenches . ‘ : ‘ : 2 ° TABLE XV. SEwaceE Frow.—Gallons per Minute . 5 ; TaBLE XVI. Sewage Fiow.—Cubic Feet per Second : : . TapLe XVII. RAINFALL ON DRAINAGE ARFAS.—Total Volume, Cubic Feet ‘ : ; ; : ° ° . TasLe XVIII. RAINWATER.—Cubic Feet per Second Rainflow, corre- sponding to Rate of Rainfall per Hour . . ° Tapue XIX. Kutter’s CoEFFICIENT “C” roR DIFFERENT VALUES oF /RBR AND n A ; 5 : : ; : Usrrut MEMORANDA . : ; i : ; ; PAGE 92 95 112 115 116 131 182 133 134 135 137 PART I. GENERAL FORMULA. STANDARD NOTES ON SEWER FORMULA AND SEWERAGE CALCULATIONS. PART I. GENERAL FORMULA. A=Sectional Area. P=Wetted Perimeter. H.M.D.=Hydraulic Mean Depth. H.M.D.= = P CIRCULAR SEWERS. LDP Fil Ge he. : B2 A (full) =d? x A P (full) =d x m 4a : A of segment =~", / (06262)? + C? (semi-chord C may be found by right-angled trigonometry) ne AED. eas or A of segment (85 7 — sin °) 5 Perimeter of segment=number of degrees x °017453 rad. EGG-SHAPED SEWERS. kK-—-—~—~-— 8 ~--->5-- 5) Let R =rad. of crown Ri= ;, sides =mxR Re= , invert=nxR then the foliowing equations are correct for all values of R, R,, Ro, ¢, h and a, and for all shapes of four-centred egg- shaped sewers. In the equations the values of sin ¢ and cos ¢ have to be determined. ‘They can be calculated as follows: Since angles OPA and OPB are=®¢, we may calculate from the triangles thus :— - RR aie 8 a Pe Rs nn a=mx Rx cos > h=b[n+(m—n) x cos ¢] then Case 1.—Sewer filled to line AB. Total area below springing line AB= we <5 (w=) (+ ~ ca — 2m (»- 1) x COS 6| =¢ x R? Perimeter below springing line AB= ¥ Ps %, 2x Rx [nx o+m(Z—o) [aor Case 2.—Sewer filled above line AB. #1IG.3. R2 Area=—| x (204 wW—w—sin w) Perimeter =R(c; + w—7) 7 Case 3.—Sewer filled below AB, FG. F. By Area = R? x j e—m x are ( sin | +o [en x (m—1) mxR ey eli m R-2| or +Rx of 2(m-1)-ma/ 1-(—4)° Ge y] mxR Perimeter=R | ee ve oe ( ters \] mxR 8 or the area abcd (see Fig. 5) can be deducted from area 3 full. In the case of the ordinary egg-shape, with conjugate diameter=1'5 transverse diameter, the following method may be employed :— | ay | | Fi G27 r=radius of crown Ta 60° tract this from area 2 full. This will be the area of the lower part, the height H of which above invert is H =2r—pn=r(2—8 sin a) and the wetted perimeter of which= oS Find area area =30"( bh 5 sin 2a—4 sin «) and sub- 2xax3rT perim. ? full— 180 Oase 4.—Sewer filled to crown. - Perimeter= (c; +7) x R or, when it is required to find at the outset the area and perimeter of an egg sewer filled to crown, the following formulz are useful :— 10 FIG. (. Let A=area. R=radius of sides. r PE crown. Ty i invert. P=perimeter. D=total depth. d=distance between centres of large and small circles equal to D—(r+7r,) Then we have r of 2 2 Ne 6° (R?—1,7) + 90 (rend | —d (R-r) p= Zl (R—1)) +90 (rn) | ll 2 R= 3 ( ar Ie Se YT) rT; The angle 6° aubinded by the arc forming sides may be obtained from its sine or tangent, for EXAMPLES. —Required the area and perimeter of the sewer shown in Fig. 7a, having a radius of l ' } 5R —« SR SRA- -SR+ FT G7 crown=2 ft. , the water level coinciding with spring- ing line, also if flowi ing 1 ft. below springing line. 12 Here R. (crown) =2 R, (sides) =mx R=15x R=38 Ry (invert) =n x R="5 x R= 1 Therefore m=1°5 m= “5 fal sin Ge 5—=sin 30° m—n 1°0 cos ¢=cos 30°=sin 60° ="866 Then by formula (see Case 1) :— 3°1416 2 Area to springing line=R? Ea % — 2(°5236—°433) —1°5 x 866 | =c x R?=2'0541 R?= §'2164 square feet Perimeter to springing line—2 R E x 52364+1°5 (1°5708 - 5236) | =c, x R= 3°6652 R=7:3304 feet Further, by formula (see Case 5) :— ' Ay . 2 « ~ be a e Se eG, Area to line CD=—R?* x [2 0541 — 2°25 x are( sing-3 z) | t- a R— wl 2°25 x r—2| = 43216 square feet Perimeter to line CD=R[3°6652—8 x *3404] —5'2886 feet © Notre —In this formula occurs the expression : are( sin) which is solved as follows: == }=="33=s1ne 194, Length of arc=number of degrees x ‘017453 Therefore 19°5 x (017453 = "3404 N \ FAGIZ E Area of brickwork = (inner perimeter + zt)t External perimeter=inner perimeter + 27t Number of bricks—As in sewer work the bricks are radiated to the proper curves, with their faces parallel and normal to the perimeter, we must treat each ring separately, thus :— Number of bricks per ring.—For the first ring divide the inner perimeter P by the thickness of a course of brickwork increased by that of the mortar joint at the inner edge, which gives the number of bricks to go round. 14 Number of bricks per yard length of sewer.— Multiply the number thus found by 36 (inches) and divide by the sum (in inches) of the length of a single brick plus the mortar joint at one end. If there are more rings than one substitute for ¢ in the second of the above two formule the sum of the width of a brick plus mortar joint between the two rings. Examete.—Required the number of bricks per V7 FIG.7§ yard length of the sewer shown in the accompany- 15 ing figure. Size of bricks 8{ x 4; x 2f1n., mortar joints} in. thick. r=rad. of crown in feet. Inner perimeter=.2 xr feet. 1st Course.—Perimeter = 7°93 x r To go round, pat bor ee eee 5D xr 3 Per yard length, number=9~~7**0_ 198 xT 2nd Couwrse.—Perimeter =7'93 x r+ 2m x ~= 7°93 x r+2°386 To go round, number= (7°93 x r+286)— = 32 x r+ 9°44 Per yard length, number = (32 x r+ 9144) = 128 x r+37°8 By means of the above formule, if the size of bricks and thickness of mortar joints are given, tables of brickwork can be readily calculated for all the various sizes by simply substituting the values of r. Reader's Memoranda. INS Reader's Memoranda. —wWw\/\w— PARTe ll. STANDARD SECTIONS OF SEWERS. 19 PARTS I: STANDARD SECTIONS OF SEWERS. CIRCULAR SECTION. / a 1B FIG.&. Area. Perim. ie ny OP Depth of Flow. "7854? 3°14164 °25d Full 632d? 2°095d “296d 3 556d? 1‘911d 292d 25, "395d? Eagle Zod Pee "229d" 1°2381ld "186d er 154d? 1:047d 147d ae By Eytelwein’s formula the maximum discharge of a circular sewer not under pressure occurs when the angle * | ACB = 52° 02 20 —i.e., when the depth of flow is 7(1+ cos 25° 54’) =1°899r ="Y5d By Kutter’s formula the maximum discharge takes place at ‘93d—7.e., when angle ACB=60° PHILLIPS’ METROPOLITAN (STANDARD) EGG-SHAPE. [ee re i ee 21 Area. Perim. ELE. De Depth of Flow. 45947? 7°930r “5 79r Fall 3°5187? 52917 665r 3 3°028r? 4788r ‘6317 24 2°037r? 3°783r 5387 35, 11369? 2°750r + *413r ue "74577 2°211r 3377 i, By Eytelwein’s formula the maximum discharge takes place when ¢=623° The transverse diameter of this sewer compared with that of a circular sewer of equal discharging capacity is as ‘8388 to 1:00. This sewer flowing full will deliver twice the quantity delivered by a circular sewer with equal transverse diameter flowing 5 full. If the egeg- sewer flows 3 full it wwill deliver ie times the quantity of the circular sewer flowing } full. If both be flowing $ full, the circular sewer will deliver 5-7ths of the quantity delivered by the ege. The relative proportions of the egg and acircular sewer to deliver equal volumes, provided they both flow full and the fall is identical, are represented by the equation :— Diam of circle : radius of egg :: 0300 : O'116; 0°300 or diam. of circle=rad. of egg a jie of egg x 2°59; 16 _ diam. of circle x 0°39 ‘300 ei or rad. of egg=diam. of circle x To ascertain the horizontal diameter by which to construct a standard egg-sewer equal in discharging capacity to a circular sewer of any diameter: De- duct the ninth part from the diameter of the circle, the remainder is the horizontal diameter of the equivalent ege. The H.M.D. of a standard egg sewer, or any part of same, may be found by simply multiplying the H.M.D. aE a sewer, the radius of whose crown is 22 unity, by the radius of the crown of an egg-sewer of the same relative proportions, the H.M.D. of which it is required to find. INVERTED STANDARD EGG-SHAPE. FIG./0. Area. Perim, H.M.D. Depth of Flow. 45947? 7°930r *579r Full 3°849r? 5°719r "6739 s., 3°458r? 5'181r ‘6677 2, 2°55777 ANAT 6167 3,, Lt (192 3°142r *500r +,, 10767? 2°639r "408 4,, 23 NEW EGG-SHAPE. Area. - Perim, H.M.D. Depth of Flow. 4°46077 7°852r "5697 Full 3 4 9) 28897 46997 615r ey ai, . 2 99 10177" 26497 "8847 Ss x 4 24, HAWKSLEY’S EGG-SHAPE, ——-----> Fia./a. Area. Perim. H.M.D. Depth of Flow. 3°982r? T° 208r “H538r Full 2°6867" 4°337r *620r z,, 1:02877 2°596r *B98r 2 eee 2 2 As compared with a circular sewer of same diameter the area is as 1°27 to 1:00. Consequently, when the areas are equal, the diameters will be as 8 to 9 nearly. HRRATUM. Fie. 13, Page 25: Instead of angle 146° 1 ’, read 106° 15 \ ‘ ; t we Ae ti } i { 4 Py ne AE hay \ A a4 4 i t \ 4 MY 4 emia bh 4 ne \ } i i \ 1 i { } if Qe 20 Therefore (1) to find diameter of circular sewer of equal discharging capacity add the eighth part of the transverse diameter ; (2) conversely, given a circular sewer to find diameter of equivalent egg, deduct the ninth part of the diameter of circular sewer, the remainder will be the transverse di- ameter of the egg sewer. FOUR-CENTRE ELLIPSE (Hortzontat). ¥ x a ——S—em =O oS ‘2 FIG. s3. Area. 1 Perim. SM: Depth of Flow. 4°691a? 7:930a *592a Full 3°785a? 5'060a “7480 gy, 3:32802 4°655a ‘7154 roe 2°345a? 3°965a 5920 3, 1°362a? 3°275a “4164 1s "905a? 2°870a 3154 1, 26 FOUR-CENTRE ELLIPSE (Uerienur). Area. Perim. oe SNE BY Depth of Flow. 4°691a? 79300 5920 ‘ull B10" 5°508a 686a " 1:366a2 2-953a 462 ‘917? 2°427a °378a bo Qo ne or a2 bo iS) we) op) Ou Q ou O bo | Bal Col bol Colts | 27 The diameter of this ellipse, compared with a circular sewer of equal discharging capacity, is as ‘8272 to 1:00. VARIOUS OTHER SECTIONS. ELONGATED STANDARD EGG-SHAPE (ror INcREASED HEADWAY). + ° S/o’ 1,669.4 f—-—---—-- eer 28 Area (full) = 1°358d? Perimeter = 4"243d H.M.D:=°321d AB=12 CD AE=CD AF=:CD GH=:i CD CH=10D LM ='833d GH ='414d IK =parallel to LM Area CBDEC =°602d? Perimeter CBD =1°'849d JACKSON’S PEG-TOP SHAPE. FIiGaslon Area. Perim. 4°15 47? 7°756r 2°5839r? 4°614r 969r? 2°5417 H.M.D. 5367 *560r *381r Depth of Flow. Full Col Colne 9 ” OVOID SHAPE, (wits Four INTERNAL CENTRES). Rad. of invert ='382 R. Maximum discharge when ¢=533° 30 CATENARY SHAPE (Boston, U.S.A., MAIN DRAINAGE). 31 SEMI-CIRCULAR CROWN, SEGMENTAL INVERT (OuTFALL SEWER). Area (full) = 19127? Perim. =5°236r H.M.D. ='365r SEMI-CIRCULAR CROWN, ELLIPTICAL INVERT (OuTFALL SEWER), 1 | | | | 1 | | t 25d te 26h - 254 2544 = Area (full) ="7267d? Perim. =2°91061 H.M.D. ="249d Maximum discharge when ¢=493° F/IG.20. Construction: Divide AB then EC CD FC GH into 11 parts, eat ott (oe 459 ie 8 f pa i 8 Awd, Fy > en jhe Steg ite as eae ;" ; aly t “ll , a - id fh H viz - E as! J ‘ iS. - “Sie, ¢ y ~ . =" i Lae = | . ¢ > t ee - e % Lr > A a { 2 ‘ - *@ a > _ : - My a ’ _ i ae ss } 44 ee i . 2 4 7 ia ve ‘. » % ; t A, P ’ yey: A re “at ; ay -, ‘ + ee > ’ * awe ® a © e 4 z Ly . = * af = > « a am 4 iF y f . t = - ~9 - ; ~ ; f = 3 a > sf . ce ey ce 4 . . a4 : ‘7 “} — vr, ' 7 ay. J ae SS ’ a a oF “hat I t oh Maes . eli v7 sq! cs i pie : 5 » “~~ Ao le 1 a | « 3 Jy b pols Mi, Ts ae ‘ Po had aa a ae 1 r ar aris WE ta a eee a ~ Reader's Memoranda. Ww Reader’s APemnoranoda. i /\fv~ = fReader’s Memoranda. —WN\/\w— Reader’s Memoranda, —wWh\/\w— Aue Le SEWER DISCHARGE FORMULA. D2 37 PART ITI. SEWER DISCHARGE FORMULA. It is astonishing that English sewerage engineers of the present day give so little attention to a sub- ject of great importance—namely, the actual dis- charge of sewers of all sizes. Whilst in countries which may, as regards sewerage works, be said to be behind England (as, for instance, Germany and the United States of America) important experi- ments on sewer discharge have been and are being carried out, little or nothing appears to be done in this country to further investigate the subject. It. seems hardly credible that, in the hght of recent investigations, the great majority of English engi- neers should still base their calculations on tables of discharge derived from obsolete formule which have been proved to err as much as from 30 to 40 per cent. Moreover, the author has found that the number of those who are acquainted with what may be termed the inner history of sewer discharge formule is very limited; therefore he believes that a brief analysis of some of the more important formule that have been proposed from time to time will prove of more than ordinary interest to a large circle of engineers engaged in or connected with sewerage works. Chezy and Hytelwein’s Formula.—About a century ago two eminent engineers, Chezy, a Frenchman, and Hytelwein, a German, found that the flow of water in channels could be expressed by the general formula :— 38 Vaca [Rx Ss where V=mean velocity of water, feet per second. area of cross section, sq. ft. R=hydraulic mean radius =——___——__? wetted perimeter, lin. ft. inclination of water surface. S =slope = sey length of channel. c =a coefficient determined by experiment. This is the fundamental formula from which nearly all subsequent ones have been deduced. Chezy and Hytelwein found the value of ¢ to be 93:4, assuming it to be constant for all variations of size and inclination; a fallacy that was only dispelled after a long time, when it was discovered that the coefficient was not a constant but a variable. Never- theless, even in very recent times, numbers of engi- neers have conducted experimental gaugings on some particular sewer under their charge, and, having arrived at a constant c which differed materially from the one fixed by the two experi- menters above named, have simply substituted their own constant in the general formula, ignoring all the time the fact that the assumption of a constant value for c is a fallacy. If a hundred experimenters were to gauge a hundred different-sized sewers, one each, they would find greatly different values, differing among each other probably as much as 40 per cent. in extreme cases. In this connection the author feels compelled to sound a note of warn- ing on the subject of sewer discharge gaugings generally. Such gaugings, if undertaken with the object of establishing new values of the coefficient c, and if any reliance is to be placed on the results obtained, should only be undertaken by men well 39 versed in hydraulics, who are competent to take all the necessary precautions in connection with and avoid all those errors which are liable to destroy the value of the experiments. But, above all, it is absolutely necessary that the experiments be con- ducted or superintended persona ipsissima, and not relegated to subordinates. It seldom happens that in a system of town sewers the conditions are favourable for conducting experimental gaugings on a scientific basis without necessitating a con- siderable amount of preparation for that special purpose. One of the first conditions is that the length of sewer experimented upon should have a uniform slope and a free outfall. Further, there should be a tank at the outlet, so as to make the measurements of quantities positive. The employ- ment of weir gauges is objectionable, for the reason that the discharge over such weirs has to be calcu- lated by a formula, the correctness of which depends upon a certain coefficient of discharge, which varies enormously according to the form of weir employed and other circumstantial conditions. To determine the mean velocity by floats is also an unreliable mode of procedure. The mean velocity is easily and correctly deduced from the positive tank measure- ments. Then, again, while any one experiment lasts the depth of flow in the sewer should be perfectly steady. This is a condition difficult to satisfy in town sewers, unless special means are provided for feeding the experimental sewer from some reser- voir or large sewer at its head. One of the most favourite times chosen for experimental gaugings is during a storm, but it is in reality the worst time that could be selected, for the following reasons: As has been shown in a previous chapter, no sewer ever runs full bore eacept when wt ts put ” 40) under pressure, a condition to which ordinarily ne sewer should ever be subjected where it can be avoided. But inasmuch as few systems of sewers can be designed large enough to carry away storm water without a certain amount of gorging taking place towards the lower portions of the system, and especially in the main outfall sewers, therefore the fact of a sewer running full bore, or nearly full bore, is primd-facie evidence of its being under pressure, and to endeavour to determine with accu- racy the head producing the pressure on the sewer is a problem the solution of which requires excep- tional care. But granted we have a sewer which does not run under pressure during storms, then the probabilities are that the depth of flow will net be constant, but will be continually changing according to the progress of the storm, and to attempt to deduce a coefficient of discharge under such conditions would be entirely misleading. Weisbach’s Formula.—The next important for- mula proposed was that of Weisbach. It has since been simplified and modified by others, as have also the other formule; but for the purpose of our in- vestigation it will be best to give all formule in their original constitution, as then their develop- ment one from the other can be better appreciated. The Weisbach formula is :— |My | Peal in which there appear new terms, namely :— 2g =acceleration due to gravity. A and B=empirical constants. 41] It will be seen that the coefficient ¢ is expressed by the bracketed portion, and is not a constant, as in the previous formula, but varies with the velocity. D Arcy and Bazin’s Formula.—Then camé the two eminent French engineers, who, after extensive experiments, arrived at the conclusion that the hydraulic mean radius had a considerable influence on the value of the coefficient c. Moreover, they were the first to discover the important retarding effect produced on the quantity discharged by the friction of the material of which a channel i is com- posed. The formula is :— aL eco cae dane where R=hydraulic mean radius. a@ and B=variables changing with the degree of roughness of the channel. but, although this formula looks very much like that of Weisbach, it will be seen that it really ex- presses totally different laws. Kutter and Ganguillet’'s Formula.— The last- mentioned formula, which was the outcome of the experiments of the two French engineers, formed the basis of those researches and experiments undertaken by the two eminent Swiss engineers, Kutter and Ganguillet, which for their thorough- ness and logical reasoning, combined with mathe- matical investigative skill, take high rank among practical investigations, not only in this, but also in other fields of engineering. It is perhaps not generally known that the experiments were chiefly conducted by Kutter himself, whilst the mathe- matical calculations were for the most part left in the hands of Ganguillet. The formula reads :— 4.2 A164 V8iL_, 00281 arp eee RxS RxS ee) n rf : =e, ‘ 1 + (4164 2 an where n=coefficient of roughness of the material of whiclr the channel is composed. Briefly stated, Kutter found that the coefficient of discharge c varies. 1, With the degree of rough- ness of the wetted perimeter, decreasing with the increase of roughness. 2, With the value of the hydraulic mean radius, increasing with its increase. 3, With the slope, decreasing with its increase in large streams, and increasing with its increase in small channels. Further, c increases. 1, With the increase of R, and most rapidly when R is small. 2, With the decrease of the resistance to flow—.e., with the decrease of roughness of the perimeter, so that for constant values of R and 8, 7 1s also greatest for the smoothest channel, and smallest for the roughest channel. This influence of roughness. upon c is also greatest for the smallest value of R. 3, With the decrease of 8, if R is greater than 33 ft. (1 métre), and also in small channels if the wetted perimeter is very rough in comparison with the area of cross-section. 4, With the increase of S, if R is greater than 33 ft., and if the wetted perimeter is smooth. Or the above laws may be summarised as follows: 1, C, or the velocity, and consequently the discharge, varies with every change in the value of R, 8 and n, and if the slope and x remain the same, then c increases with the increase of R—.e., with the increase of the diameter. 2, c increases with the increase of slope for all diameters whose H.M.D. is less than 3% ft., and 43 with an H.M.D. greater than 33 ft. an increase of slope gives a diminution of c. TABLE I. Values of ©. 12 ft. diameter. ; 20 ft. diameter. 1 in 1,000 1 in 40 1 in 1,000 1 in 40 eee 137°9 146°0 14.5°7 It will thus be seen that by Kutter’s formula, when’ R=3 ft.—that is, less than 33 ft.—an increase in the slope from 1 in 1,000 to 1 in 40 makes a slight increase in the co-efficient; but when R is 5 ft.—that 1s, more than 35 {tthe same increase in the slope causes a slight decrease in the value of c. The values of x for different materials, as found by Kutter, and subsequently corroborated by thousands of guagings, chiefly by German and American engineers, are as follows:— n='O010 for rendered surfaces in pure cement, glazed, coated or enamelled stoneware and iron pipes; glazed surfaces of every kind in perfect order. n='O11 for rendered surfaces with two parts sand to one cement; for uncoated iron pipes, cement pipes, well jointed and in best order. n='013 for ashlar and well-'aid lrickwork; earthen and stoneware pipes, in good condition but not new, and genera!ly the surfaces mentioned with n='010 and ‘O11 when in bad condition. n='015 for rough brickwork, well-dressed stone- work, iron and cement pipes, with imper- fect joints and in very bad condition. n=='O17 fer brickwork, ashlar and stoneware in bad condition. 44 The effect of varying n can be seen from the fol- lowing table :— TABLE II. (Robert Moore, M.AM.SOC.C.E.) Giving values of c in Kutter’s formula (when S=-001 constant). Values of n. R “010 O11 °012 013 - *015 017 ‘J 93°8 82°2 72°7 65°0 53°2 44:6 *2 113°1 100°0 89°1 80°2 66°3 56°2 3 123°8 L11°0 98°8 90°2 75'0 63°4. ‘4: 132°5 118°0 106°0 96°2 80°4 68°8 iy, 138°6 123°8 111°2 101°2 85°1 72'8 6 143°3 128°3 115°7 105°3 88°8 76°4 7 147°4 131°9 119°3 108°7 92°0 79°3 ‘8 150°8 135°1 122°3 111°6 94°6 819 “9 153°7 137'8 125°1 114°2 97°0 84°2 10 1562 140°5 127°4 116°5 99°1 86°0 1°2 1604 1446 131°5 120°4 102°7 89°4, 1'4 1640 147-9 134°7 123°7 105°7 92°2 16 1670 150°8 137°4 126°2 108°2 94°5 18 169°5 153°2 139°7 128°7 110°3 96°6 2°0 171°6 155°4 141°8 130°5 112°3 98°4 22 173°5 1573 143°7 132°3 114°0 100°0 2°4 1752 159°0 145°3 133°9 115°4: 101°4: 2°6 176°8 160°5 146°8 1385°3 116°8 102°8 2°8 178°2 161°8 148°1 136°7 118°0 104°0 30 179°4 163°2 149°3 137°9 1192 105°1 34: 18:7 165°3 151°4 140°0 121°3 107°1 3°8 183°6 167°2 153°3 141°8 123°0 108°8 Ar2 185°3 168°8 155°0 143°4 124°6 110°3 A’6 186°8 170°3 156°4 144°8 125°9 111°6 50 188'1 171°6 157°7 1460 127°2 112°9 It will have been already noticed when examining Table I. that the variation of slope produces only a comparatively slight variation of the coefficient c. Now it has been found that if a slope of 1 in 1,000 be taken as a standard, then for slopes usually met with in ordinary sewer practice the differences will 45 average only about 3 percent. The subjoined table will make this clear. TABLED LLY, Showing the effect of S=variable aid S=‘001 constant :— S=variable. S='001 constant. ; : Veloc. ft. Discharge Velocity Discharge Diam. Incline. per sec. c. ft. pers. ft. pers. c. ft. per s. 5 lin 4,400 2-001 39.3 2°08 40°0 T°. in 1,150 4986 191°9 5°00 192°2 It is therefore evident that in the Kutter formula. S may, for all practical purposes, be taken as 1 in 1,000=-001 constant. Substituting ‘001 for S in the formula it becomes 1811 ‘00281 oe: G6 tor ( 00281\_” Ri ete te Sue a ear and substituting the values of x we obtain 225°6 Z| when n='010, V= Le oe | RxS F $ x = VR 225°6 me "4.45 wh R x Ss 1+— sf BE € and so on for the other values of n. Flynn’s Simplified Kutter Formula.—Now, calling the numerator K, and substituting x for the frac- tional numerator over “R, we have the general formula 46 K ghrA. and we can now compile the following table:— “TABLE IV. When x= K x ‘010 225°6 “445 ‘O11 209'1 489 °012 195°4 084 ‘013 183°8 578 ‘O15 165°2 667 O17 150°9 °756 The above abbreviation and simplification of the Kutter formula is due to the late P. J. Flynn, o.£., a well-known American hydraulic engineer, and it is known as “ Fiynn’s Simplified Kutter Formula.” Its beautiful simplicity must commend it to all sewerage engineers, and it is therefore not sur- prising to find all the more recent tables and diagrams of sewer discharge of American engineers based on this formula. The original Kutter formula has been almost exclusively used by German and American engineers during the last decade; and, as a rule, even English engineers acknowledge that it is the most scientifically correct one that has ever been devised, but owing to its complexity, no doubt, other simple, but less reliable and less correct, formule have hitherto been preferred in England. However, with the adoption of Flynn’s modifications, the “complexity” of Kutter’s formula disappears. He who supplies a long-felt want deserves well of his fellow-men. ‘This is very forcibly shown by the delight with which the extensive tables of sewer discharge recently published in THe Surveyor 47 were received by a large number of municipal and sanitary engineers. The author’s aim is to draw attention to the labour-saving tables of calculated results due to the late Mr. Flynn, which render the application of Kutter’s formula, and of other sewer formule, a matter of the greatest ease and pleasure. Looking again at the general formula V= v A/RxS 1+ a wR and supposing we wish to apply it to the solution of a sewer discharge problem, it will be at once appa- rent that, although we can take the values of K and # from Table IV., we require tables of R, 8, /Rand VS, but more particularly the two latter, in order to avoid tedious calculations. The fault of a great many of the tables printed in English _standard text-books is that they are incomplete— z.e., they do not proceed by units, but skip by tens and twenties, and the chances are the engineer in nine cases out of ten will find them useless. From the general formula V=c/RxS the following additional formule are deduced Vec/Rx /S (lye erm V For velocity oe /8 ) (3) 48 and further, as Q=A x V, therefore [Qe A xe./Rx/8 (4) Axc/ R= (5) For discharge ny ae a eas? ) The above six formule are readily applied to the following six problems, frequently occurring in sewerage calculations :— PROBLEM. Formula. Required. Given. (1 Velocity. Diameter and Inclination. (2) Diameter. Velocity and Inclination. (3) Inclination. Diameter and Velocity. (4) Discharge. Diameter and Inclination. (5) Diameter. Discharge and Inclination. (6) Inclination. Diameter and Discharge. In the appendix will be found tables of area (A), hydraulic mean depth (R), WR, sine of slope (S) and /S. The value of these, more especially the two latter, in expediting sewerage calculations will be apparent to anyone who has ever had such calcula- tions to do. Reverting once more to the fundamental formula V=c/RxS this, as has been shown above, can be written =ce/Rx JS and as we possess tables of C, VR and VS, etc., the calculation resolves itself into one of simple multiplication. la —! Ni gne qReader’s MDemoranda. —Wh\/\w— feat oe Caen sayh. & Reader’s Memoranda. —W/\(\w— on A Reader's Memoranda. Reader’s Memoranda. —V\/\w— fReader’s Memoranda. —w\/\Ww— PART IV. DIAGRAMS OF SEWER DISCHARGE | AND VELOCITY. ol PART IV. DIAGRAMS OF SEWER DISCHARGE AND VELOCITY. The advantages of diagrams over tables of calculated results are threefold: 1, Diagrams possess the great advantage of presenting to the eye a clear conception of the relation of results derived from a variety of assumptions in any given solution; 2, Serious errors in their construction cannot remain unnoticed; 3, The same informa- tion is presented in but a small fraction of the space required for tables. RELATIVE DISCHARGE AND VELOCITY AT DIFFERENT DEPTHS OF FLOW. It has already been pointed out in Part II. (see Fig. 8) that, if calculated by the old formula, such as Eytelwein’s, the maximum discharge of a circular sewer would take place when depth of. flow=°95 d and the angle ACB=52°. But if the more correct formula of Kutter be employed, the maximum discharge would take place at ‘93 d, corresponding to an angle of 60°. Now it seems strange to an observant mind that to this day unanimity is want- ing as to the exact depth at which the maximum discharge does actually occur. It only goes to show how great is the difficulty of conducting sewer gaugings which may be termed exact in the BZ 52 strictest sense of the word, and what a large field there still remains open to the experimenter. How- ever, the author hopes that he has made it clear in the preceding parts that Kutter’s is by far the most correct formula to employ. The subjoined table will prove useful in com- paring the relative proportional values of discharge and velocity if calculated by Hytelwein’s and Kutter’s formula respectively—.e., when C remains constant and when it varies. The values by Kutter’s are averages for the different sizes of pipes, but the variation due to size of pipe is comparatively in- significant. The depth is given in terms of the diameter. TABLE A. Giving proportional values of velocity and dis- charge for circular sewers at different depths of flow. (Values for full pipes are taken as unity.) Eytelwein (c constant). Kutter (¢ variable). Depth. Velocity. Discharg . Velocity. Discharge. 1:0 (fall) 1:00 1:00 1:00 1:00 90 1:09 °99 1:14 1°08 °80 1:10 ‘94 1°15 “99 ‘75 (% full) 1:09 ‘88 114 ‘92 “70 1:08 "82 112 84 60 1°05 66 1:08 ‘68 50 (2 full) 1°00 50 1°00 ‘50 “40 93 °3D *89 °33 °30 83 “21 “75 19 25 (4 full) ‘76 15 66 ‘13 ‘20 ‘70 "10 “DT ‘08 10 50 ‘02 B84 "02 In the foregoing table the velocity and discharge when flowing full are taken as unity. But as recent formule and experiments seem to teach us that the maximum discharge and velocity occur when the sewer is flowing not quite full, some have advocated 53 that the points of maximum discharge and velocity sheuld rather be taken as unity, as shown below. TABLE B. (Based on Kutter’s formula.) Giving proportional value of velocity and dis- charge for circular sewers at different depths of flow. (Mazimum velocity and discharge are taken as unity.) ; Depth. Velocity. Discharge. 1:00 (full) "86 ‘916 93 96 1°000 ‘90 98 "992 ‘81 1°00 "924, ‘80 "99 912 ‘75 (% fuli) ‘99 "850 ‘70 98 “776 POC 93 ‘620 ‘50 (2 full) ‘86 ‘450 °40 76 "802 30 "64 168 ‘25 (4 full) ‘BT ‘118 ‘20 "48 ‘072 "10 28 ‘016 But considering that no sewer ever can run quite full by gravitation alone, and that it must be put under pressure to do so, it is more probable that further investigation and experiments will reveal the fact that a sewer running under a head just sufficient to fill it to the crown discharges at least the same quantity as when running at its maximum capacity by gravitation only. Fig. 21 gives in a condensed form the substance of a paper contributed to the “ Proceedings” of the Institution of Civil Engineers, in 1889, by Mr. R. M. Gloyne, a.m.t.c.e. The table and curves give the proportional values of area, perimeter, hydraulic mean depth and discharge at various depths of O60] 00 Of 00 7] soem p see | 88s- | éxe- | Famke Toor | ae [zeor [eso v | +ert| 662. f 00° oo°r 90° oo] § [nasa] 029A OW | 38d) Say]: ; azls9m | in G1 2, SY4AMIAS UvVIAIYVID Aow~ SIAWND Hi dad (22D “QT PUB G SO]QBY, OSTB 90g) ‘e[nULIOJ 8,uteMpeyAq Aq pojndwoo st wevisetp siyy, ‘MOTT JO SHLdHC LNAUMAAIC LV ‘SHUMAG CAdVHS-DOY GUVGNVLY GNV YVINOUIQ Yod ‘aDUVHO “SIQ GNV ALIOOTHA ‘HIG NVA OITAVYCAY “AALANINA GALLAAA ‘VENW AO SHAIVA ALVNOILYOAOUg Mid? H-M.0.|VeLociT 7) rg ul 3 ul "n a ul Q < z uw ’ oC. wv ul a .2) u WA wl > al 3) a] : SANREGRANEBNOAARD m Ww) id AZT ¢ Sins vile 700 N91 9 O! OD} ac/b4t-| ° 56 flow, but, unhappily, they are based on Hytelwein’s formula. In Figs. 22 and 28, therefore, the author gives similar diagrams, based on Kutter’s formula, and derived from several diagrams supplied to the author by Mr. Robert Moore, M.AM.SOC.C.E., and Mr. Arthur L. Adams, Assoc.M.AM.S0OC.C.E. SEWER DISCHARGE DIAGRAMS. The bent of Americans towards labour and time f1G.22. — RATIOS OF VELOCITY AND DISCHARGE FOR CIRCULAR SEWERS PARTIALLY FULL TO SAME WHEN FULL. This diagram is computed by Kutter’s formnia, and gives also the angle corresponding to the line of maximum velocity and maximum discharge. saving appliances is well known, but few English engineers are probably aware to how wide an extent this tendency is manifesting itself in the American engineering profession by the conversion of formulz and the reproduction of tables and data into handy This diagram is computed by Kutter’s formula. height of the sewer and the volume of discharge and the velocity of flow with sewer running full are all taken as unity. Oc AA Pt Ur aay | hi Ub ak sREADwE Ne MOB eeees SREBEAT: t++4 a BERET a EHH HHH 4 fon} 2 De 0 + © IS Co] o io] oOo oO oO Oo o oO "ABJOLUDIC] ABMIG OF MO}4 40 Yydaq 40 O140y ° 07 0.8 09 1.0 1) 06 03 0.4 02 0.) ; : Ratio of Velocity and Volume for partial Depths tothe same with full Sewer, i La 0.0 Pe Ee CEE EEE EEE EEE EEE EEE H+ 4 0.5 00 The 23. Fic. RATIOS OF VELOCITY AND DISCHARGE WITH SEWER PARTIALLY FULL Find on vertical scale the ratio of the depth of flow to the sewer diameter and on the horizontal scale the ratio of the velocity and volume at that depth to the same when sewer is flowing full depth. WHEN FULL. THE SAME TO Dracram 1.—Computed by Kutter’s formula, with N=°0138. With N=‘012 add 10 per cent. Take inclination on left hand vertical scale, and find dis- charge in cubic feet per minute on the top horizontal scale. D1acRAmM 2.—Same formula as Diagram 1. Take inclina- is ew boig 1 404 Ul aad absoyrsig She & e 2 3 ¢ bog 10p UI vad ison ] 43 a9 ieee} = lA as oe fa [S rey! qk aun an a0 2088 BRIS aB ty on Hy Baste 650 __ harge for Diag.2. Fies. 24 and 25. DISCHARGE AND VELOCITY OF. Fiow IN 6-IN, TO 24-IN, PIPE SEWERS FLOWING FULI. Cub. ft. per Min. Disc aneeee faire oe at see a t= TTVich! Sesh weany; i ui aug § 1 boig 405 1014091) u4} Ss S wos S See 2 big 404 uoiporipry 0 400 400 = oo tion on left hand vertical scale and find discharge in cubic feet per minute on the bottom horizontal scale. DiacRAMs 3 and 4.—Take discharge in cubic feet per minute on right hand vertical scale and find velocity in feet per minute on horizontal scales. Dr1aGRAM 1.—Computed by Kutter’s formula, with N =:013. With N='015 deduct 18 per cent. Take inclination on the right hand vertical scale and find discharge in cubic feet per minute on the bottom horizontal scale. ‘er may i aneie to} ve aes aiote PPPS TP 5 S ny se supaaceCesaccaiee a curtain sine 3 rr sagan ~ : a eran RSE ENCE SCR Seb TEN ro NT ACN ers ae SER SEN NAS © Se. 2 5 cose ene ase RN Nal eee * SEEN Bas ceootacecssns satan taenten te fou os PS i a OT SO eee PINT TM KT TAT TA baa = an NR Na 7 WARE 3 oF te tHe aisthemscesnnstast sae NENT ao 09% ore sie ae : passes a Soe a 5 be Les oe ae He ULE Ye 4] WA MANNS ‘aa oS g So Ss sy w w wo wo 2 bog G 405 UW 49d 4yqr7y u: Sart \ Velocityin Ft per Min , Diag 2 EN DiacRaM 2.—Take discharge in cubic feet per minute on left hand vertical scale and velocity in feet per minute on top horizontal scale. DISCHARGE AND VELOCITY IN CIRCULAR SEWERS FLOWING FULL. D1aAGRAM 1.—Computed by Kutter’s formula, with N =‘013. With N=‘015 deduct 18 per cent. Take inclination on the riyht hand vertical scale and find discharge in cubic feet per minute on the bottom horizontal scale. f=) S Se ~] 2 Ss Ss fo) Ss Cm im S cu Ss a iS. Ss ul oud CY AN] ae Host rH seueueuesekan—< LTH Gusntcaran wa SagS5cRER PN apeiiitt H HoH ry] ESTA ] a seseace aeeces CN sank a PRN a Beh OWS i he a ss si CAT see Set ! PS me ae {| Sy ae S v2) _ L NH : RON So pe LoS AN seas Pe Tes auccance Fe aa a o > buses pram ob rag = 3 xe . o EPS £ 'e o CoS = cco o coo o Sooo 3 H seca: say caps. 3 Ss we ne = cH ee OE * 5 | PAs = ry] KZ EP, Agia Cag i‘ fi A ‘a 4 HHH Ber, Ae Zapauuauedonds BoA ove Be Pacer, Cae _& 0ve Foe at pe er q3) ar Pa rieaal ms Her V, marasesece er He o Savy n 49 ap ap. 7 4p.57.ap.4E".60 Coie = fran ap287ap Ke ara a Pra £ = a 5 8 4 DiaGRAM 2.—Take discharge in cubic feet per minute on left hand vertical scale and find velocity in feet per minute on top horizonal scale. DISCHARGE AND VELOCITY IN STANDARD HGG-SHAPED SEWERS FLOWING FULL. 61 diagrams. Moreover, that section of the profession devoted to sewerage matters cannot complain of having been neglected in this respect, for they have been favoured with a large number of diagrams of sewer discharge. Nearly all these diagrams are plotted differently, and they each and all possess distinct advantages of their own. The most handy diagrams—remarkable for com- pactness, combined with clearness, and fairly wide range—are those given in Figs. 24 to 27. Like Vig. 23, they are due to Mr. Arthur L. Adams. As it is generally of importance to know the velocity at a given inclination and discharge, the author believes that the ingenious method of plotting the velocities in the manner shown will be greatly appreciated. Though reduced to a some- what small scale, the diagrams will be found sufficiently accurate for all but final calculations, and even for part of final work. i cf pales ie eee a f LY aie Reader’s Memoranda. —" \/\ MWn— Reader’s Memoranda. ——WV/\Vn— Reader's Memoranda. —/\ Wve- Reader’s Memoranda. w/w Reader’s Memoranda. Reader's Memoranda. —~" VAVAN, —— PARTY. THE RELATION BETWEEN RAIN- FALL AND SEWER DISCHARGE. 65 PARE. V: THE RELATION BETWEEN RAINFALL AND SEWER DISCHARGE. In the modern combined system of sewerage—in which the sewers must take not only the sewage proper, but also the rainfall—it is of paramount im- portance to know exactly for what volume of rain- fall provision should be made. The calculation of the volume. of dry weather flow—d.e., sewage proper—is a simple as well as comparatively un- important matter, because the dry-weather flow is a known quantity, varying, it is true, between certain hours of the day, but, nevertheless, calculable within a considerable degree of accuracy; whilst rainfall is subject to such sudden fluctuations and bears such an enormously increased proportion to the dry-weather flow, that it really forms the governing factor in the design of sewers on the combined system. Having ascertained the quantity of water supplied per head of population, and the density of population per acre, the flow of sewage proper is easily arrived at. But, on the other hand, if we attempt to answer the question, ‘ What volume of rainfall will the sewers have to convey?” we are at once beset by innumerable difficulties. The consideration of the subject divides itself into two principal sections: (1) The actual rainfall on any given area or district; (2) the proportion of such rainfall which will reach the sewers. F 66 RAINFALL STATISTICS. The rainfall records of the British Isles are perhaps the most complete of any country, and are being perfected and amplified from year to year; but it may at once be stated that they are of com- paratively little use to the sewerage engineer, inas- much as they only give the total rainfall per twenty-four hours, and in a few instances for shorter periods. What he requires to know is not the total precipitation for lengthy periods, but the duration of heavy precipitations of short duration, as these alone tend to overtax the capacity of sewers, and therefore play a most important part in determininyg the size of the latter. The Government supply marvellously accurate Ordnance maps, on which we can lay out sewerage systems with the greatest ease and expedition ; they lend to public authorities the money necessary for carrying out such works, and exercise a benevo- lent control over the expenditure, so that the money shall be spent on efficient works. The Meteorological Office has a large staff of observers in every locality used to accurate observations; is it then asking too much that the existing staff might, at no great additional expense, be utilised to supply that information which is the very essence of the sewerage engineer’s requirements—namely, rainstorm records ? But if the Government cannot be prevailed upon to grant the above facilities, it remains for municipal engineers to urge their cor- porations to undertake the work of observation in their own particular locality. HKvery municipal community possessing, or likely to require, a sewerage system should be equipped with auto- matic recording rain guages, to be distributed in svitable positions over the district, as sometimes 67 only portions of an entire district may be affected. At present we are somewhat groping in the dark, because there are few statistics to go upon. Of course it may be that some of our older engineers, if wise, have accumulated data which would be of value if communicated to the profession at large and tabulated in proper form; but the author be- lieves that on the whole little has been done in this country to elucidate the subject. The sooner a systematic series of rain-storm records is initiated the better, for in order to allow of reliable deduc- tions being made they should embrace a period of many years. SIZE OF SEWERS. Although the whole volume of even heavy storms is easily carried off from a small area by an ordinary- sized drain, it is quite impracticable to build main outfall sewers of sufficient size to convey the dis- charge of the numerons tributaries comprising the network of a large drainage district, which may all be running full bore at the same time during a storm. A proportion of snch rainfall must there- fore be kept out of the main outlet sewers by the construction at suitab'e points of storm overflows discharging into natural watercourses. Supposing now that we have obtained careful observations of the maximum rate of precipitation to be expected during heavy downpours in the locality for which we want to design a sewerage system, the question arises, ‘What proportion of the total volume will find its way into the sewers P”’ This depends to a large extent upon the nature of the surface, whether paved or unpaved, and if the latter, upon the degree of porosity of the ground. But there is another point that must be considered. Having arrived at the maximum rate of rainfall as F2 68 well as the proportion of same likely to be absorbed by the surface, we next have to inquire how quickly the remaining proportion will find its way into and become concentrated at the outlet. This will depend chiefly upon the size and configuration of the drain- age area. Take the case where a heavy storm is bursting over a district. The steeper the slopes of the drainage valley the quicker will the discharge at the outlet reach a maximum. Further, the shorter the district in proportion to its breadth—.e., the shorter the time necessary for the water from the remotest parts of the district to travel to the outlet— the quicker will the maximum concentration at the outfall take place—.e., the quicker will all parts of the district contribute to the flow at the outfall. Mr. E. Kuichling, m.4M.soc.c.z£., city surveyor of Rochester, N.Y., one of the most able investigators of this problem of storm-water discharge in town sewers, has, from a large number of gaugings, de- vised a formula for proportioning the size of sewers, which embodies the expression of the relation of the probable maximum intensity of rainfall to its dura- tion, and thus takes account of the time necessary for the storm wave to become concentrated to its maximum intensity. But before giving Kuichling’s formula it may be interesting to review some of the principal formule that have been proposed from time to time. Probably the best known and most extensively used is that of the Swiss engineer, Burkli-Ziegler. Burkli-Ziegler’s formula :— 226 where Q = water reaching the sewer, cubic feet per second per acre. 69 R=average intensity of rain during the period of heaviest fall, in cubic feet per second per acre - (found to vary from 1°75 to 2°75). C =coefficient varying from ‘31 for rural districts to “75 for paved and well-developed surfaces. Average value =°625. S = general slope of atea per thousand. A = area of drainage district in acres. In this formula Q increases with R, C, and 8, and diminishes as A increases; but the formula takes no account of the shape ot the watershed. It is, moreover, based on guagings of comparatively small areas; hence, when applied to large areas, it has generally proved unreliable. Hawksley and Bazalget e adopted the SB formula :— Log. p=2 Log. eae: N+68 where D = diameter of circular sewer in inches, to carry off a rainfall of 1 in. per hour. A = number of acres drained. N = length of feet in which the sewer falls 1 ft. This formula contains only two variables—the area and the slope—without taking account of any of the other functions entering into the problem, and, besides, only allows for a maximum rainfall of lin. per hour. It is, therefore, not surprising that in a number of cases where sewers have been pro- portioned by this formula additional relief sewers have had to be constructed subsequently. Colonel Adams’ formula, as simplified by Kuich- ling, reads :— iy (8 [58 Q= 1085 Ar] or where Q = maximum discharge of outlet sewer, cubic feet per second. r = rate of rainfall, lin. per hour. S = sine of general slope of surface of district. 70 McMath, of St. Louis, next proposed the following : Q=0R,'/ 58 a! where Q = cubic feet per second discharge from whole area drained. C =proportion of total rainfall that will reach the sewers, the value of which will, of course, depend principally upon the nature of the surface, varying from about “5 per cent. for paved city districts to as low as 25 per cent. for undeveloped suburban areas. R = cubic feet of water falling upon an acre of surface per second during the period of greatest intensity of rain, which is practically the same as the rate of rainfall in inches per hour. S = mean slope of surface per thousand. For paved city surfaces Mr. McMath found that the quantity of water reaching the sewers may be computed by writing the formula Q = 2:0625,'/ 8 a’ Looking at the heterogeneous constitution of these various formule, it is not surprising to find that if applied to the same sewer problem they should give results differing to such an extent as to cause grave doubts as to the possibility of devising any formula that will adapt itself to all the varying conditions underlying the relation between rainfall and sewer discharge. Capt. R. L. Hoxie, M.am.so0.¢.£., rightly says: ‘It requires no argument to point out the impracticability of such eeneralisations as are involved in empirical formule for maximum flood flow. They are useful, as each suggests its relation to the cases to which it is made to conform, and so widens the field explored ; but there is no legerde- main in hydraulics which can solve a problem of 71 twenty independent variables by the use of one or two. These empirical formule, which can only be applied: with confidence within the lmits of the experiments on which they are based, are too often mistaken for devices by which a few hours of ele- mentary computation may snffice instead of labor- ious thought and thoroughness of investigation.” Having thus seen that there is no royal road, no simple universal formula, for accurately proportion- ing the size of sewers in relation to rainfall, let us once more refer to Mr. Kuichling’s experiments an | investigations, above alluded to. ‘he principal conclusions at which he arrived may be summarised as follows :— (1.) The percentage of the rainfall discharged from any given drainage area by the sewers during the period of maximum flow is nearly constant for rains of considerable intensities and lasting equal periods of time. In other words, supposing we have a drainage area of 300 acres, and supposing that during the period of maximum flow produced by a rainfall of ¢in. per hour lasting twenty minutes—say 35 per cent. of the whole rainfall is discharged—then during a rainfall of 1 in. per hour lasting an equal time—vwz., twenty minutes—the percentage of discharge would also be about 35 per cent, (2.) The said percentage varies directly with the degree of urban development of the district—viz., with the amount of impervious surface thereon. (3.) The said percentage increases rapidly and directly or uniformly with the duration of maximum intensity of rainfall, until a period is reached which is equal to the time required for the concentration of the drainage waters from the entire tributary area. 72 (4.) The said percentage becomes larger when a moderate rain has immediately preceded a heavy shower, thereby partially saturating the permeable territory and correspondingly increasing the extent of impervious surface. The above conclusions, further, led Mr. Kuichling to the opinion that, “Instead of employing any of the known formule, the safer method will be to estimate the probable future amount of impervious surface on the given area, either with reference to the density of population or in any more reliable manner that may be devised, and to assume that all water falling on paved surfaces will run off without loss. Further, since the topography of the area 1s supposed to be known, the slopes and length of the longest tributaries to the outlet sewer can readily be determined, as well as their approximate diameters, and thence also the velocities of flow therein. From these elements the time required for the flood waters to reach the outlet sewer from the most distant parts in the area can next be found; and when the relation between the probable maxi- mum intensity of the rain and its corresponding duration are known, the maximum rate of rainfall belonging to the time so found can then be deduced. The dimensions of a sewer so computed will be found adequate until the original assumed amount of impervious surface, or density of population, has been exceeded.” From the above considerations Mr. Kuichling has evolved a formula which, if judiciously employed in combination with the above method of reasoning, must be regarded as embodying the latest advance in this complicated problem of storm-water dis- charge, Kuichling’s formula reads :— Q=Aat (b-—ct). where Q = sewer discharge, cubic feet per second. A = magnitude of drainage area. a, b, c=certain empirical constants deduced from the re- lation of the maximum intensity of rainfall to its duration. These constants will vary for different localities. t =time required for the concentration of the sterm water at the outlet. In conclusion the author ventures to express a hope that English engineers may soon take the lead in investigations of sewerage problems, which, for the time being, they seem to have relinquished to their American confréves. The installing of numerous automatic recording rain guages is a sine qua non to the attainment of “this object. Hqually necessary, perhaps even more so, 1s the fixing of automatic recording storm guages in the sewers themselves, so that the actual rainfall and the actual discharge of the sewers may be compared without that element of uncertainty which is bound to be associated with guagings conducted without the aid of automatic instruments of precision. Storms have a way of bursting over a district just when they are least expected, and some of the best records may be lost unless automatic guages are resorted to. Ss Tale ed Ee INA 81) Ds CH; APPENDIX. It has already been pointed out in a previous chapter that from the general formula Vec/RxS the following formule are deduced :— f: ‘Vi a= c/ R x V8 JR As For velocity 4 rear oe PS ae Vi and further, as Q=A x V, therefore ia Q=(AxcVR)x V8 —~ 9 Ax¢/7 R)= == For discharge ae ) /S§ ree Q Sh (Axc/R) L (1) (2) (3) (4) (5) (6) The above six formule are readily applied to the solution of the following six problems, frequently occurring in sewerage calculations :— 78 PROBLEM. Formula. Required. Given. (1) Velocity. Diameter and Inclination. (2) Diameter. Velocity and Inclination. (3) Inclination. Diameter and Velocity. (4) Discharge. Diameter and Inclination. (5) Diameter. Discharge and Inclination. (6) Inclination. Diameter and Discharge. EXAMPLES SHOWING APPLICATION OF THE TABLES. EXAMPLE No. 1. Find Velocity (given Diameter and Inclination).—A glazed stoneware pipe sewer, 18 in. diameter, has an inclination of 1 in 232. Find velocity of sewer when flowing full, also when 4 full. Take n='012, By formula (1) V=c/RxV/8 Then (by Table V.) c,/ B for an 18-in. pipe, with n="012 equals 63°83 Further (by Table XI.) ./ S for 1 in 232=-065653 And 63°88 x (065653 =4°19ft. per second velocity, flowing full Also (by Table A, Part IV., p. 52, Kutter) velocity 4 full=‘66 x velocity full, therefore 4°19 x ‘66=2°76 ft. per second velocity when { full. EXAMPLE No. 2. Find Diameter (given Velocity and Inclination).—A standard egg-shape brick sewer is to have an inclination of 1 in 519, and the velocity when flowing 3? full is not to exceed 6 ft. per second. Find the diameter. Take n='O15. — V By formula (2) ¢./ R = S the, Then (by Table XI.) \/ 8 for 1 in 519 =:043895 ype Bp 136°7 an ee a ee a a 7S 043895 Searching in Table IX. under c./ R for % full we find the value nearest to 136°7 to be opposite diameter 5 ft. x 7 ft. 6in., which is the required diameter. EXAMPLE No. 3. Find Inclination (given Diameter and Velocity).—A cast-iron circular sewer is to be 5ft. 8in. diameter, and to have a maximum velocity of 6 ft. per second flowing fall. Find the inclination. Take n=‘O15. By for fate ‘CATS 2ey + Then (by Table VI.) c/ RB i 5ft. 8in. diameter and Athy =015 ls 126, and = 047619 n='015 equals an war anos 7 Searching in Table XI. under ee we find the nearest value to ‘047619 to be opposite 1 in 441, which is the required inclination. a a CE EXAMPLE No. 4. Find Discharge (given Diameter and Inclination).—A new egg-shape concrete sewer, 2ft. x 3ft. diameter, is to have an inclination of 1 in 475. Find the discharge when flowing 4 full. Take n="015. By formula (4) Q=(A xc./ R)x /S Then (by Table X.) (Axc/ R) for 2ft. x 3ft. diameter and 3 full equals 50:17 Further (by Table XI.) / 8S. for 1 in 475='045883 and 5017 *:°045883 = 2°30 cubic feet per second, the discharge. a Ue Cha sea aa 80 EXAMPLE NO. 5. Find Diameter (given Discharge and Inclination) —A glazed stoneware pipe sewer is to discharge 11} cubic feet per second flowing full, and to have an inclination of lin 280. Find the diameter. Take n=‘013. By formula (5) (A xc wih} oo Then (by Table XI.) /S8 for 1 in 280=-059761 and Searching in Table V., under (A x cr/ R) and under ‘013, we find the nearest value to 192°44 to be opposite 23 in., which is the required diameter. Say 24-in. pipe. EXxAaMPLe No. 6. Find Inclination (given Diameter and Discharge).—A standard egg-shape brick sewer, 4ft.x 6ft. diameter, is to. dis- charge 70 cubic feet per second flowing full. Find inclination. ‘Take n=‘O15. Q By formula (6) Ws = (Lee ee Then (by Table 1X.) (Axc4/R) for sewer, 4 ft. x 6 ft. diameter, flowing full +2019°5 and Q pee (Axcs/ R) 20195 = '034.66 Searching in Table XI., under WS: we find the nearest value to ‘03466 to be opposite 1 in 832, which is the required inclination. Sack ena sl ‘PABURS = Ver For Pipe Sewers, 6in. to 24in. diameter, flowing full. V (feet per second) =c /BRx/S8 Q (cubic feet per second) =(A x c./ BR) x / 8 A R Sect. As Avea. mA in.| sq.ft. | ft. 6| °196 |°125|- 7| °267|°146 |: 8} °349|°167|- 9| °442)°187|- 10| °545 |°208 |- 11} °660|°229)- 12| °785 |°250}: 13} °922|°271 |: 14 | 1°069 | "292 |- 15 | 1°227|°312 |: 16} 1°396 |°383 |° 17 | 1576 | 354 |° 18 | 1°767 | 375 |- 19 | 1°969 | °396 | 20 | 2°182 |°417 |- 21 | 2°405 | °437 |- 22 | 2°640 | °458 | ° 28 | 2°885 |°47S|- 24 | 3°142 |°500 e/R (for Velocity). AxeceV/R (for Discharge). n='011 30°93 34°94, 38°77 42°40 45°83 49°46 52°85 55°95 59°13 62°22 65°21 68°26 71°08 73°90 76°76 79°33 82°11 84°75 87°36 n="012 27°45 31°05 34°51 37°80 40°95 44°22 47°30 50°11 52:99 55°78 58°50 61°26 63°83 66°41 69°03 1388 73°92 76°33 78:72 n="013 24°60 27°87 31°00 34°00 36°87 39°84: 42°65 45°22 47°85 50°42 52°90 55°44, 57°80 60°17 62°58 64°73 67°07 69°29 71°49 n='011 n='012 |n='013 6°06 9°33 13 53 18°74 24°98 32°64 41°49 51°59 63°21 76°35 91°04 107°6 125°6 145°5 167°5 190°8 216°8 244°5 274°5 5°38| 4°82 8'29| 7°44 12°04} 10°82 167715 15:08 22°32} 20°09 29°18| 26°30 37°15 | 33°50 46°20} 41°69 56°64 51°16 68°44] 61°87 81°66| 73°85 96°55 | 87°37 112°8 | 10271 180°8 | 118°5 150°6 | 1386°5 171-7 | 155°7 195°1 | 177°1 220°2 |199°9 247°3 | 224°6 G For Diam. Lent) ct e waewnwnwnwnwnwnnnNnnnnnnrnvbWvwb 7 B IHOoPWNWEr O in DBIRWIPWONHOrFOO®W Otrcular bo TisiE = Ve Sewers, 2ft. to 12 ft. diameter, flowing full. V (feet per second) =c./Rx/8 Q (cubic feet per second) =(A x c /B)xX/8 A R be aD rene ahs sq. ft. ft. 3°14 *500 3°41 "521 3°69 "542 3°98 "562 4°28 583 4°59 *604 4°91 *625 5°24 648 5°58 667 5°94 ‘687 6°30 ‘708 6°68 "729 707 ‘750 Tal 4 787 "792 8:29 *812 8°73 °833 Ou) *854 9°62 "875 10°08 °896 10°56 ‘O17 VR ft. “707 "722 ‘736 ‘750 "764 tid. “790 804, ‘817 829 842 "854 866 878 *890 ‘901 913 "924 935 "946 957 cVR 715 73°7 75°7 778 79°9 —681'8 83°8 85'°9 (for Velocity). n='013 | n=°015 60°1 61°9 63°7 65°5 67°3 69°0 70°7 726 743 76:0 776 79°2 80°8 824: 840 85'5 87°1 88°6 90°1 91°6 93°1 AxceV/R (for Discharge). n='013 224°6 251°1 279'1 309°2 341°5 375°4 411°3 450°5 490°9 532°8 578°0 6248 6741 726°0 780°6 836°7 896°3 957°3 1021°1 1087°7 1157°2 n=°015 188°8 211'2 234°9 260°5 287°9 3166 347°3 380°5 414°8 451°2 489°0 528°8 570°9 6151 661°8 709°6 760°4 812°4 866°9 923°7 983°1 Diam, ite in A ~ Sect. Area, sq. ft. ee tt a DAIAAIBWMOAAIAINNNKNAATTNE EEE LRP ASP BOO CORWODRWOHOCHOON 11°04 11°54 12°05 12°57 13°10 13°63 14°19 14°75 15732 15:90 16°50 17°10. 17°72 18°39 18°99 19 638 20°20 20°97 21°65 22°34 23.04 23°76 24°48 25°22 25°97 26°78 27°49 28°27 30°68 33°18 35°78 38.48 41°28 44°18 4717 50°27 e/R ; (for Velocity). n="018 n="015 AxeVR (for Discharge). n='013 | n="015 "968 “979 “990 1:000 1:010 1°021 1.031 1:041 1051 1061 1:070 1:080 1:089 1099 1'109 1118 1127 1187 1146 1.155 1°164: 1173 1181 1°190 17199 1:208 1216 1°225 1'250 1°275 1299 1323 1°346 1°369 1°392 1414 111°3 113'1 114°9 116°5 118"1 119°8 121°4 123°0 1246 126°2 127°7 129°3 130°7 182°4 134°0 135°4 1369 138°5 139°9 14.1°4 142°9 1443 145°6 14771 148°6 150°1 151°4: 152°9 1570 1612 165°2 169°2 173°0 1769 180°8 1845 94°6 96°1 97°5 oo: 100°5 102°0 103°4 104°8 106°2 1076 108°9 110°3. 111°6 113°0 114°4, 115°7 LEE 118°4 119°7 121°0 122°2 123°5 124°8 1260 127°3 128°6 129°7 131°0 13846 138°3 141°8 145°3 148-7 152°0 155°5 158°7 1229°7 | 10450 1805°3 | 1109°6 13884°1 | 1175°2 1463°9 | 1245°3 1546°9 | 1315°8 1633°5 | 1890°8 17220 | 1466°7 1813°8 | 1545°7 1908°0 | 1627°0 2007°0 | 1711°4 2206'1 | 1796°5 2211°1 | 1886°8 2316°9 | 1977-7 2429'1 | 20741 2543°9 | 2172°9 2659°0 | 2272°7 2778°7 | 2376°7 2908°5 | 2482-0 38029°4 | 2590°5 3159°0 | 2702°1 3292°3 | 2816°7 3429°2 | 2984°8 35662 | 3056°4: 3710°9 | 3177°3 3859°7 | 3305°6 4012°2 | 3486°3 4162'7 | 3566°6 4322°9 | 3702°3 4816°8 | 41380°3 53397 | 4588°3 5911°5 | 50747 6510°6 | 5591°6 7142°0 | 6186°8 78142 | 6717°0 8527°9 | 7833°5 9272°6 | 79783 G2 84: Ue ee SS re A Roy ey ie Diam.| geet, | AT Area. HA ffs ins) Sq. 20. ft. ft. 8 83 | 58°46 | 2°062 | 1°486 8 6 | 56°74 | 2:125 | 1.458 8 9 | 60°18 | 2°187 | 1°479 G9 0 |) 68°62 | 2°250. | 1°500 OS 8h i67 20 e sla a bal 9 6 | 70°88 | 2°3875 | 1°541 9 9 | 7466 | 2°487 | 1°561 10 O| 78°54 | 2°500 | 1°581 1G 3B} 82°52 71-2562 1 COL 10 6 | 86°59 | 2°625 | 1.620 10 9 | 90°76 | 2°687 | 1°639 11 O | 95°03 | 2°750 | 1°658 11 3 | 99°40 | 2°812 | 1°677 11.64103°9" 4) 2875 41-696 11 9 |108°4 2:9387 | 1°714 0 11131 | 3°000 | 1°782 eV R AxceV/R (for Velocity). | (for Discharge). n='013 | n="015 | n="013 | n="015 188°2 | 162°0 | 10059 | 8658°8 191°9 | 165°3 | 10889 | 9377°9 195°4 | 168°4 | 11753 | 10128 199'1 | 171°6 | 12663 | 10917 2026 | 1747 | 18613 | 11740 205°9 | 177-7 | 14597 | 12594 209°3 | 180°7 | 15624 | 138489 212'8 | 188°7 | 16709 14426 2162 | 186°7 | 17837 15406 219°4 | 189°5 | 18996 | 16412 222°6 | 192°4 | 20205 | 17462 225°9 | 195°2 | 21464) 18555 229°] | 1981 | 22774 | 19694 232:4 | 201°0 | 24189 | 20879 935°4 | 203°7 | 25533 | 22093 238°6 | 206°5 | 26981 | 23352 85 L8L. 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OO8- 918: 89L- Sos. 9€L- 6&8. POL- OG8- GL9- OO8: OF9. OSL. 809. “43 "Ay (‘a’°W°H) uy a CT-6 8SE-1 PPS.1 00-92 908.1 g9-8 6E8-T S6L-T 89-76 882-1 LI-8 | OG8.-T CVL-T 61-86 69<.T 69-1 008.-T 169.1 g8-16 192-1 66-L 1836-1 6€9.T £9.06 TS. 61-9 19Z-T | 889.1 86-61 616-1 98-9 OFZ. LEG.1 90-8T S61.T P6-S 612-1 Q8P-T 18-91 ELI-T PG.G S6I-T rer. SL-ST GST.T GT-S | Q4T-T $86.1 $9-FI TST LL | VSLT oes. 99.81 OLT-I TPP GSI-T 183.1 PC.61 680.T L0-¥ 60I.-T O0&Z-T 9g-IT 990. T. PL 980-1 SLIT 19.0T FPO-T GP-S 690-1 LOL-T TL-6 160.1 IL-€ LE0.T 910-1 ¢8-8 866. €8-G 610-1 gz0.T 60-8 P16. Go.G L86- €L6- FG-L 6F6- “43 °bs “95 sar “45 “bs "3 *(vory) Ca’°W'H) | ‘(vety) Vv ayy a Vv uy a TM + "TMA = “Tad FL-OP F6-LE 08-96 61-86 TL.TE 91-66 L8-L6 C0.96 86-06 89.66 6-06 96-61 78-L1 8€.91 66-71 99.81 6E-6L SI-T1 Fig isi 9 iw OcoorrrrDDDADO CONFODOO ri re OD OD OD CD OD . HNN PP EER EWWWHWWWNHNNNNWN Dimensions, in. ft. ani. Os. 3.0 BSE Be) 4x 3 6 Gx 3 9 8x 4 O 10% 4 3 x4 6 2x4 9 4x5 0 62x25) 73 8 x5 6 10. x 5 9 OF <6) 0 Bevcets) ja 4x 6. 6 6x6 9 8x 7 O DOex Vea oO x70. 6 Oex.f 9 4x8 O 6 x 8. 38 Bex 8. 6 10x 8 9 One OL FO 93 New Eee-SHarpe SEWERS (continued). eV/R (for Velocity). T— “018 82°9 87°7 92°4: 97°0 101°4 105°8 110°0 114°3 118°4 122°4 126°4 1380°2 1340 137°6 141°2 144°9 148°5 151°9 155°4 1588 162°2 165°4 168°7 1718 175°0 2 Full. AxcVR (for Discharge). m="015 n='013 n=°015 69°9 239°6 202°0 74:2 297°3 251°5 78°3 363°1 807°7 82°1 437°5 370°3 861 521°2 44.2°5 89°9 613°6 521°4 93.5 7150 607°7 97°2 827°5 703°7 100°7 950°7 808°6 104°2 1073°2 922°2 107°7 1127°3 1045°8 IE 1381°4 1178'8 114°4 1549°0 1322°5 LV77 1725°5 1476°0 120°8 1914°7 1638°0 123°9 2119°0 1812°7 127°1 2385°9 1999°3 1380°2 2562°5 2196°5 183°2 2806°5 2405°6 136'2 3061°7 2625°9 139°1 3331°6 28571 142°0 3614°0 3102°7 144°8 3912°1 3357°9 147°6 4222°8 3628'°0 150°5 4550°0 3913°0 ic) ot ° AMInIanaaniktLEREKRROWWWWWNNHNY NW hd New Hee-SHare SEWERS (continued). Dimensions. = _ _ feat COMDPNODADENODCADENTCOADENO ee OS Ie PE: DONE ONS ON OG) Oe OK ON OKO) COST OMe SR ON INU OS OK ODM MDM DDNINNNDAAQH OOo & SB Co to Fh co . = P OCOAWOOSWOODRDWODDBWOORWOURDWSO (for n=*013 58°9 62°4 66°1 69°4. 72°8 761 on 82°3 85°4: 88°3 91°2 94°1 96°9 99°9 102°5 105°3 108°0 110°5 113°2 115°7 118°4 120°9 123°3 125°7 128°1 94: e WR Velocity). n="015 49°3 53°4 55°5 58°3 61:2 64°1 66°6 69°4, 21 T4°7 77-2 19°7 82°1 84:7 87°0 89'5 91°8 940 96°3 98°5 100°7 102°9 105°0 107°2 109°2 Full. AxeV/R (for Discharge). n=°013 60°1 743 91°2 110°3 131°8 155°Z 181°2 209°9 241°7 274°6 3119 351°9 3944 440°6 488°9 542°3 598°3 6564 719°9 785°6 856°0 929°7 1007°4 1057°3 Ilfe2 n=*015 50°3 63°5 76°6 92°7 110°8 130°8 152°5 177-0 2040 232 3 2640 298'1 3341 373°5 415°0 460°9 508°6 558°4 612°5 668°8 7281 7913 857°8 927°3 999°2 in any distance divided by that distance. *500000 "4.47214, "408248 377978 °353553 *333333 °316228 *301511 *288675 277350 267261 °258199 *250000 °242536 235702 *229416 "223607 218218 °213200 208514: °204124 *200000 "196116 "192450 "188982 "185695 "182° 74 179605 176777 ‘174077 95 TABLE XI. (P. J. Flynn.) Values of vs for Inclinations of 1 in 4 to 1 in 2000. s=sine of angle of inclination =fall of water surface Slope lin 34 35 36 37 38 39 40 Js 171499 *169031 166667 "164399 "162221 °160125 "158114 156174 "154303 "152499 150756 149071 147444, 145865 "144337 142857 141421 "140028 138676 137361 136085 134839 133630 132453 "131305 "130189 °129100 128037 ‘127000 °125988 Slope lin 64 65 66 vs "125000 "124035 123091 °122169 "121268 "120386 "119524, ‘118678 ‘117851 117041 "116248 "115470 114708 "113961 "113228 °112509 "111803 ‘111111 "110431 "109764. "109109 "1084.65 107833 107211 *106600 *106000 "105409 "104828 104257 "103695 96 mf es J | 086387 ‘086066 085749 085436 "085126 ‘084.819 084516 084.215 ‘083918 083624, ‘083333 ‘083046 ‘082760 082479 082199 ‘081923 "081650 °081379 081111 103142 102598 ‘102062 101535 "101015 ‘100504 ‘100000 ‘099504: 099015 098533 ‘098058 ‘097590 ‘097129 096674: 096225 095783 095346 094916 "094491 094072 "093659 ‘093250 "092848 "0924.50 092057 ‘091669 ‘091287 ‘090909 090536 ‘090167 ‘089803 089442 ‘089087 ‘088736 "088388 "088045 ‘087706 087370 087039 086711 "080845 "080582 080322 "080065 ‘079809 079556 079305 ‘079057 ‘078811 078568 078326 078087 ‘077850 077615 ‘077382 ‘017152 ‘076923 ‘076697 ‘076472 076249 ‘076029 ‘075810 075593 ‘075378 075164 074953 074744 074536 074329 "074125 ‘073922 073721 073521 073324 073127 "0729382 072739 072548 072357 ‘072169 ‘071982 ‘071796 ‘071612 ‘071429 071247 ‘071067 ‘070888 ‘070710 070434. ‘0703859 ‘070186 ‘070014: 069843 "069673 °069505 ‘069338 "069172 "069007 "068843 ‘068680 "068519 Slope lin 214 215 216 217 218 219 220 221 ° 222 223 224 225 226 227 228 229 230 231 232 233 234, 235 2386 237 238 239 240 241 242 243 244, 245 246 247 248 249 250 251 252 253 Af 8 °068358 "068199 ‘068041 ‘067885 "067729 ‘067574 "067419 "067267 "067116 ‘066965 ‘066815 ‘066667 "066519 "066372 066227 ‘066082 "065938 "065795 ‘065653 °065512 065372 "065233 "065094 ‘064957 ‘064820 ‘064685 "064549 064416 "064283 "064.150 ‘064018 ‘063888 ‘063758 "063629 °063500 "063372 "063246 ‘063119 ‘062994. *062870 Slope lin 254 255 256 257 258 259 260 261 262 263 264. 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284. 285 286 287 288 289 290 291 292 293 97 callie 062746 294 062622 295 062500 296 062378 297 062257 298 062137 299 062018 300 "061899 301 ‘061780 302 061662 303 061546 304 061430 305 061314 306 ‘061199 307 061085 <08 060971 309 ‘060858 310 ‘060746 311 060634. 312 060528 313 0604.12 314 ‘060302 315 ‘0601938 316 ‘060084: 317 ‘059976 318 059868 319 059761 320 059655 321 059549 322 059444 323 059339 324 059235 325 059131 326 059028 327 ‘058926 328 ‘058824 329 058722 330 058621 331 058520 332 058420 333 Js 058321 "058222 "058124: "058026 057929 057831 057735 0576389 057544: 057449: 057354. 057260 ‘057166 ‘057073 056980 056888 "056796 "056705 056614 056523 056433 ‘056344 "056254 056165 ‘056077 055989: 055902 055815 055728 055641 ‘055556 055470 055385 055300 "055216 055132 055048 054965 054882 054799 B61 262 363 364 365 366 367 363 369 370 371 372 373 054717 054.636 054.555 054474 054393 "054312 054.232 054153 054074 0538995 "053916 *053838 053760 "053683 "053606 058529 053452 053376 ‘053300 053224 053149 *0538074 °052999 °052925 "052851 052778 052705 °052632 "052559 "052486 052414 "052342 ‘052270 "052199 ‘052129 ‘052060 °051988 051917 ‘051847 ‘051778 Slope lin 374 375 376 377 378 379 380 381 382 383 384. 385 386 387 388 389 390 391 392 393 394, 395 396 397 398 399 4.00 401 402 4.03 404. 405 406 407 408 409 410 41] 412 413 98 Js 051709 051640 "051571 "051502 "051434 "051366 °051299 "051231 "051164 051097 "051031 °050965 "050899 "050833 ‘050767 050702 050637 050572 050507 050443 ‘050379 °050315 050252 *050188 7050125 *050062 °050000 "049938 049876 "049814. 049752 04.9690 049629 049568 049507 049447 049387 049326 "049266 049207 049147 "049088 049029 048970 048911 "048853 048795 048737 048679 048621 043564 "048507 "0484.50 "048393 "048337 048280 048224. "048168 048113 048057 "048001 047946 047891 "047836 047782 047728 ‘047673 047619 "047565 047511 047458 "047404 047351 047298 047245 047193 047140 047088 "047036 "046984 Slope lin 454 455 456 457 458 459 460 461 462 ~ 463 464 465 466 467 468 469 470 471 472 +73 ATA, 475 476 477 478 479 480 481 482 483 484, 485 486 487 488 489 490 491 492 493 Vs "046932 “046880 "046829 046778 "046726 "046676 °04.6625 046575 046524 046474, 0464.24 046374 046324, 046274 | -046225 "046176 046126 ‘046077 "046! 29 “045980 045932 045883 *045835 "045787 "045739 ‘045691 "045644. °04.5596 *045549 *04.5502 °04.5454, 045407 "04.5361 045314 *045268 °045222 *045175 045129 "045083 "04.5087 Slope lin 494. 495 496 497 498 499 500 501 502 503 504: 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524, 525 526 527 528 529 530 531 532 533 99 Js 04.4992 044947 "044901 -°044856 "044811 044.766 044721 "044677 044632 "044588" "04.4544, 044499 044.455 04.44.12 044.368 044324, "044281 044.237 "044.194 044151 "044.108 "044.065 044022 043979 043937 043895 043853 "043811 043769 043727 "043685 043644. 043602 043561 043519 043478 043437 043396 04.3355 044315 Slope lin 534 535 536 537 528 53Y 540 541 542 — 543 544, 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 A 8 043274 043234 043193 0431F3 043113 043073 043083 04.2993 042953 042914 04.2874 "04.2835 042796 042757 042718 "04.2679 "042640 "042601 "042563 04.2524 042486 04.2448 04.24.10 042371 *042333 04.2295 04.2258 0422: 0 04.2183 04.2145 042108 042070 042033. "04.1996 "041959 "041922 "041885 041848 "041812 041776 100 5 a ] re lope trae va ie vs ae 574 ‘041739 614. °040357 654. 575 04.1703 615 010824 655 576 041667 616 °040291 656 577 *041630 617 "040258 657 578 *041594 618 °04.0226 658 579 °041559 619 0401938 659 580 041523 620 "040161 660 581 "041487 621 040128 661 582 ‘041451 622 *040096 662 583 ‘041416 623 °040064: 663 584 °041280 624 "040082 664 585 04.1345 625 “040000 665 586 °041309 626 ‘039968 666 587 "04.1274 627 "039936 667 588 ‘0412389 628 "039904, 668 589 04.1204, 629 "039873 669 590 ‘041169 630 "039841 670 591 °0411385 6381 "089809 671 592 °041100 632 "039778 672 593 "04.1065 633 "039746 673 594, 041031 634 "039715 674 595 °040996 635 "039684. 675 596 ‘040961 636 "0396538 676 597 04.0927 637 ‘039621 677 598 "040893 638 "089590 678 599 04.0859 639 0395°9 679 600 040825 640 "039528 680 601 040791 641 "039498 681 602 ‘040757 642 °039467 682 603 ‘040723 643 "039436 683 604. *04.0689 644, "039405 684 605 "040656 645 °039375 685 606 04.0622 646 "039344. 686 607 "040589 64:7 °039314. 687 608 °04.0555 648 °C39284, 688 609 °040522 649 0392538 689 610 "040489 650 "0389223 690 611 "040 156 651 "039193 691 612 °04.04.22 652 "039163 692 613 "04.0389 653 "0391383 693 ve 039103 039073 039043 "035013 038984: 038954. "038925 038895 038866 ‘038837 *038808 038778 038749 038720 "038691 038662 "038633 ‘038604. 038576 038547 "038518 038490 038461 "038433 "038405 038376 038348 038820 "038292 038264. ‘038236 "038208 *038180 038152 "038125 038097 *03806)) *038042 "038014. 037987 vay | Se 037959 734 037932 "35 037905 736 037878 137 037851 738 ‘037824. 739 "037796 740 037769 TAY 037743 749 ‘037716 743 "03,689 744, ‘037662 745 037636 746 * -037609 747 037582 748 037556 749 037529 750 037503 "51 037477 102 037450 753 037424, "5A 0373898 755 037372 756 ‘037346 757 ‘037320 758 "037294, 759 ‘037268 760 037242 761 037216 762 037190 "63 ‘037164. 764 037139 "65 °037113 "66 037088 "67 ‘037063 768 037037 769 037012 770 036986 771 "036961 (ne: ‘036936 773 101 Vs 036911 ‘036885 ‘036860 086835 ‘036810 036783 03676 1 ‘026736 036711 ‘036636 ‘036662 ‘036637 036613 ‘036588 036563 ‘036539 ‘036515 ‘036490 036466 036442 ‘036418 036394 ‘036370 036346 036322 036298 ‘036274. ‘086250 036226 ‘036202 ‘036179 ‘036155 036131 ‘036108 036084. 036061 “036038 036014 ‘035991 ‘035967 Slope lin 774. 775 776 ri | 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794, 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 ve "035944. 085921 °035898 "035875 °035852 "085829 "035806 "0385783 °035760 035737 °0385714 "035691 ‘035669 "035646 °035623 ‘035601 *035578 °085556 "035533 °035511 "035489 "035466 0385444, 0854.22 "0353899 O853t7 "0385355 "085333 °0353811 °0385289 °035267 , (0385245 0385223 . 085201 "085179 °085158 "035136 °035115 °0350938 "035071 102 fee |b ver aah] ed | 814, *035050 854 *034219 894, 033445 815 "035028 855 "034199 895 033426 816 035007 856 °084179 896 ‘033408 817 °034985 857 034159 897 033389 818 "034964 858 "034139 898 033370 819 "034943 859 °034119 899 "033352 820 084922 860 034099 900 033333 821 °0384900 861 *034080 901 "033315 d22 "034879 862 *034060 902 "033296 823 °034858 863 *0384040 903 033278 824 034837 864 ‘034021 904, 033259 | 825 "034816 865 "034001 905 "033241 826 "084794 866 *03398 | 906 *033223 $27 °034773 867 "0383962 907 033204: 828 "034752 868 "033942 908 033186 829 °034731 869 "033923 909 033168 830 "034710 870 *033903 910 033149 831 °034689 871 "033883 911 033131 832 *034669 872 ‘033864 912 "033113 833 034.648 873 "033845 913 ‘033095 834 034627 874 "033825 914 033077 835 "034606 875 °033806 915 *033059 836 "034586 876 033787 916 "033041 837 "034565 877 °033768 O17 "033023 838 "034544 878 033748 918 *033005. 839 034524 879 *033729 919 032987 840 °034503 880 033710 920 "032969 841 "034483 881 °033691 921 "032951 842 034462 882 033672 922 032933 843 034442 883 °033653 923 "032915 844 034421 884 "033633 924, 032897 845 * 34401 885 033614 925 032879 846 034381 886 "033595 926 "032862 847 *034360 887 "083577 927 ‘032844 848 084340 . 888 "033558 928 ‘032826 849 "084320 889 "033539 929 ‘032809 850 *034300 890 ‘033520 930 032791 851 "034279 891 ‘033501 931 082774 852 0384259 892 033483 ° 932 "032756 853 "034239 893 033464 933 032738 032721 032703 "0326856 032669 °032651 032634 "032616 "032599 032582 "032565 032547 "032530 °032513 032496 032479 "032461 032444, 082427 "032410 032393 082376 "032359 "032342 032325 "032309 032292 082275 "032258 "032241 "032224 "032208 *032191 032174 032158 032141 032125 032108 "032091 082075 "032059 Slope Je pho 974 975 976 977 978 979 980 981 982 983 984. 985 - 986 987 988 989 990 991 992 993 994, 995 996 997 998 999 ~ 1000 1001 1002 1003 1004: 1005 1006 1007 1008 1009 1010 1011 1012 10138 103 032042 "032026 *032009 "0319938 031977 "031960 "031944 "031928 .031911 "031895 031879 031863 031847 031830 .031814 031798 031782 031766 031750 031734 031718 031702 031686 031670 031654. 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"030234: 1134 "029696 1055 030787 1095 °030220 1135 029683 1056 ‘030773 1096 ‘030206 1136 "029669 1057 ‘030758 1097 030192 1137 029656 1058 0380744: 1098 0380178 1138 029643 1059 030729 1099 030165 1139 029630 1060 030715 1100 °030151 1140 029617 1061 "0380700 1101 030137 1141 "029604. 1062 ‘030686 1102 030124 1142 "029591 1063 030671 1103 "030110 1148 029578 1064 ‘030657 1104, "0380096 1144 029566 1065 ‘030643 1105 030083 1145 029553 1066 "030628 1106 "030069 . 1146 029540 1067 030614: 1107 ‘080055 1147 ‘029527 1068 ‘030599 1108 "030042 1148 "029514 1069 "030585 1109 "0380028 1149 "029501 1070 030571 1110 ‘030015 1150 029488 1071 080557 1111 ‘030001 1151 029476 1072 "030542 1112 029988 1152 029463 1073 "030528 1113 029975 11538 0294.50 1074 "0380514 1114 029961 1154 029438 1075 "030499 1115 |- °029948 1155 029425 1076 030485 1116 029934 1156 029412 1077 ‘080471 ala He Bg ~ 7029921 1157 029399 1078 ‘030457 1118 "029908 1158 029386 1079 0304.43 1119 029894 1159 ‘029374. 1080 030429 1120 029881 1160 029363 1081 0380415 1121 029868 1161 029348 1082 ‘030401 1122 029854 1162 "029336 1083 ‘030387 1123 "029841 1163 029323 1084: ‘030373 1124 029828 1164 029311 1085 0303859 1125 "029814: 1165 |- °029298 1086 030345 1126 029801 1166 "029285 1087 0303831 1127 029788 1167 029273 1088 ‘030317 1128 029775 1168 "029264 1089 0303803 1129 ‘029761 1169 "029248 1090 "030289 1130 029748 1170 029235 1091 030275 1131 "029735 1171 029223 1092 0380261 1132 ‘029722 1172 "029210 1093 ‘030247 1133 029709 1173 "029198 *029185 029173 029161 "029148 °029136 *029123 029111 "029099 *029086 029074: "029062 "029049 029037 029025 029013 ‘029001 "028988 028976 028964: °028952 "028940 "028928 028916 "028904. 028892 *028880 028868 028855 028843 028831 028819 "028808 028796 028784 028772 028760 "028748 "028736 "028724, 028713 +028665 ‘028653 028641 ‘028630 ‘028617- ‘028506 ‘028595 028583 028571 “028559 ‘028548 028536 “028525 028513 028501 928490 028478 028467 028455 028444 028433 028421 ‘028409 ‘028398 “028387 028375 "028364. "028352 028341 "028329 "028318 028307 "028295 028284 028273 028262 "028250 4am | EEE | ‘028701 ‘028689 ‘028677 028239 028228 "028217 028205 028194. 028183 028172 028161 028149 028138 028127 028116 028105 "028094, 028083 ‘028072 028061 028050 "028038 ‘028027 "028016 "028006 "027995 027984 ‘027973 ‘027962 027951 027940 "027929 027918 "027907 027896 "027886 ‘027875 ‘027864 "027853 027841 027831 027821 ‘027810 027799 027789 027778 "027767 027756 027746 027735 "027724 027714 027703 027692 027682 027671 027661 "027650 ‘027639 027629 027618 027608 027597 027587 "027576 "027566 027555 027545 027534: 027524 027514 027503 027493 027481 027472 027462 027451 027441 027431 027420 "0274.10 ‘027400 027389 027379 027369 027359 027349 027338 027328 . 027318 027308 027298 "027287 "027277 "027267 °027257 027247 027237 027227 027217 -027207 027197 ‘027186 027176 "027166 027156 027146 "027186 °027126 ‘027116 027106 027096 "027086 027077 027067 "027057 027047 027037 "027027 027017 "027007 "026997 ‘026988 8 026978 "026968 026958 026948 026939 026929 026919 "026909 026899 "026890 "026880 "026870 026861 "026851 026841 026832 026822 026812 "026803 026793 "026784 026774 026764 026755 026745 026736 026726 026717 026707 "026698 "026688 026679 026669 "026659 °026650 026641 026631 026622 026612 026603 Slope lin 1414 1415 1416 1417 1418 1419 1420 1421- 1422 1423 1424, 1425 1426 1427 - 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444, 1445 1446 1447 1448 1449 1450 1451 1452 1453 Ss "0265938 *026584 "026575 °026565 *026556 "026547 "026537 °026528 _*026519 *026509 *026500 "026491 "026481 0264.72 "026463 026454 "0264.44, "026435 "026426 "0264.17 "026407 °0263898 "026389 "026880 "026371 "026361 "026352 © °026343 "0263384 026325 °026316 '026307 "026298 *026288 ‘026279 026279 "026261 *026252 "026243 ‘026234 Slope lin 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464: 1465 1466 1467 1468 1469 1470 1471 - 1472 1473 1474 1475 1476 1477 1478 1479 1480- 1481] 1482 1483 1484. 1485 1486 1487 1488 1489 1490 1491 1492 1493 107 Js *026225 026216 026207 026198 "026189 026180 ‘026171 026162 026153 °026144: 026135 026126 °026118 °026109 *026100 "026091 026082 026073 °026064: °026055 026047 "026038 "026029 °026020 °026011 °026003 025994. "025985 "025976 ‘025967 025959 "025950 025941 "025933 "025924. ‘025915 025907 "025898 "025889 "025880 Slepe Jin. 1494, 1495 1496 1497 1498 1499 1500 1501 1562 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 Js "025872 ‘025863 ‘025854, 025846 ‘025837 ‘025828 ‘025820 ‘025811 “025803 "025794. "025786 025777 ‘025768 ‘025760 ‘025751 ‘025743 025734. ‘025726 025717 ‘025709 ‘025700 025691 ‘025683 ‘025675 ‘025666 ‘025658 ‘025649 025641 025633 025624. 025616 ‘025607 025599 ‘025591 025582 025574. ‘025566 (025557 ‘025549 ‘025540 Slope lin 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 v # 025532 — 025524 ‘025516 ‘025507 025499 "025491 025482 025474 "025466 025457 "025449 : 025441 - 025433 025425 025416 025408 0254.00 025892 025384 0253875 025367 -||> 025359 025351 - 025843 025835 025327 ° 025818 | 025310 | 025302 | 025294 - 025285 025278 025270 025262 "025254 025246 : 025238 025230 "025222 "025214 108 aoe or 1574 | °025206 1575 | ‘025198 1576 | °025190 1577 | *025182 1578 | :025174 1579 | ‘025166 1580 | ‘025158 1581 | °025151 1582 | ‘025142 1583 | *025184. 1584 | 025126 1585 | :025118 1586 | ‘025110 1587 | 025102 1588 | *025094. 1589 | ‘025086 1590 | 025078 1591 | 025071 1592 | ‘025063 1593 | °025055 1594 | :025047 1595. | -025039 1596 | ‘025031 1597 | -025023 1598 | ‘025016 1599 | -025008 1600 | 025000 1601 | ‘024992 1602 | 024984, 1603 | ‘024976 1604 | :024969 1605 | ‘024961 1606 | ‘024953 1607 | *024946 1608 | ‘024938 1609 | -024930 1610 | :024622 1611 | ‘024915 1612 | :024907 1613 | ‘024899 Slope lin 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634. 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 vs 024691 024884 ‘024876 ‘024868 024861 024853 024845 ‘024838 ‘024830 (024822 ‘024815 ‘024807 ‘024799 024792 024784 024776 024769 024761 ‘024754 024746 ‘024'739 024781 “024723 ‘024716 ‘024708 024701 ‘024693 ‘024686 024678 024671 ‘024664 ‘024656 ‘024648 024641 024633 ‘024626 024618 ‘024612 ‘024603 ‘025596 Slope lin 1654: 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 — 1668 1669 1670 1671 1672 1673 1674: 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 v6 °024589 "024581 "024.574, "024566 *024559 "024.551 . *024.544. "024.537 ~ 024.529 *024522 "024.515 "024507 °024.500 "0244.92 "024485 "024.478 ‘024470 ‘024.463 "0244.56 0244.48 "024.441 "024434. 0244.27 °024.4.20 024413 *024405 . 024398 024.390 "024383 "024376 °024369 ‘0243861 "024354 024347 "024340 "024332 "024325 024.318 "024311 "024304 Slope lin 1694: 1695 1696 1697 1698 1699 1700 . 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714, 1715 1716 17}7 1718 1719 1720 1721 1722 1723 1724. 1725 1726 1727 1728 1729 1730 1731 1732 17383 109 vs 024297 024290 024282 024275 024268 024261 024254. 024246 (024239 ‘024232 ‘024225 024218 024211 024204. ‘024197 ‘024.190 024183 024175 ‘024168 024161 ‘021154 024147 024140 024133 024126 ‘024119 ‘O24112 ‘024105 ‘024098 024091 024084 ‘024077 ‘024070 02463 “024056 024049 024042 "024035 024028 024021 Slope lin 17384 1735 1736 Liod 1738 1739 1740 1741 1742 1743 1744 1745 1746 L747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 . 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 Js 024015 °024008 "024001 *023994. °023987 ‘023980 "023973 °023966 "023959 023953 "023946 *023939 *023932 "023925 ‘023918 ‘0238911 °023905 *023898 "023891 023884 "023878 023871 "023864 "023857 ‘023850 °023843 023837 "023830 "023823 "023816 "028809 ‘023803 "023796 °023789 "023783 "023776 "023769 "023762 "023756 ‘023749 023742 023736 023729 023722 023716 "023709 023702 023696 "023689 023682 ‘023676 023669 028662 023656 "023649 023643 023636 023629 023623 023616 ‘023610 023603 023596 023589 023583 "023577 023570 023564. 023557 023551 023544. "023538 023531 023525 "023518 023512 023505 023499 "0234.92 023486 "023479 023473 023466 "023460 023453 023447 "023440 023434 023427 023421 023415 023408 023402 "023395 "023389 023383 023376 ‘023370 023363 023357 023351 023344 023338 023331 023325 023319 023313 023306 "023300 023294. ‘023287 023281 023275 "023268 023262 "023256 023250 "0282438 023237 023230 023224 "023218 023212 023206 023199 023193 ‘023187 023181 023174 023168 023162 023156 °023150 023143 ‘023137 023131 023125 023119 023112 023106 023100 023094 ‘023088 023082 ‘023076 ‘023069 023063 ‘023057 023051 023045 023039 023033 "023027 023020 023014 "023008 "023002 "022996 022990 "022984 022978 022972 022966 022960 lil 022954 022948 022942 "022822 ‘022704. 022588 "022473 022361 112 TaBLe XII. Quantity of Brickwork for Circular Sewers. 2 ft. to 10 ft. diameter. Circular Sewers. Diameter. Cubic Yards of Brickwork per Lineal Yard. (gi abut 42 in. Work. 9 in. Work. 133 in. Work, j18 in. Work 2 “31 ‘be — = ek “32 “74: — — 2 2 33 “76 —_ — Ze 34: “78 — — 2 4 35 *80 | — _— 2 0 36 *82 — _- 2 6 37 85 —_ —_— eet | °39 ‘88 _ —_ 7A | “40 ‘90 _ — 2.9 “41 5 D2 — — 2 10 "42 94, — — galt “A3 ‘96; — | — 3° 0 “44, 98 — —- <3. hl. “45 1:00 — — ieee 46 1°02 — — 3 3 “AT 1°04, — — 3 «4 48 1:06 —_ —_ 3 5 “49 1:08 — — 3-6 ‘51 Leap aoe — ae fi 52 1:14 — — 3. 8 53 116 — — 3 a 54 1i8 —- — 3 10 55 1°20 _- — 3 11 56 1:22 —_ — 4 O 57 1°24 2°01 = 4 1 58 1:26 2°04 — 4 2 *59 1°28 2°07 — 4 3 ‘60 1'30 2°11 = A 4 ‘61 1°33 2'14 =e 113 BRICKWORK FOR CIRCULAR SEWERS (continued). Circular Sewers. Diameter. Cubic Yards of Brickwork per Lineal Yard. ft. in 44 in, Work, 9in. Work. | 134 in. Work. |18 in.Work 4° 5 63. + 1°36 2°18 © — 4-6 64 1°38 2°21 = 4 7 65 1:40 2°25 — 4 8 66 1°42 2°28 ae 4. 9 ‘67 144 ~~. 2°31 == 4 10 ‘68 146: 2°34 as 4 11 ‘G0 & 148 PET Te = 5 QO iO cat LO 7a 240 : soe Seek “71 : 1:52 | » 2.43 = D2 72.3 154 . 2:46 a 53 ae 1:56 | 2:49 - 5. 4 “74 158 j 2°52 —— 5:5 WO, <3 1:60 2°55 ee 5 6 fg eee 1:63 | 2°60 i Bg “78 166.3 2°64 == 5 °8 "79 : 1:68; 2°67 = Dal'td ‘80. 1:70 2°70 = 5 10 ‘81 (| 1°72 2°73 = 5 11 ce Wifes 1°74 2°75 = 6 O 83; rege 2°79 3°92 6 1 "84, E804 2°84 4,00 6 2 °85 1°82 288 4°04 6 3 86: 1°84, 2°91 4,08 6 4 38 304 186. 2:94 - 412 6 5 89; S8i 8 297 4:16 6 6 90. 1:90 3°00 4°20 Ged ‘Ol i 1°92 Od 4°24 6 8 ‘92 I'94 3°06 4°28 6 9 ‘9371. 1:96 309 4°32 6 10 "94, 1:98 3°12 4°36 6 1l 95 2°00 oo 4°40 AY, ‘06 2°02 ° 318 4°44. ftte 8 "s O(a 2°04 3°21 4,48 ws 2 ‘98 2°07 3°25 4°52 114 BRICKWORK FOR CIRCULAR SEWERS (continued). Circular Sewers. Diameter. Cubic Yards of Brickwork per Lineal Yard. ft. in. 4} in, Work. 9in. Work. | 134 in. Work, |18in.Work fg ey | 7 3 99 2°10 3°30 4°60 7 4 101 2°12 3°33 464. G25 1:02 2°14 3°36 468 7 6 1:03 2°16 3°39 4°72 ees. 1.04 2°18 3°42 4°76 7 8 1:05 2°20 3°45 4°80 rp 1:06 2.22 3°48 484. 7 10 1:07 2°24: 351 4°88 ead 1:08 2.26 3°54 4°92 8 0O 1:09 2°28 3°57 496 Ret & 110 2°30 3°60 5.00 Sen 111 2°33 3°64 5°04 8 3 113 2°36 3°68 5°12 8 4 1°14 2°38 3°72 5°16 8 5 115 2°40 3°75 5°20 8 6 1:16 2.42 3°78 5°24. Sy 117 2°44, 3°81 5°28 8 8 118 2°46 2°84 5°32 & 9 1:19 2.48 2°87 5°36 8 10 1:20 2°50 3°90 5°40 8 11 121 2°52 3°93 5°44 9 0 1:22 2°55 3°97 4°49 Ord 1:24 2°58 4°02 5°55 9 2 1°25 2.60 4°05 5°60 9 3 1.26 2°62 408 5°64 9 4 1°27 2°64, 411 5°63 9 5 1°28 2°66 4°14; 5°72 9 6 1°29 2°68 4°17 5°76 9°47 1°30 2°70 4°20 5°80 9 8 1°31 2°72 4°23 5°84 9.9 1°32 2°74 4:26 5°88 9 10 1°33 2°76 4°29 5°92 9 11 1°34 2°79 4°33 5°96 10 -0 1°36 2°81 4°37 6°02 115 Taste XIII, Quantity of Brickwork for Standard Hgg-Shape and New Hgg-Shape Sewers. Otte Xoo its. tO, O16 Xo {uy clameter. Norse.—The quantity of brickwork for a new egg-shape sewer is from 1 to 2 per cent. less than that of a standard egg-shape sewer of equal internal dimensions, and for all practical purposes may there- fore be taken as equal to same. Standard Egg-Shape. Dimensions. Cubic Yards of Brickwork per Lineal Yard. ft. in ft. in. 44 in, Work. 9in. Work. {134 in. Work. were SPO 38 86 1°44 AT ey a a "Al "91 1.52 240% (3:5 6 ‘43 97 1°60 zn 62% 3°49 46 1:02 1°68 2°38 x 4 0 “49 1°08 tee fF 210 x 4 8 OZ 113 1°85 3 0x 4 6 D4 1:19 1:93 Bn a, ho 4 sD 57 1:24 2°01 ar 3 5 0 60 1°30 2°10 mo: Xb 3 63 1°35 2°18 Bao. xeD 6 65 1°41 2°26 S10) MH Ov 68 1°46 2°34 Bee OF 36) G0 -O 71 1°52 2°42 a2 x.6 3 74 1°57 2°51 4°-4x 6 6 vids 163 2°60 4 6x 6 9 79 1°68 2°67 4° 8rx 7 O 82 1°74 2°75 410“ 7) 3 85 1-79 2°84: 5 Ox 7 6 88 1°85 2°92 SesZix wy 9 90 1:90 3°00 5 4x 8 0 93 1:96 3°08 On. 69x78 3 96 2°01 3°17 me 8 eB eG 99 2°07 3°25 610 x &® 9 1°01 2°12 3°33 6 0x9 0 1:04 2°18 3°41 116 TABLE XIV. Cubic Yards of Hxcavation per Lineal Yard of Trenches, 2 ft. to 15 ft. wide and 4 ft. to 20 ft. deep. ee ee ee WIDTH. A ver- age Depth. DAARBAARMMIATNKAANMAAIT EAA LA BRERA DR EAL oo Se TRON ROH OCODNATRAONHOHOOMNIDTRWNHHO 9! OQ” g/ |’ "926 945 "964. ‘888 "908 "927 °946| °983 965 | L002 984} 1°021 1-000 | 1:040 1019 | 1:069 1038 | 1088 1°057 | 1:107 1:076 | 1126 1°095 | 1°145 1°111) 1°164 1°130) 1°183 1°149} 1°202 1°168 | 1°221 1°187 | 1°240 1°206 | 1°259 1°225 | 1:278 1°244,| 1°297 1°263 | 1°316 1°282 | 1°335 1301 | 1°354 1320 | 1°378 1°383 | 1°392 1°352| 1°411 1°371| 1°430 1°390 | 1°449 1°409 | 1°468 1°428 | 1'487 9! pH 9) 3! ‘963 | 1:000 ‘983 | 1-021 1:008 | 1:042 1:023 | 1:063 1:043 | 1:084 1063 | 1:105 1033 | 1:126 1°103| 1:147 1:123] 1:168 1143 | 1:189 1:163|1:210 1.183} 1:231 1203 | 1250 1:223| 1-271 1:243 | 1-292 1:263 | 1°313 1:283 | 1:334 1°303 | 1°355 1°323 | 1:376 1:343 | 1:397 1363 | 1-418 1:383 | 1:439 1:403 | 1:460 1°423 | 1-481 1443 | 1:500 1463 | 1°521 1483 | 1°542 1508 | 1°563 1523 | 1-584, 1°5 £3] 1-605 9! 4// 1:037 1°058 1:079 1°100 1121 1142 1:163 1'184 1°205 1:226 1247 1268 1°289 1°310 1331 1°352 1°373 1°394, 1°415 1°436 1457 1-478 1°499 1°520 1541 1562 1583 1604 1°625 1646 9! 5! OM 6” 1074 1'096 1118 1°140 1'162 1°184 1°206 1°228 1°250 1:272 1°294 1316 1°343 1°365 1°387 1'409 1°431 1453 1475 1:497 1519 W111 1134 1157 1'180 1°2038 1'226 1.250 1273 1°296 1319 1°342 1°365 1°388 1°411 14384 1°457 1.480 1°503 1526 1549 1°572 1541 | 1°595 1563 | 1°618 1°585 | 1°641 1°611 | 1°664 1°638 | 1°687 9! yd 9! 9” 1148 1172 1°196 1°220 1°244 1°'268 1°292 1°316 1°340 1°364 1°388 1°412 1°435 1°459 1°483 1°507 1°531 1°555 1°579 1°603 1°627 1651 1675 1699 1°722 1°746 1185 1°210 1'235 1°260 1°285 1°310 1°335 1°360 1°385 1°410 1°435 1°460 1°48] 1'506 1°531 1556 1581 1°606 1°631 1°656 1681 1°706 1°731 1°756 1-777 1°802 1°655 | 1°710| 1°770| 1°827 1°677 | 1°733 1699 | 1°766 1°721 |1°789 1°794.| 1°852 '1°818 | 1°877 1°832 | 1:902 9! 9// 1222 1°248 1274 1300 1°326 1352 1°378 1°404 1°430 1°456 1°482 1507 1'528 1554 1°580 1°606 1°632 1°658 1684, 1°710 1°736 1°762 1788 1812 1833 1859 1°885 1911 1937 1'963 Aver- age Depth. or) jor) et Oorowuon O TAT AT ATT TAT AT TAT TIAIBDAAW, ee ORF CHMNANbONH Ly EXCAVATION IN TRENCHES (continued). 9! 0” 1:447 1:466 1485 1°504, 1523 1°542 1°555 1574 1°593 1°612 16381 1°650 1°669 1°688 1:707 |1°726 1745 1°764 eT 9! y// 1506 1525 1544 1°563 1582 1601 1°620 1639 1°658 1677 1696 1°715 1°734. 1°753 1772 1°791 1°810 1°829 1851 9! git 1563 1583 1603 1°623 1°643 1663 1°685 1°705 1°725 1°745 1765 1°785 1°805 1°825 1°845 1°865 1885 1°905 1°926 WIDTH. 9! 3” 9! 4l! 1°626 | 1°667 1°647 | 1:688 1°668 | 1°709 1°689 | 1°730 1°710)1°751 1°731 | 1°72 1°750 | 1°811 1°77111°833 1°792 | 1°851 1°§13 | 1°875 1°834 | 1°896 1°855 | 1°917 1°876 | 1:938 1°897 | 1:959 1°918 | 1-980 1°989 | 2°001 1-960 | 2°022 1°981 | 2°043 2°000 | 2:071 9! 5! 1°743 1°765 1:787 1°809 1831 1853 1°879 1901 1923 1°945 1:967 1'989 2°011 2°033 2°055 2077 2°099 2°121 2°148 9! 6” 1°812 1°835 1858 1881 1904, 1°927 1°944. 1967 1990 2°0138 2°036 2°059 2°082 2°105 2°128 /2°151 2174 2°197 2°222 9 ULL 1856 1880 1904. 1928 1.952 1976 2°009 2°033 2°057 2-081 2°105 2°129 2°153 2177 2°201 2°225 2°249 2278 2°296 9! g/ 1927 1°952 Lote 2°002 2°027 2°052 2°070 2°095 2.120 2°145 2°170 | 2°195 2°220 2°245 2°270 2°295 2°320 2°345 2°364 9! 9! £989 2°015 2°041 2°067 2°093 2°119 2°189 2°165 2°191 2°217 2°243 2°269 2°295 2°321 2°347 2°373 2°399 2°425 2°444 118 HXCAVATION 1N TRENCHES (continued). WIpDTH. 4 i) 7 age i=) ia’) 4o) ct =e DHAAAAPAAAHRHAAOONI NH IH 1xovrorgy eae EE EEL REP P DR tt be CONAORWNH OH OCUMONAARWNK OK OCOMONATKRWNFO 2/ 10” 1°259 1°285 1311 1°337 1°363 1°389 1415 1441 1°467 1°493 1°519 1°545 1574. 1°600 1 626 1°652 1:678 1°704 1°730 1°756 1°782 1808 1°834 1:860 1889 1915 1941 1:967 1'993 2°019 2°045 2°071 2°097 2°123 9! 11” 3/ OQ” 3/ 3” 1°296 1°323 1°350 1°377 1°404 1°431 1°458 1°485 1512 1°539 1566 1°333 | 1°444. 1°361 | 1°474 1°389 | 1°504 1417 1445 1473 1°500 1°528 1°556 1584: 1612 1°593 | 1°640 1°621 1°648 1675 1°702 1°729 1°756 1°783 1°810 1°837 1°864. 1891 1918 1°944 1-971 1:998 2°025 2°052 2°079 2°106 2°133 2°160 2°187 1666 1534 1564 1594: 1624: 1654: 1°684 1-714 1744 1774 1806 1°694 | 1°836 1°722 1866 1°750 | 1°896 1°778 1806 1°834 1862 1°926 1°956 1986 2°016 1°890 | 2:046 1918 1946 1974 2°000 2°028 2'056 2084: 2°112 2°140 2°168 2°196 2°224 2°252 2:076 2°106 2°136 2°167 2197 2°227 2°257 2°287 2°317 2°347 2°377 2°407 2°437 3/ 6” 1°555 1°587 1°619 1°651 1683 1-715 1°750 1°782 1°814 1°846 1878 1910 1°944 1976 2°008 2°040 2°072 2°104. 2°136 2°168 2°200 2°232 2°264. 2°296 2°333 2°365 2397 2°4.29 2°461 2493 2°525 2°557 2°589 2°621 3/ 9g! 1666 1701 1736 aver ga 1°806 1°841 1°876 1911 1°946 1981 2°016 2°051 2°083 2°118 2°153 2°188 2°223 2°258 2°293 2°328 2°363 2°398 2°433 2°468 2°500 2°535 2°570 2°605 2°640 2°675 2°710 2°745 2°780 2°815 4/ Qo” 1777 1814 1851 1°888 1°925 1°962 2°000 2°037 2°074: 2111 2°148 2°185 2°222 2°259 2°296 2°333 2°370 2°407 2°444, 2°481 2°518 2°555 2°592 2°629 2°666 2°703 2°740 2777 2.814 2°851 2°888 2°925 2°962 2°999 4! 3” 4/ 6” 1°888 | 2°000 1°927 | 2°042 1°966 | 2°084. 2°005 | 2°126 2'044 | 2°168 2°083 | 2°210 2°122 | 2°252 2°161 | 2°294, 2°200 | 2°336 2°239 | 2°378 2°2'78 | 2°4.20 2.317 | 2°462 2°361 | 2°500 2°400 | 2°542 2°439 | 2°584 2°478 | 2°626 2°517 | 2°668 2°556 | 2°710 2°595 | 2°752 2°634 | 2°794 2°673 | 2°836 2°712 | 2°878 2°751 | 2°920 2°790 | 2°962 2°833 | 3°000 2°872 | 3042 2°911 | 3°084. 2°950 | 3°126 2°989 | 3°168 3°028 | 3°210 3°067 | 3°252 3°106 | 3°294 3°145 | 3°336 3°18413°378 4! 9! pag wef 2155 2199 2243 2287 2331 2°375 2419 2°462 2507 2551 2°595 2°639 2683 2°727 2°771 2815 2°859 2903 2°947 2/991 3-035 3-079 3123 3°167 3-211 3°255 3-299 3°343 3°387 3431 3:485 3°529 3573 WATT TIT AYIA pote me OFM ODPONOOKWNH OO 119 EXCAVATION IN TRENCHES (continued). WiptH. ae aig 3/ 0” 3/ 3” 3/ 6” 3/ 9” 4/ 0” 4/ 3” Qt eS (Re eee a 3°420 | 3°617 2°522 | 2°722 | 2°917 2°552 | 2°754 | 2°952 2°582 | 2°786 | 2°987 2°612 | 2°818 | 3°022 2°642 | 2°850 | 3°057 2 672 | 2°882 | 3°092 2°702 | 2°914.| 3°127 2°732 | 2°946 | 3°162 2°762 | 2°978 | 3°196 2°792 | 3°010 | 3°232 2°822 | 3°042 | 3°267 2°852 | 3°074 | 3°302 2°888 | 3°111 | 3°333 3 036 | 3°223 3'0738 | 3°262 3°111 | 3°305 3 148 | 3°344 3185 | 3°383 3°222 | 3°422 3°259 | 3°461 3°462 3°500 3°542 3°584 3°626 3°668 3°296 | 3°500 | 3°710 3°333 | 3°539 3°370 | 3°578 3°407 | 3°617 3444 | 3°656 3°48] | 3°695 3'518 | 3°734 3°555 |3°777 3°752 3°794 3°836 3°878 3°920 3°962 4000 3°661 3°694, 3°738 3°782 3826 3°870 3914 3°958 4°002 4°046 4090 4°T34 4178 4222 120 EXCAVATION IN TRENCHES (continued). WIDTH. Aver- 5/ QO” F 28 pO 5/ 3 5’ 6” | 5! 9” 6/ 0” 6’ 3” 2°222 2°268 2°314 2°360 2°406 27452 2°498 2°544: 2°590 2°636 2°682 2°728 2-778 2'°824. 2°870 2°916 2°962 3°008 3°054 3°100 3°146 3°192 3°238 3°284 3°334 3°380 3°426 3°472 3'518 3°564 3°610 3°656 3°702 3°748 a MPODANOQAPRWNFORFOUMNTAAIKRWNEH OS AAAABWAMWAHAONAIANTCKAINAIKKAITBAEREAABAA BREE a OCOANOuUuhWN- © 2°333 2°382 2°431 2°480 2°529 2°578 2°627 2°676 2°725 2-774 2°823 2°872 2917 2°966 3015 3°064 3°113 3°162 3211 3.260 3°309 3°358 3°407 3°456 3°500 3°549 3°598 3°647 3°696 3°745 3°794 3°843 3°892 3°941 2444)\ 2-555 2495 | 2-608 2546 | 2°661 2-597 | 2°714 2-648 | 2467 2699 | 2820 2-750 | 2:873 2-801 | 2-926 2852 | 2-979 2-903 | 3-032 2°954| 3-085 3005 | 3138 3:056| 3195 |3°107| 3-248 3158] 3-301 3:209| 3354 3°260| 3407 3311 | 3-460 33621 3°513 3°413| 3:566 34641 3-619 3°515| 3672 3566 | 3°725 3617 | 3°78 3667 | 3°834. 3°718| 3°887 3-769 | 3940 38201 3993 3°871| 4:046 3-922 | 4:099 3:973| 4152 4°024| 4205 4075 | 4-258 4'126| 4311 2 666 2.722 2°778 2°834: 2°890 2°946 3.000 3°056 3°112 3168 3°224, 3°280 3°354 3°390 3°446 3502 3°558 3614 3°670 3°726 3°782 3°838 3°894. 3°949 4000 4056 4112 4°168 4°224. 4280 | 44.57 4°334 | 4°515 4390 | 4°573 4°446 | 4°631 4502 | 4689 2777 2°835 2°898 2°951 3°009 3°067 3°125 3°183 3°241 3°299 BBD 7 3415 3°473 3-581 3°589 3°647 3°705 3°763 3821 3°879 3°987 3°995 4053 4°111 4°167 4225 4283 4341 4399 6/ 6” 2°888 2°948 3°008 3°068 3°128 3°188 3248 3°308 3°368 3°428 3°488 3°548 3612 3672 3°732 3°792 3852 3'912 3°972 4032 4°092 4°152 4°212 4272 4°334, 4°394. 4°454, 4°514, 4°574 4°634 4694, 4754 4814, 4874 6/ 9g!” 7 0” fs 3! 3°222 3°289 3'306 3°423 3°490 3°557 3°624 3691 3°758 3°825 3°892 3°959 4°029 4096 4°163 4°230 4°297 4364 4°431 4°498 4565 4632 4699 4766 4°834, 4°901 4°968 5°035 5°102 3000 3°063 3°126 3°189 3252 3°315 3°378 3°441 3504 3°567 3°630 3'6938 3°751 3°814 3°877 3°940 4003 4066 4°129 4°192 4°255 4°318 4°381 4°4.4.4, 4500 4°563 4626 4689 4°752 4°815 4878 3111 3°176 3°24] 3°306 3371 3°436 3°501 3°566 3°631 3°696 3°761 3°826 3°890 3°955 4°020 4°085 4°150 4215 4°280 4°345 44.10 4475 4°540 4605 4,667 4°732 4797 4°862 4°927 4°992 | 5169 5°055 | 5°236 4°94] | 5°122 | 5°3038 5004 | 5°187 | 5370 5°067 | 5°252 | 6437 — Aver- age Depth. on) | So 6 11 PH SOrFoUopmInubwNnre oOo HWW ys sta 5/ 0” 121 EXCAVATION IN TRENCHES (continued). 5/ 3" 5/ 6” WIDTH. 6/ 3” 5/ Q// 4 o” 6/ 6” vid QO” Gt 3” 3794 3°840 3888 3-934. 3980 4026 4072 4118 4-164 4210 4256 4302 4348 4-399 444A 3°990 4°039 4-082 4131 4°180 4229 4°278 4°327 4°376 44.25 4°47 4, 4°523 4°57 2 4621 4°666 | 4177 4°228 4°276 4327 4°378 4°429 4°480 4°531 4582 4633 4684 4°735 4,786 4837 4888 4°364. | 4°558 | 4°747 4417 | 4°614 | 4.805 4°470 | 4°666 | 4°860 4°523 | 4°722 | 4918 4576 | 4°778 | 4°976 4°629 | 4834 | 5°034 4682 | 4°890 | 5°092 4°735 | 4°946 | 5°150 4°788 | 5°002 | 5°208 4°841 | 5°058 | 5°266 4°894 | 5°114 | 5°324 4947 | 5°170 | 5°382 5°000 | 5°226 | 5°440 5°054: | 5°282 | 5°498 5°111 | 5°333 | 5°555 4934 4994 5054 5114 5°174 5°23 t 5°294, 5°354 5°414 5°474 5534. 5°594 5°654 5714 5777 5°317 | 5°504 5°382 | 5°571 5°444| 5°638 5°509 | 5°705 5574) 5°772 5°639 | 5°839 5°704| 5°906 5°769 | 5973 5°834| 6°040 5°899 | 6°107 5964 6174 6'029 | 6°241 6°094.| 6°308 6°159 | 6°375 6°222 | 6'°444 122 EXCAVATION 1N TRENCHES (continued). DAAHRHABAWOAMNMAMNAMAANANANRRADRAABRRAAA me OO MOTO 1 dee aad CONF SOF COONAN AWNHERO a OO TDs WipTH. 7 9!’ 8! 0” g/ 3 8/ 6” 8/ 9g!’ g/ QO” 9! 6” 10’ 0” | 10’ 6” 3°4.44. 3°516 3°588 3°660 3°782 3°804 3°876 3°948 4°020 4°092 4-164. 4°236 4°305 4377 4449 4°521 4°593 4665 4737 4°809 4°88] 4953 3 | 5°025 5:097 5°167 5°239 5311 5°383 5°455 5°527 5°599 5671 5°743 5°815 3°555 3°629 3°703 3777 3°851 3°925 3°999 4°073 4°147 4°221 4°295 4°369 4°4.4.4, 4°518 4592 4666 4°740 4814, 4°888 4°962 5'036 5°110 5°184 5°258 5°334 5°408 5°482 5°556 5°630 5°704 5°778 5°852 5°926 6 000 3°666 | 8°77 3°742 | 3°856 3°818 | 3°935 3°894.| 4°01 4: 3°970| 4.093 4°046 | 4°172 4122} 4°251 4°198 | 4°3380 4°274| 4°409 4°350 | 4°488 4426 | 4°567 4°502 | 4°646 4583 | 4°722 4°659 | 4°801 4°'735 | 4°880 4811 | 4°959 4888 | 4°938 4964 | 5°117 5°040} 5°196 5°116 | 5°275 5°192 | 5°354, 5°268 | 5°433 5°344| 5°512 5°420| 5°591 5°500 | 5°667 5'576 | 5°746 5°652 | 5°825 5°728 | 5°904 5°804. | 5°983 5°880 | 6°062 5°956 | 6°141 6°032 | 6°220 6°106 | 6°299 6.184 | 6°378 3°888 3°969 4050 4131 4°212 4°293 4374 4°455 4536 4617 4°698 4779 4°861 4942 5°023 5°104 5°185 5'266 5°347 5°428 5°509 5°590 5671 o°752 5°834 5°915 5°996 6:077 6°158 6°239 4000 4°083 4166 4249 4°332 4°4.15 4°4.98 4581 4664, 4747 4°830 4°913 5000 5'083 5°166 5.249 5°332 5°415 5°498 5581 5664 o°T47 5°830 5913 6:000 6°083 6°166 6°249 6°332 6°415 6°320 | 6498 6°401 6482 6°563 6581 6°664 6.747 4°222 4°310 4398 4°486 4574 4662 4°750 4838 4°926 5014 5102 5°190 5°278 5.3866 5°454. 5542 5°6380 5718 5°806 5°894. 5°982 6070 6°158 6°246 6334 6°422 6°510 6°598 6°686 6774 6°862 6°940 7028 7116 44.4.4, 4°537 4630 4.723 4°816 4909 5°002 5°095 5°188 5281 5.874 5°467 5.556 5°649 5°742 5°835 5°928 6021 6°114 6°207 6°300 6°393 6'486 6°579 6°667 6°760 6°853 6'946 7°039 7132 7°225 7°318 7411 7504 4666 4763 4860 4°957 5°054 5151 5°248 5°345 5°442 5°539 5°636 5°733 5°834 5931 6'028 6°125 6°222 6'°319 6°416 6513 6°610 6°707 6°804 6901 7°000 7097 a 7194 — 7291 7388 7485 7582 7-679 7776 78738 123 EXCAVATION IN TRENCHES (continued). WIptH. Avel i age 7 6” | Tt 9’ 9/ QO” 8/ Bi g/ 6” 8/ 9g!’ | 9/ 0” g! 6” 10’ 0’ 10’ 6” Depth z | 6 10 |5°700| 5°887 | 6:074. 6°260 | 6°457 6°644.| 6°880 | 7°204.}'7°597 | 7°970 6 11 | 5°770| 5959 | 6148 | 6336 | 6°536 | 6°725 | 6917 | 7°292 | 7-690 | 8:067 7 O |5°832 | 6°026 | 6°222 | 6:416 | 6°610| 6 804.| 7000 |'7°388 |7°777 | 8° 166 7 J |5°'902| 6098 | 6296 | 6°492 | 6°689 | 6°885 | 7°083 | 7°4:76 | 7°870 | 8°263 7 2 |5°972|6°170 | 6°370| 6°568 | 6°768 | 6-966 | 7166 | 7-564 | 7-963 | 8°360 7 3 |6°042| 6°242 | 6°444 | 6°644.| 6°847 | 7-047 |'7°249 | 7°652 | 8:056 | 8°457 7 4 |6°1)2/|6°314.| 6°518 | 6-720 | 6°926 | 7°128 | 7:332 | '7°740 | 8°149 | 8°554. 7 5 |6°182! 6°386 | 6°592 6°796 | 7°005 | '7°209 | 7°415 | 7°828 | 8°242 | 8°651 7 6 |6°252'| 6°458 | 6°666 | 6°S72 | 7084. | 7-290 | 7 498 | 7-916 | 8°335 | 8°748 7 7 |6°822 | 6°530 | 6°740| 6-948 | 7°163 | 7°371 | 7-581 | 8°004 | 8°4.28 | 8°845 7 8 |6°392| 6 602 | 6°814.|7°024.| '7°242 | 7.4.52 | 7°664.| 8°092 | 8°520 | 8°942 7 -9 |6°462 | 6'674.| 6°888 | 7°100 | 7°321 | 7-533 | 7°747 | 8°180 | 8°612 | 9°039 7 10 | 6°582 | 6°746 | 6-962 | 7°176 | 7°4.00 | 7-614. | 7°830 | 8°268 | 8°704 | 9°188 7 11 |6°595 | 6816 | 7:036 | 7-257 | '7°4:79 | 7-695 | '7:918 | 8°356 | 8°797 | 9°235 8 o |6°666| 6888 | 7°11147°338 | 7°555 | '7°777 | 8°000 | 8°4.44 | 8°888 | 9°3383 124 EXCAVATION IN TRENCHES (continued). WIDTH. Aver- age Depth. ADAEAAAARHMAAAIOOIAIHNIKIIaanan»1Le LEAL DALAL ALL et OOIAMIPWNRFOKCKHOONATIBRWNRFORFMOCOONOOABRWNHO a Li oO 11.6%) 127-0" 12/ 6” | 13! 0” 13/ 6” 4°888 4°990 5°092 0°194 5°296 5°398 5°500 5°602 5°704 5°806 5°908 6'010 6112 6°214 6°316 6°418 6°520 6°622 6°724 6°826 6'928 7030 7-132 7233 7334 7436 7-538 7640 7742 7844 7946 8:048 8'150 8°252 5°111| 5°333 5218 | 5°444 5°825 | 5°555 5'432 | 5°666 5°539|5°777 5646/5 888 5-753 | 5999 5860 | 6110 5967 | 6°221 6074 | 6332 6181 | 6443 6'288 | 6°554 6'390 | 6°668 6497 | 6°779 6'604. | 6890 6°711 | 7°001 6818 | 7112 6925 | 7°228 7032 | 7°334 7139 | 7445 7:246 | 7°556 7°353 | 7667 7-460 |7°778 7°566 | 7°889 7667 | 8°0U0 7-774,|8'°111 7881 | 8222 7988 | 8°333 8095 | 8°4.44 8'202 | 8°555 8°309 | 8°666 8'416 | 8°777 8'523 | 8'888 8°630 | 8°999 5°5655 | 5°777 5°671 | 5°897 5°787 | 6°017 5°903 | 6°137 6°019 | 6:257 6°135 | 6°377 6°251 | 6 497 6°367 | 6°617 6°483 | 6°737 6°599 | 6°857 6°715 | 6977 6'831 | 7-097 6°946 | 7°224 7062 | 7°344 7178) 7°464 7°294| 7°584 7410 | 7°704 7526 | 7°824 7642 | 7-944 7°758 | 8:064 7874 | 8184 7990 | 8°304 8°106 | 8°424 8°222 | 8°544: 8°334| 8°667 8°450 | 8°787 8°566 | 8:907 8°682 | 9:027 8°798 | 9'147 8°914| 9°267 9°030 | 9°387 9°146 | 9°507 9°262 | 9°627 9°378 | 9°747 6:000 6°125 6°250 6°375 6°500 6625 6°750 6°875 7:000 7125 7250 7375 7°500 7625 7°750 7875 8:000 8°125 8°250 8°375 8°500 8°625 8°750 8°875 9°000 9°125 9°250 9°375 9°500 9°625 9°750 9°875 10000 10°125 14/ QO” 6°222 6°352 6°482 6612 6°742 6°872 7:000 7130 7°260 7°390 7°520 7°650 7778 7-908 8°038 8168 8°298 8°4.28 8558 8688 8°818 8948 9°078 9°208 9°334 9°464 9°594 9°724 9°854 9°984 10°114 10°244, 10°373 10°502 14’ 6” 6'444 6°578 6°712 6°846 6°980 7114 7248 7382 7516 7°650 7784 7918 8°056 8°190 8°324 8°458 8°592 8°726 8°860 8994 9°128 9°262 9°396 9°530 9°667 9°801 9°935 10°069 10°2038 10°337 10°471 10°605 10°739 10°873 15/ ol 6°666 6°805 6'°944 7-083 7°222 7361 7500 7639 TIS 7917 8°056 8°195 8'°334 8:473 8°612 8751 8°890 9:029 9°168 9°307 9°446 9°585 9°724 9°863 10°000 10°139 10°278 10°417 10°556 10°695 10°834 10°973 11°112 11°251 Oss sts 125 EXCAVATION IN TRENCHES (continued). WIDTH. LEO? | OFCOM ON OaAb Whe 8°354. 8°456- 8°555 8°657 8°759 8861 8963 9°065 | 9°167 9°269 9°370 9°4.72 6573 9°675 9777 12)" OUT 9°222 9°333 9°444. 9°555 9°666 9777 9°888 10°000 10-111 10°222 10°333 10°444, | 10°555 10°666 12’ 6” 1856" 13°67 14/ 0” 14/ 6” 15’ QO” 9°4.94, 9°610 9:722 9°838 9°954, 10°070 10°186 10°302 10°318 10°4:34. 10°550 10°666 10°782 10°898 4 fe a a 9°867 9°987 LO ETT 10°231 10°351 10°471 10°591 10°711 10°831 19°951 11071 LETOL 11°311 11°431 11°555 10°250 10°375 10°500 10°625 10°750 10°875 11°000 11125 11°250 11°375 11°500 11°625 11°750 11°875 12-000 10°631 10°760 10°889 11°019 11149 11:279 11°409 11-589 11°669 11°799 LLO29 12°059 127189 12°319 12°444. 11:007 | 11'390 11°141 | 11°529 11:278 | 71°667 11°412 | 11°806 11°546 | 11°945 11-680 | 12°084 11°814,| 12°2238 11°948 | 12°362 12°082 | 12°501 12°216 | 12°640 12°350 | 12°779 12°484 | 12°918 12°618 | 13°057 12°752 | 138°196 12°888 | 13°333 Average Depth. OOWDOOMOOM® ORODODOROROROBOABSCOAWSOOAWSOARABWOOAWS 126 EXCAVATION IN TRENCHES (continued). WIDTH. 9! 0” Hy! 3” / 9) 6” 9! g// erty 1:833 1:889 1-945 2-000 2-056 2°112 2-168 2-222 2°278 2°334 2-390 2-444. 2-500 2-556 2°612 2-666 2777 2°888 3-000 3111 3°222 3°333 3°444 3°555 3°666 B47 3-888 4-000 4111 4/222 4333 | 4°444, 2°000 2°062 2°124: 2°186 2°250 2°312 2°374: 2°436 2°500 2°562 2°624: 2°686 2°750 2°812 2°874. 2°937 3°000 3°125 3°250 3°375 3°500 3°625 3°750 3°875 4,000 47125 4°250 4°375 4-500 4625 4°750 4875 5°000 2°222 2°291 2°360 2°4.29 2°500 2°569 2°638 2°707 2777 2°846 2°915 2°984 3°055 3124. 3193 3°2638 3°333 3°472 3611 3°750 3°888 4027 4°166 4°305 4°4.4.4, 4°583 4°722 4861 5°000 5°139 5:278 5417 5°555 2°4.44, 2°520 2°596 2°672 2°750 2°826 2°902 2°978 3°055 J 131 3°207 | 3°283 3361 3°437 | 3513 3°589 3°666 3°819: 3°972 4°125 4278 4°431 4°583 4°736 4°888 5041 5°194 5°347 5°500 5°653 5°806 5°959 6111 3! Oo” 3/ 3” 3/ 6” 3/ Gg!’ 2666 2°749 2°832 2°915 3°000 3°088 3'166 3°249 3°333 3416 3°499 3°982 3°666 3°749 0000 3°916 4000 4166 4333 4500 4666 4°833 5°000 5'166 5°3338 5500 5°666 5°833 6:000 6166 6°333 6°500 6666 2°888 2°978 3°068 3°158 3°250 3°340 3°430 3°520 3 611 3°701 3°791 3°881 3972 4-062 4°152 4°243 4°333 4513 46938 4°873 5055 5°235 57415 5°595 DTT. 5957 6137 6317 67500 6°680 6°860 7040 7222 3111 3°208 3°305 3°402 3°500 3°597 3°694 3°791. 3°888 3°985 4082 4:179 4277 4374, 4471. 4,568 4666 4860 5055 5250 5444, 5638 5833 6°027 6°222 6°416 6°610 6°805 7°000 7194 7°388 7582 TTT 3°333 3°437 3541 3°645 3°750 3°854 3°958 4062 4°166 4270 4°374 4°478 4°583 4°687 4°79] 4895 5°000 5°208 5417 5625 5°833 6041 6°250 6°458 6°666 6°874 7082 7°290 7500 7708 7916 8124 8°333 4’ 3°5D5 3°666 3777 3°888 4000 4°U11 4°222 4°333 474.44 4555 4666 ATTTS 4°888 5°000 5111 5°222 5°333 5°555 5777 6°000 6°222 6'°444. 6°666 6888 7111 7333 | 7555 TTT7 8'000 8°222 8444 8'666 8888 EXCAVATION IN TRENCHES (continued). 127 WiptrH. ees 4! 3! A! 6” 4! 9! 5! 8 0} 3°777 | 4000 | 4.222) 4°444, 8 3 | 3:895 | 4125 | 4354) 4°583 8 6 | 4°013.| 4250 | 4486] 4°722 8 9 | 4131 | 43875 | 4618 | 4861 9 O| 4250 | 4°500/ 4°750] 5:000 9 3 | 4368 | 4625 | 4882] 5189 9 6 | 4-489 | 4°750 | 5°014| 5:278 9 9! 4:607 | 4875 | 5146] 5°417 200.04) 04722.) 5°000 | 5°277;| 5°555 10 3 | 4840 | 5125 | 5409 | 5694 10 6 | 4°958 | 5°250 | 5°541 | 5°833 10 9 | 5076 | 5375 | 5674 | 5972 11. O | 5193 | 5500} 5°805) 6111 IL 3} 5'311 | 5625 | 5°937 | 6250 11 6 | 5°429 | 5°750 | 6069 | 6°389 Jl 9 | 5°547 | 5°875 | 6201 | 6°528 12 O | 5°666 | 6°000 | 6°333 | 6°666 12 6 | 5902 | 6250 | 6597 | 6°944 138 O| 61389 | 6:500} 6861 | 7222 138 6] 63875 | 6°750 | 7:125| '7°500 14 O| 6611 | 7:000 | 7°389 | 7:777 14 6 | 63847 | 7°250 | 7°653 | 8°055 15 0} 7:083.| 7500 | 7917 | 8333 15 6 |} 7319 | 7°750| 8181 | 8611 16 O |} 7555 | 8°000 | 8444} 8888 16 6] 7-791 | 8250 | 8708 | 9166 17 O| 8027 | 8°500| 8972) 9°444 17 6 | 8263 | 8°750 | 9°236| 9°722 18 O |} 8500 | 9:000 | 9°500 | 10 000 18 6 | 8736 | 9°250 | 9°764 | 10°278 19 O | 8972 | 9°500 | 10°028 | 10°555 19 6 | 9:208 | 9°750 |10°292 | 10°833 20 O | 9°444 | 10°000 |10°555 | 11°111 5! gi 5/ 6” 4666 | 4°888 4°812 | 5-041 4-958 | 5:194 5104 | 5:347 5°250 | 5°600 5°396 | 5°653 0°542 | 5-806 5°688 | 5:959 5°833 | 6-111 5979 | 6-264 6125 | 6:417 6271 | 6°570 6'416 | 6°722 6561 | 6°875 6708 | 7-028 6°854 | 7-181 7:000 | 7:333 7°292 | '7°639 7583 | 7:944 7875 | 8:°250 8166 | 8°555 8°458 | 8°861 8°750 | 9-166 9°042 | 9:472 9°333 | 9°777 9°625 | 10°083 9917 | 10°388 10°209 | 10°694 10°500 | 11-000 10°792 | 11°306 11°084 | 11612 11°375 | 11°918 11°666 | 12°222 5/ Q/’ S111 5271 5°431 5°591 5°750 5910 6070 6°230 6°388 6548 6°708 6°868 7027 7187 7347 7507 7666 7°986 8°305 8°625 8°945 9°265 9°585 9°903 10°222 10°542 10°862 11°181 11°500 11°820 12°139 12°458 12°777 6/ oO” 5°333 5.500 5°667 5°834 6°000 6°167 6'334. 6501 6'°666 6°833 7000 7°167 7333 7°500 7667 7834 8:000 8°333 8°666 9°000 9°333 9°666 10°000 10°333 10°666 11000 11°333 11°666 12°000 12°333 12°666 13°000 13°333 DRBODBDOAROAOGDADHAGDHAIOADOAWNOOAawovuanownawe EXCAVATION IN TRENCHES (continued). 128 WIDTH 6/ 6” 6’ 9! ll 0” 7! 3” vid 6” 7! 9! 8/ OQ” 5777 | 6000 | 6222| 6444) 6666} 6888} 7111 5°958 | 6188 | 6417] 6646] 6875] 7:104| 7°333 6139 | 6376 | 6612] 6848} 7:084| 7:320 | 7°555 6°320 | 6564] 6807] 7:049| 7292 | 7586 | 7:°777 6500 | 6°750 | 7:000| 7:250!} 7°500| 7:°750| 8°000 6681 | 6938 | 77195 | 7452) 7709 | 7:966| 8:222 6862 | 7°126| 7°390| 7°654)| 7:918|} 8182| 8444 7-043 | 7314 | 7°585 | 7°856| 8127 | 8°398| 8-666 7°992 | 7500 | 7°777 | -8'055 | °8'333"| 8611) 2 Shee 7-408 | 7688 | 7972] 8:257| 8542] 8827] 9111 7°584.| 7876] 8167] 8459] 8751} 9°048 | 9°3338 7765 | 8064 | 8°362| 8660] 8960! 9°259 | 9°555 7:944,| 8°250 8555 8861 9°166 9°472 9°777 8125 | 8434] 8750] 9:063| 9°375 | 9°688 | 10°000 8°306 | 8626 | 8945 | 9°265 | 9°584} 9904 | 10:222 8'487 | 8814] 9140] 9°465 | 9°798 | 10°120 | 10 444 8666 | 9°000 | 9°3833 | 9°666 | 10°000 | 10°338 | 10°666 9°027 | 9°375 | 9°722 | 10°169 | 10°417 | 10°764 | 11°111 9°388 | 9°750 | 10°111 | 10°472 | 10°833 | 11°195 | 11°555 9°750 | 10°125 | 10°500 | 10°875 | 11°:250 | 11°625 | 12-000 10°111 | 10°500 | 10°889 | 11°278 | 11°666 | 12°055 | 12°444 10°472 | 10°875 | 11°278 | 11°681 | 12°083 | 12°486 | 12°888 10°833 |11°250 | 11°666 | 12°083 | 12°500 | 12.917 | 13°333 11°194 | 11°625 | 12°055 | 12°486 | 12°917 | 13°347 | 13°777 11°555 |12°000 | 12°444 | 12°888 | 18°333 | 18°777 | 14°222 11°916 | 12°375 | 12°833 | 18°291 | 18°750 | 14°208 | 14-666 12°277 |12°750 | 18°222 | 13°694 | 14°166 | 14°689 | 15°111 12°638 |13°125 | 18°611 | 14097 | 14°583 | 15°070 | 15°555 13°000 |18.500 | 14°000 | 14°5CO | 15°000 | 15°500 | 16°000 13°361 | 18°875 | 14°389 | 14°903 | 15°417 | 15°9381 | 16°444 13.722 |14°250 | 14°777 | 15°306 | 15°833 | 16°361 | 16°888 14088 | 14°625 | 15°166 | 15°709 | 16°250 | 16°792 | 17°333 14°444 |15°000 | 15°655 | 16°111 | 16°666 | 17°:222 | 17°777 129 EXCAVATION IN TRENCHES (continued). 17°875 | 18°416 | 18-958 | 19°500 | 20°584 | 21°666 | 22°750 | 23°833 18°333 | 18°888 | 19°444 | 20°000 | 21°111 | 22°222 | 23-338 | 24°444. WIDTH. Aver: | | age g/ 3” 8’ 6” g/ 9! g/ 0” g/ 6” 10’ 0” 10/ 6” ll’ 0” Depth fan: 0 7°333 | 7555 | 7777; 8:000| 8444) 8888} 9°333 | 9°777 8 8 | °7562}| 7°791 | 8020; 8250] 8708] 9166) 9°625 | 10°083 8 61 7791 | 8:027 | 8263] 8500} 8972] 9:444] 9°917 | 10°3889 8 9 8019 | 8263 | 8°506 |} 8°750| 9°2386 | 9°722 | 10°209 | 10°695 9 O 8250 | 8500 | 8°750 | 9°000} 9°500 | 10°000 | 10°500 | 11°:000 9 -3 8479 | 8°736 | 8993 | 9:250| 9°764 | 10°278 | 10°792 | 11:306 9 6 8°708 | 8972 | 9°236 | 9°500 | 10°028 | 10°556 | 11°084 | 11°612 9 9 8937 | 9:208 | 9°479 | 9°750 | 10°292 | 10°834 | 11°375 | 11°918 10 O 9'166 | 9°444, | 9°722 | 10°000 | 10°555 | 11°111 | 11°666 | 12°222 10 3 9°395 | '9°680 | 9°965 | 10°250 | 10°819 | 11°389 | 11°958 | 12°528 10°°6 9°624 | 9°916 |10°208 | 10°500 | 11°083 | 11°667 | 12°250 | 12°834 10 9 9°852 | 10°152 |10°451 | 10°750 | 11°347 | 11°945 | 12°542 | 13°140 11 O | 10°083 | 10°888 | 10°694 | 11°000 | 11°611 | 12°222 | 12°833 | 13°444 11 3 | 10°312 | 10°624 |10°937 | 11°250 | 11°875 | 12°500 | 18:125 | 18°750 11 6 | 10°541 | 10°860 |11:180 | 11°500 | 12°139 | 12°778 | 13:°417 | 14°056 ll 9 | 10°770 | 11:096 | 11°428 | 11°750 | 12°408 | 13°056 | 18°709 | 14361 12 O |} 11:000 |11°3383 | 11°666 | 12°000 | 12: 666 | 13°333 | 14.000 | 14666 12 6 | 11°458 | 11°805 |12°152 | 12°500 | 13°194 | 13°888 | 14°583 | 15°277 13 O | 11°916 | 12:277 |12°638 | 13000 | 13°722 | 14-444 | 15°167 | 15°888 18 6 | 12°375 | 12°750 | 13°125 | 13°500 | 14°250 | 15-000 | 15-750 | 16°500 14 O | 12°888 | 13°222 |13°611 | 147000 | 14°777 | 15°555 | 16°333 | 17°111 14 6 | 13:291 | 18°694 | 14°097 | 14°500 | 15°305 | 16°111 | 16916 | 17°722 15 O | 13°750 | 14°166 | 14°583 | 15°000 | 15°833 | 16°666 | 17-500 | 18°383 15 6 | 14208 | 14°688 | 15°069 | 15°500 | 16°361 | 17:222 | 18-088 | 18°944. 16 O | 14°666 | 15:111 |15°555 | 16°000 | 16°888 | 17-777 | 18°666 | 19°555 16 6 | 15°125 | 15°588 |16°041 | 16500 | 17 416 | 18°388 | 19°250 | 20°111 17 O | 15°583 | 16°055 |16°527 | 17-000 | 17-°944 | 18°888 | 19°833 | 20°722 17. 6 | 16°041 | 16°527 | 17-013 | 17°500 | 18-472 | 19°444 | 20°416 | 21°3338 18 0 | 16°500. | 17-000 | 17°500 | 18°000 | 19:C00 | 20-000 | 21:000 | 22°000 18 6 | 16:958 |17°472 |17-986 | 18°500 | 19 528 | 20°555 | 21°588 | 22°611 19 O | 17°416 | 17°944 |18°472 | 19°000 | 20°056 | 21°111 | 22°167 | 23°:222 6 O 130 EXCAVATION IN TRENCHES (continued). WIDTH. age ale Gt 20! 12’ 6” 13’ 0” Tey Gye 14/ 0” 14/ 6” | 15’ 0” 10°222 | 10°666 | 11°111 | 11°555 | 12°000 | 12°444 | 12°888 | 13°333 19°166 | 20°000 | 20°834 | 21°666 | 22°500 | 23°338 | 24-166 | 25°000 19°805 | 20°666 | 21°529 | 22°388 | 23°250 | 24-111 | 24972 | 25°833 20°444 | 21°333 | 22°222 | 23°111 | 24000 | 24°888 | 25°777 | 26°666 21°083 | 22:000 | 22°917 | 23°833 | 24°750 | 25°666 | 26°583 | 27-500 21°722 | 22°666 | 23°611 | 24°555 | 25°500 | 26°444 | 27-389 | 28:333 22°361 | 23°333 | 24°306 | 25°277 | 26°250 | 27°222 | 28-195 | 29°166 23°000 | 24000 | 25000 | 26°000 | 27:000 | 28-000 | 29-000 | 30°000 23°639 | 24666 | 25°695 | 26°722 | 27°750 | 28°777 | 29°806 | 80833 24 278 | 25°333 | 26°390 | 27:444 | 28°500 | 29°555 | 30°611 | 31°666 24917 | 26-000 | 27:083 | 28°166 | 29°250 | 30°338 | 31°417 | 32°500 25°555 | 26°666 | 27°777 | 28°888 | 30-000 | 31:111 | 32°222 | 33°333 8 0 8 3 | 10°542 | 11-000 | 11°458 | 11°916 | 12°375 | 12°833 | 13-291 | 13°750 8 6 | 10°862 | 11-333 | 11°805 | 12°277 } 12°750 | 18°222 | 13°694 | 14°167 8 9 | 11°182 | 11°666 | 12°152 | 12°688 | 18°125 | 18°611 | 14097 | 14°584 9 O | 11°500 | 12-000 | 12°500 | 13°000 | 13°500 | 14-000 | 14°500 |-15°000 9 3 | 11°820 | 12°333 | 12°847 | 13°361 | 138°875 | 14°389 | 14-908 | 15°417 9 6 | 12°140 | 12°666 | 13194 | 18°722 | 14-250 | 14°778 | 15°306 | 15°834 9 9 | 12°460 | 13-000 | 13°541 | 14°083 | 14°625 | 15°167 | 15°709 | 16°251 10 O | 12°777 | 13°383 | 18°888 | 14°444 | 15°000 | 15°555 | 16-111 | 16°666 10 3 | 18°097 | 13-666 | 14°235 | 14°805 | 15°375 | 15°944 | 16°514 | 17-088 10 6 | 13°417 | 14-000 | 14°582 | 15°166 | 15°750 | 16°383 | 16°917 | 17°500 10 9 | 18°737 | 14°333 | 14°929 | 15°527 | 16125 | 16°722 | 17-320 | 17°917 11 O | 14°055 | 14°666 | 15°277 | 15°888 | 16°500 | 177111 | 17-722 | 18°333 11 3 | 14°375 | 15-000 | 15°624 | 16°249 | 16°875 | 17-500 | 18125 | 18°750 11 6 | 14°695 | 15°333 | 15°971 | 16°610 | 17°250 | 17°889 | 18°528 | 19°167 11 9 | 15°014 | 15-666 | 16°318 | 16°971 | 17°625 | 18°278 | 18°931 | 19°584. 12 O | 15°333 | 16000 | 16°666 | 17°333 | 18°000 | 18°666 | 19°3338 | 20°000 12 6 | 15°972 | 16-666 | 17°361 | 18°055 | 18°750 | 19°444 { 20°139 | 20°833 13. O | 16611 | 17°333 | 18°056 | 18°777 | 19°500 | 20°222 | 20°945 | 21°666 13. 6 | 17:250 | 18-000 | 18°750 | 19°500 | 20°250 | 21-000 | 21-750 | 22°500 14 O | 17888 |18°666 | 19°444 | 20°222 | 21-000 | 21°777 | 22°555 | 23°333 14 6 | 18°527 | 19°333 | 20°139 | 20°944 | 21°750 | 22°555 | 23°361 | 24°166 O 6 O 6 O 6 O 6 O 6 O TABLE 131 XV. Gallons per Minute Sewage Flow due to Population. Maximum Flow (Half in Six Hours). At per Head. 40 Gis. 20 Gus. | 25 Glls. | 30 Gils, | 40 Gus. Glls. per Minute. 14, 28 56 84. 111 139 166 194: 222 250 278 556 833 1110 1390 1666 1944, 2220 2500 Average Flow during}T'wenty- Four Hours. 3 aees At per Head. 20 Gus. |25 Glls.}30 Gulls. Glls.per|Glls. per|Glls. per Minute. ; Minute. | Minute. 500 ve 8°5 10 1000 14, 17 21 2000 28 30 42 3000 A2 52 62 4000 56 70 83 5000 69 86 104 6000 83 104, 125 7000 97 121 146 8000 lll 139 167 9000 125 156 187 10000 139 174 207 20000 278 347 417 30000 416 520 625 40000 555 694 833 50000 694. 867 1042 60000 833 1041 1250 70000 972 1215 1458 80000 | 1110 | 13888 1667 90000 | 1250 1562 1875 100000 | 1390 ! 1736 | 20838 2778 Gils. per/Glls. per|Glls. per|Glls. per Minute. | Minute. | Minute. | Minute. 14, 17 21 28 28 35 42 56 56 70 83 112 84: 104: 125 166 19 Bh 139 167 222 139 174 208 278 166 209 250 334 194: 242 292 388 222 278 338 4.4.4. 250 313 375 500 278 347 417 556 556 694: 833 | 1110 833 | 1041 | 1250 | 1666 1110 | 1388 | 1667 | 2220 1390 | 1736 | 2083 | 2778 1666 | 2082 | 2500 | 3882 1944 | 2428 | 2916 | 3888 2220 | 2775 | 33834 | 4440 2500 | 3122 | 3750 | 5000 2778 | 3473 | 4166 | 5556 TABLE Vile Cubic Feet per Second Sewage Flow due to Population. Popula- 1 tion, 500 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 380000 4.0000 50000 60000 70000 80000 90000 00000 Average Flow during Twenty- Maximum Flow (Half in Six Four Hours. Hours). At per Head. At per Head. 20 Galls.| 25 Glls. | 30 Gils. | 40 Gils. | 20 Glls.| 25 Glls.| 30 Glls. | 40 Gills, Cubic ft.|Cubic ft.|Cubic ft.|Cubic ft.|Cubic ft.|Cubic ft.| Cubic ft. | Cubic ft. per sec. | per sec. | per sec. | per sec. | per sec. | per sec.| per sec. | per sec. ‘018 023 027 037 ‘037 04.5 ‘056 ‘O74 037 "045 "056 | °074 ‘O74 ‘098 Aagt "148 074. "093 ‘T1l "148 148 139 *222 "296 otal "139 ‘167 °*222 "222 "278 °333 444, "148 °185 "222 | ‘296 "296 370 “AAA, "592 °185 231 277 370 370 "462 *555 “740 °222 ‘278 "300 “44.4, "44.4, 555 "666 °888 °259 B24 *388 as ite 618 647 ed 1°086 "296 370 "44.4, "592 592 ‘740 °888 1:184 333 ‘416 “500 *666 *666 833 1:000 1°332 370 "462 “00 “740 “740 *925 1110 1°480 "740 ‘925 | 1:110 | 1°480 | 1:480 | 1-850 2°220 2:960 1'110 | 1°388 | 1°665 | 2°220 | 2°220 | 9°780 3°3380 444.0 1°480 | 1°850 | 2°200 | 2°960 | 2:960 | 3°700 4440 5°920 1°850 | 2°310 | 2°770 | 8700 | 3°700 | 4°620 5'550 7-400 2°220 | 2°780 | 3°330 | 4°440 | 4°440 | 5°550 6°660 8°880 2°590 | 3°240 | 3 880 | 5°180 | 5-180 | 6°470 7°770 | 10°3860 2°960 | 3°700 | 4440 | 5°920 | 5°920 7°400 8°880 | 11°840 3°330 | 4°160 | 5°000 | 6°660 | 6660 | 8330 | 10-000 13°320 3°700 | 4°620 | 5°550 | 7:-400 | 7-400 9°250 | 11°100 | 14°800 133 Taste XVII. Oubic Feet of Rainfall on Drainage Areas. Total Volume. Depth of Rainfall in Inches, Acres. z | : ; 1 D Cubic Cubic Cus ic Cubic Cubic Cubic Feet, Feet. Feet. Feet. Feet. Feet. 1 363 454 908 1815 3630 7260 2 726 908 1815 3630 7260 14520 3 1089 1362 2723 5445 10890 21780 4 1452 1816 | 38630 7260 14520 29040 5 1815 2270 4.540 9075 18150 36300 6 2178 2724 5445 10890 21780 43560 7 2541 3178 6353 12705 25410 50820 8 2904 3632 7260 14520 29040 58080 9 3267 4086 8168 16335 32670 65340 10 3630 4540 9080 18150 36300 72600 Nore,—The range of this table may be extended by simply moving the decimal, and also by addition, thus: Required total volume of }in. of rain- fall on 673 acres— 600 acres = 5145 x 100 = 544500 70 ,, = 6353 x 10 = 63530 aki foe 2723 = 2723 673 acres with }-in, rainfall= 610753 cubic ft. 134 TasLeE XVIII. Cubic Feet per Second of Rain Water corresponding to Rate Acres. | Cubic Feet | Cubic Feet | Cubic Feet per Second. OOmaOTID eb od = (op) © —_ of. Rainfall per Hour. Rate of Rainfall (Inches per Hour). ae per Second. + per Second. 25 “50 “75 1°00 1°25 1°50 1°75 2°00 2°25 2°50 ak 2 Cubic Feet per Second. ‘30 1°00 1°50 2°00 2°50 3°00 3°50 4:00 4°50 5°00 Cubic Feet per Second. | SCOONOOBRWNH _ 9 =~ | ; ‘Cubic Feet per Second. Nortr.—It is usual in general calculations to assume that only } the rainfall will In that case the figures in the table must be divided by 2. The range of the table may be extended in the manner explained under previous run off within the hour. table (xvii.). 135 TABLE ATX, (T. HigHAM.) (Supplemental to Table I1., Part 3, Page 44). Values of Kutter’s coefficient ‘‘C”’ for different values of ./R and n (s=‘001 constant). w= OL v= "O11 ='012 JR C Diff. 01 C Dit. Ol C Diff. OL 2 70°0 2°09 60°7 1:88 53° 1270 “3 909 1°59 79°5 1°46 703 1:34, “A, 106°9 1:26 94-1 1:16 83°7 1:08 5 119°5 101 1058 "95 94:6 "89 6 129°6 "84, 115°2 ‘79 103°4 15 ng 1380 ‘70 123°1 ‘67 110°9 63 ‘8 145°0 ‘60 1298 57 117-2 ‘BS: ‘9 151°0 52 135°5 “4.9 122-7 Ay 1:0 156°2 “45 140°4. 43 127-4 42 a 160°6 39 144°8 38 1316 37 “9 1646 35 1486 +34 135°3 33 3 168'1 “31 151°9 ‘30 138°5 29 “4, 171°2 28 1550 27 1415 26 5 1740 "25 157°7 25 1441 “24, 6 1765 23 160°2 22 146°5 “22 ay 178°8 “21 162°4. ‘20 148°7 20 8 1809 19 164°4 19 150°7 18 ‘9 182'8 17 166°3 17 152°5 Vy, 2-0 184°5 16 168°0 16 154°2 16 ‘ 186'1 15 169°6 15 155°8 14, 2 187°6 14, L7G 14 157°2 13 a 189°0 13 172°4 13 158°6 iG 136 TABLE X1X. (continued). n='013 n='015 | n='017 JR |. | ———— C Diff. *01 C Diff. °01 | C | Diff, °01 | “2 47°3 1°56 38'1 1°3] 316 Ls une 62°8 1°24, Duss 1:07 42°9 94. “A, vive 101 62°0 89 52°3 79 5 | 85:3 83 70°8 14 60°1 67 6 93°6 71 78°3 64 66°8 58 “4 100°7 60 846 do 72°6 50 pS rts LOG 7. 52 90°1 48 yerer’ 44. me) 111°9 AS 94.9 42 82°71 39 1:0 116°5 4O 99°] Sie 86°0 35 et 120°5 36 102'9 33 89'5 ol “2 124-0 82 106°2 30 92°6 28 q5) 127°2 29 109°2 27 95'5 26 “A 130°1 26 111°9 "25 98° 1 "24. "5 £3237 ‘23 114°4 22 100°4. 21 6 1350 21 116°6 21 102°5 20 fe 1371 20 118°6 19 1045 18 ‘Sen 130s 18 120°5 18 106°3 17 9 140°9 17 122°3 16 108°0 16 2:0 142°6 15 1:23°9. 15 109°6 15 “AI 144°1 14 125°4 14. 111°0 13 "2 145°5 13 126'8 13 112°4 He! ‘3 146°9 12 128°0 124 113°6 12 HxameLes Required *C” when /R='433, and 2='013 By Table when /R="4 OF 75°2 “s » ='03 4, =3x Diff. 1°01 = 3°03 is ie == £009", S18 'X "101 = 303 When /R =°433 and »='013, then ( =78°533 137 USEFUL MEMORANDA. Law of Discharge. The gradients being equal the discharge of sewers varies as the square root of the fifth power of the diameter (./d*). Conversion Table. | Per | Per Per Per Second. Minute. Hour. 24 Hours. Cubic feet a 60 3,600 86,400 Gallons 64 (6°235) 375 22,500 540,000 To convert cubic feet per minute and cubic feet per second into gallons per twenty-four hours :— Cubic feet permin.x 9,000=gallons per twenty-four hours. Cubic feet per sec. x 540,000=gallons per twenty-four hours. Minimum Inclination Formula. The following empirical formula will give the approximate minimum inclination for a sewer of a clear diameter of d inches, and either circular or egg-shaped :— 100 Minimum inclination per cent. =————_ 7" 5d +50 138 Hytelwein’s Formula. Eytelwein’s formula, hitherto most extensively used by English sewerage engineers, gives too high velocities for small sewers and too low velocities for > large sewers. . Approximate Maximum Rate of Rainfall. It is by no means improbable that some definite relation exists between the mean annual rainfall and the maximum rate of fall during storms. Captain Hoxie’s empirical formula, based on observations in the United States, 1s R f= — 12 Where R=mean annual rainfall in inches. + =probable maximum rainfall for one hour, in inches. Time will show whether this formula can be safely applied to English meteorological conditions, and, if so, whether 12, the denominator in the frac- tion, gives the best approach to accuracy. Approtimate Variation of Flow of Sewage. Let F=maximum flow about noon, f =minimum flow about 3 o’clock in the morning, Q=total quantity discharged per twenty-four hours in dry weather, then F ='0017 Q, f =-00027 Q. 139 ~~ Increase of Population. Let v=rate of increase per inhabitant, n=number of years, P»=population after n years, P, =population in first year, bray Py _ log. P,—log. P, P, n—1 and P, =P, x (1+v)”-1 then l+v= It is usual in designing sewerage schemes to pro- vide at the start for an increase of 25 to 33 per cent. of the existing population. Local conditions, how- ever, have a most important influence on the rapidity of increase, and each case must be carefully con- sidered. Comparative Quantity of Brickwork. A standard egg-shape sewer requires about 5 per cent. more brickwork than a circular sewer of equal sectional area. Kutter’s Coefficient of Friction (n). Kutter has conclusively demonstrated the im- portant influence which the condition of the wetted perimeter has on the discharge. This influence may be compared to the action of incrustated ships’ hulls in retarding the speed. Hence the importance of selecting, wherever possible, materials of high glaze, with as few joints as practicable. The choice of a numerical value of » is a matter of judgment and experience. For instance, whilst experiments on new glazed stoneware pipe sewers, L2 140 truly and accurately laid, give ‘010 or ‘Oll as the value of n, it must be remembered that few, if any, sewers as laid in actual practice can remain true and perfect for’ any considerable length of time. | Surfaces become incrustated, subsidences take place, joints are dislocated and solids deposited on the inverts. In that case n would become ‘013, or even ‘015, instead of ‘011, which assumes a good condition. The following table gives the average values of » under various conditions :— , TABLE OF AVERAGE VALUES OF 1. a a Condition of Surface. Material of Sewer. Perfect. | Gcod. | Fair. Bad. Glazed stoneware pipe ...| ‘O10 ‘O11 013 015 Brickwork, ordinary... ...| ‘012 013 015 017 Brickwork, glazed ... ...| “O11 012 013 014 Rendering, cement mortar| ‘011 012 013 015 Rendering, neat cement ...| ‘010 ‘O11 7012 013 Ashlar, dressed... ... «..{ ‘018 ‘014 015 017 Tron (cast), uncoated een Ole 013 014 015 Iron (wrought) and steel...| ‘O11 |. ‘012 013 014 Norr.—For general calculations *013 is usually taken for glazed pipes and ‘015 for ordinary brick sewers. This will allow an ample margin for deterioration, and has been found to agree closely with gaugings of sewers in actual practice and which had been in use for some time. For new pipe and brick sewers *011 and °013 respectively should be used. Reader’s Memoranda. i\/\Wr— Reader’s Memoranda. = MN Ww Reader’s Memoranda. iN VAV Vs: — Reader's Memoranda. —w\V\Ww— Reader’s Memoranda. —w/\Ww— Reader's Memoranda. pen aa Reader's Memorairda. —VV/\/\— Utilization of Ordinary Street Lighting for Sewer Gas Extraction and Destruction. W. DEAKIN & Co.yenginnens’ a. GUEST STREET, HOCKLEY, BIRMINGHAM. This System (J. E. Webb’s Patent), as in use at Abergavenny, Tottenham, Hereford, Southampton, the Wolverhampton Hospital (Oldbury, Birming- ham), Tettenhall (Shoreditch, London), &c., secures Street Illumination and Sewer Gas Destruction, at a cost of only One Halfpenny per lamp per hour. “It is also especially applicable for ventilating purposes. TESTIMONIALS. DEAR SIR, The five lamps which you converted from ‘' HOLMAN’S”’ to the ‘ Webb” Paten Sewer Ventilator have all been fixed and are working very satisfactorily. I calcu- late that we shall save some- thing like 450 per annum by the conversion and get a better light. JOHN PARKER, City Surveyor, —— Hereford. NEw CouRT TEMPLE, Lonpbon, E.C. DEAR SIRS, Dec. 20, 1894.: The Ventilator you have erected for the new Mortuary Block at the Wolverhampton General Hospital is working with very satisfactory results. It not only changes the airin the three rooms 5 or 6 times every hour, but t raises the temperature of all the air extracted to 600°—700° Fahr., thus cremating any disease germs that might be present. Yours faithfully, GEO. HURST STANGER, CES FE Ry LB As W. Deakin & Co.’s Specialities. i. Sewer Gas Extractors and Destructors, 2. Ventilators for Public Buildings, Hospitals, Mortuaries, Schools, Basements, Subways, &c, 3. Refuge and other Lamps, in cast Gun- Metal, Brass, or Steel. Gas Regulators and Governors in White Metal, Aluminium, &c. . Gas, Water and Steam Cocks. Gas Burners and Re- flectors. Copper Tubes, any size or strength. CAS MAID GOLD MEDAL, MELBOURNE, 1881. JOHN SPENCER, Globe @ube Works, WEDNESBURY, Staff. Manufacturer of Iron and Steel Tubes and Fittings, for Gas, Water, Steam, Hydraulic, Compressed Air, Refrigerating and Heating purposes, in Stock to 8-in. diameter. Water and Oil Mains, Well Tubes, Telegraphic Poles, &c. Light Wrought-Ironi Rain-Water Tubes. Sewer Ventilating Tubes. Tubular Line Posts, &c. ‘SEWER VENTILATOR || WRO?T IRON |] zn: Boe Office: 14 GT. ST. THOMAS APOSTLE, E.C. The “ADDISON” PATENT DRAIN STOPPER, For Testing Drains by means of Water, Smoke, &¢. We have every confidence in introducing this Drain Stopper to Local Boards, Sanitary Surveyors, Builders, &c. It is the invention of a Sanitary Surveyor who has had a large practical experience in Drain Testing, and every detail to render the Stopper effective and easy of application under all circumstances has been considered. The parts are non-corrosive, the disc of galvanized iron, the nipple of gun metal, the nut and cap of brass. SECTION 6IN. STOPPER SS Section. Section. y \N SE hhh VSV_u»2&wz “DONNOL” WASH-DOWN PEDESTAL CLOSET, IN ONE PIECE OF EARTHENWARE. This Closet has been specially designed to meet the requirements of the London County Council. The back is straight; there is about 13 in. water seal to trap, and the outlet is separate from body of closet and above the floor line, for making a cement joint into earthenware, or iron-pipes, or brass thimble. . - NICHOLLS & CLARKE, » 6 HIGH STREET, SHOREDITCH, LONDON, E. BURN BROTHERS WHITE PORCELAIN ENAMELLED Engineers, &c., 23 & 24 Charing Cross, WHITEHALL. ooh. DON, S.W. ALSO AT 1 Hanover Street, And 20 Thistle Street, HDINBURGH. Apply for particulars of Lavatories on same principle, also of Cast-Iron Gas-Tight Drainage Fittings. “ECLIPSE” Patent DRAIN-TESTER This is the ONLY SMOKE GENERATOR, of any description whatsoever, which applies a positive test to drains. 18 consists of a double-action Bellows covered with specially-prep red leat. a copper cylinder or vessel with an outer casing, which latter is filled wit In this casing a cover or float is placed ‘ich rises and falls with the ac the bellows. The hose must be conn. ~* drain or pipe to be tested, and al openings, such as ventilating pipes, pl a strokes ~f tle be.’ vs will rais the float, and if it remains stationary cv sor tight. If the flvat falls leak exists, and may be traced by using _ We Sie y A Brent advantage in using these M: ey Shen qvet crator can ascer, whether the drain is tight or not, withou ithe app . This appar is invaluable to Plumbers, Builders, Inspect...1 Nuisances, San. oy * ~D PRICES. " Machine & Tube (“zr12-"), 84/- Deal Painted Gase, 1 Plugs extra, as under. IMPROVED EXPANDING PLUGS FOR DRAIN TESTING. Made in sets, as under: Size A.—3in., with extra Rubber Rings for 3jin. and din. ... in) Vins G0 » B.—4iin., ,, me » Ring ,, 5in. ue ag ie ws. 9/6 Ge Bin's- as. bs ata: ok GH, ase ee Ge Pit Sei » D.—9in. ; canter ie ia am and ie Ba 2: ree V6 See Re LPR oes. senesced = oe ase aes Fee ats v~ - 50/0 ekss-loin, ~~... vos eo ee ate re Re ~~ ie ... 66/0 sg Ge—18in. te ges, \),!, ‘Tron Ke ey for screwing up Fly ‘Nut, each 3/0. Brass Unions for connecting Rubber Tube of Smoke Machine to Plugs, each 3/0. BURN BROTHERS, Patentees and Manufacturers of First-Class Sanitary Fittings, Water-Closets, Lavatories, Baths, Urinals, Cast-Iron “Gas-Tight” House Drainage Fittings, &c. LONDON: 23 & 24 CHARING CROSS, S.W. EDINBURGH: 71 HANOVER STREET and 20 THISTLE STREET. N. A. P. (NATIONAL) (ACCIDENT) (PREVENTION) SLIDING WINDOW FITTINGS Cost either 5s. or 12s. 6d. each set; and their application to a pair of double-hung Sashes ensures the following | ADYANTAGES :— Frames exactly similar to those of ordinary windows. Sashes which slide up and down as_ordinary windows. ~ General appearance similar to ordinary windows. Safe outside cleaning effected by top or central horizontal suspension during cleaning, thus insuring immunity from strains at the angles of the sashes, and consequent durability. Economical cleaning and repairing. Non-interference with window sill plants during cleaning. Non-interference with outside sun-blinds during cleaning. Instant removal of the sashes when desired without interfering with a single screw, thus ensuring :— (a) Ready renewal of cords without opening sashes. (6) Ready admission of cumbrous articles of furniture. (c} Whole void of window opening available for the admission of air, if desired (ad) The re-glazing of the sashes in safety within the room. (e) The painting of the sashes in safety within the room. dd a ed Pris OFFICES AND SHOWROOMS :— THE N.A.P. WINDOW CO,, 159 Victoria St., Westminster, S.W. Telegrams: «FENESTRULE, LONDON.” ~ R.HARDING & SON, Sanitary, Hydraulic & Gas Engineers, cc. 75 ARODENE ROAD, BRIXTON, S.W. HARDING’S New Perfect Drinking Fountain. AS SUPPLIED TO THE LONDON COUNTY COUNCIL. & oe WE beg: to call the attention of Public Bodies, Local Boards and furnishers of Public Gar- dens, to the merits of this Fountain. After 20 years’ experi- ence in the requirements — of Metropolitan Public (= Brinking Fountains, me and the study of late to . produceagocd serviceable Fountain at a moderate cost, we are now able, by adapting cast Iron to this design, anucombining all the most approved ap- pliances together with Harding & Son’s patent improved Strong Spring Jets, and per- fect escape for the waste water which is impossible to get stopped up, to: pre- sent a Strong, Useful, Drinking Fountain. filme ne TT | | | 75 ARODENE RD. BRIXTON, LONDON, S.W. HM The Surveyor And Municipal and County BLngineer Published on Fridays. Price dd. PREPAID ANNUAL SUBSCRIPTION (Including Postage). Twelve Six Three Montks. Months. Months. UniteD KINGDOM “ye 15s. 7s. 6d. 8s. 9d. Co vTINENT, COLONIES, Q = Lee Uacean Sree 17s. 8s. 6d. 4s, 3d. —So hua Some Press Opinions. “A handsomely-printed illustrated weekly paper, enclosed in a wrapper, and has an imposing list of contributors, of whom a considerable proportion are recognised authorities on topics relating to the special field of this publicatton.’ —Daily News. “ Articles of special interest to Surveyors comprisethc literary contents of the paper, the staff of contributors including many leading lights of the surveying profession. Well written, well edited, and certainly worth the money asked for it.”—Z£vening News (London), ““To the class for which it specially caters THE SURVEYOR must be of gr at interest and value, for it covers all the ground which their labours occupy, and does so with knowledge and energy. It is illustrated with portraits of men eminent in the surveying world, and it makes a feature of signed articles by experts.”’"—The Globe. “ Of much interest and value.”—Scotsman. ‘It appeals to a large class interested in real estate.”’—Pyctortal World. “We wish THE SuRVEYOR good luck.” —Daily Chronicle. ‘“ Influentially supported."—England. “The pro- fession has hitherto possessed no exclusive organ.’—Star. “In appearance and style is admirable.’—T7he Western Times, ‘“ Very carefully edited and well printed.”— Australian Trading World. “ Essentially a practical journal for practical men.’—Bath Gazette. ‘ Abounds with useful notes, views and papers on all matters interesting to Surveyors.’—Sanitation in the West. “Of special utility to surveyors and all those trades which the occupation of surveyors, architects and the like calls into special activity: ’—Blythe Examiner. “ Contains information on sanitary, building and other matters, which, coming from good sources, as the advice of THE SURVEYOR undoubtedly does, make it likely to have a large and wide-spread circuiation.”—Dzamond Fields Advertiser. OOOO Ot” OFFICES: “orn 24 BRIDE LANE, FLEET STREET, Ko: LONDON, E.C. < ST. BRIDE’S PRESS PUBLICATIONS. ‘Clearly printed, concisely written, and convenient in size.” 1. Out of Print. 2. Out of Print. 3. DILAPIDATIONS. By Sydney Perks, P.A.S.1., A.R.I.B.A. Price 6d., post free. 4, SHALL THE LONDON County CouNnciIL ConTROoL METRO» POLITAN RATING? By W. Harnett Blanch. Price 6d., post free. 5. Out of Print. 6. THE AGRICULTURAL HoLpiINGs (ENGLAND) Act, 1883. By William Arnold, F.s.1. Price 6d.; by post, 7d. 7. BETTERMENT. By Alfred Thomas Macer, P.A.s.1. Price 1s., post free. 8. THE Hermite System or SANITATION OF TOWNS By HUEc- tricity. By Edward J. Paterson, M.1.E.k. Price 6d. 9. CuemicaL SaniTatTion. By William Brown. Price 6d. post free ; or, if ordered in any quantity for the use of members of local authorities, at a discount of 333 per cent. 10. DRAINAGE WorRK AND SaAnitTaRY Firtines. By William H. Maxwell. Price 1s. nett; post free, 1s. 2d. 11. TABLE OF DISCHARGE FROM CIRCULAR SEWERS WHEN RuNNING Futt. By a Municipal Engineer. Price Is. nett, post free. 12. Housine oF THR LABOURING CLASSES AND BAcK-T0-BACK Hovusses. By H. Percy Boulnois, M.1.c.x., City Engineer of Liverpool]. Price 1s. nett; post free 1s. 2d. CREMATION, by Sir Spencer Wells, Bart. Tus Smoke NUISANCE AND How to ReEmepy It, by A. EH. Fletcher, Chief Inspector of Alkali, &c., Works, Local Govern- ment Board; and Sanitary Law, by Prof. A. Wynter Blyth. The set, price 3d.; post free. AGREEMENT Forms FOR TEMPORARY BuiILpINGs. Price 4s, per quire; or, with name of local authority printed in, 7s. 6d. per quire. A Synopsis oF THE WoRK OF AN OFFICIAL ENGINEER AND Surveyor. By H. Percy Boulnois, M.1.c."., City Hngi- neer of Liverpool. Price 1d., post free. London Depot: Midland Goods Station, King’s Road, Camden Town, N.W. I>] AN JAE WORKS, WILNE COTE pee iM. =p SSO Sig seo ----22 > [| eo ES Se 2s 5 Z rc 7 iluuanctin ee S255 N= Vz FOOT Sill ll = . SQwromaric TROUGH CLOSETS | —_—_————== THE “SWAN” Pot aire THE” Pe Ona elegrams : WASH-DOWN CLOSET. ‘* SKEY, TAMWORTH.” ‘“‘SKEY, LONDON.”’ ALSO MAKERS OF CABINET STANDS, URINALS, &c., &c. Buff Enamel “ ate Plain and aline! Bbenus , i Kitchen Sinks, ‘ et | Blue Bricks, wee bs Drain Pipes : : Glazed Hearth Gntainey: Tops, and Wall Tiles. SCe, SKC- 85 PRIZE MEDALS AND DIPLOMAS. THE COAL GREAT Ys TAR DISINFECTANT = FOR THE HOUSEHOLD, STABLE, KENNEL, AND FARM. Fiat | J EY E Ss of all the - F LU : D”’ Infectious Outbreak fae = ese i Diseases. | DISINFECTANT. Absolutely Safe in use, Non-Poisonous, and Stronger than Carbolic Acid. JEYES SANITARY POWDER. JEYES’ DISINFECTANT SOAPS. VERY ECONOMICAL IN USE. TOILET PAPER sanriseo with “JEYES’ FLUID.” _ Automatic Boxes for same in Walnut Wood. Embossed Board and Cardboard. Write for Descriptive Pamphlet, Price List, and full Particulars, to HEAD OFFICE: 43 CANNON STREET, LONDON. Woodville, Burton-on-Trent. Sole Manufacturers of the “ GRANITIC-STONEWARE” PIPES. || The Pipes are made from Selected Clays (not FireClay), of which g| the Company are the Sole Pro:rietors. The Clays are carefully blended to insure an impervious body specially adapted for Sanitary purposes, and the Pipes have a ‘* Toughness’ as opposed to ** Sei dorsimeatatt) which is much appreciated by Engineers, &c. SYKES’ Sedelee doled JOINT PIPES, SYKES'’ PATENT and other Specialities in Interceptors, Guilies, Channels, &c.; Invert and Junction Blocks, Sinks, Closets, Traps, &c. TESTED PIPES. LONDON DEPOT: Midland Railway New Goods Station, E Euston Road. Chief London Office: 18 NEW BRIDGE STREET, E.C; Telegrams --'' Sawerace, Lonpon.”’ TELEPHONE, Shak