CHAPTER V. SEWERAGE AND DRAINAQK (Part 2)

-323 •68 .. •668 •93 .. . ^761 •19 . . 104 •44 . .. •338 •69 .. •678 •94 .. . -766 •20 .. . ^112 •45 . .. -348 •70 .. •587 •96 .. . ^770 •21 .. . ^120 •46 . .. •353 •71 .. •595 •96 .. . ^775 •22 . •128 •47 . .. •363 •72 .. •605 •97 .. . ^778 •28 .. . 186 •48 . .. 373 •73 .. •614 •98 .. . -781 •24 .. . 145 •49 . .. 388 •74 .. •623 -99 .. . -784 '2B .. . '15S '50 . .. '3927 '76 .. '632 •100 .. . •7864 To calculate the hydraulic mean depth of any drain it is first necessary to ascertain the sectional area of water flowing. In circular pipes, with which plumbers almost exclusively are concerned, this is found by multiplying the square of the diameter by certain co-efficients, or propor- tional decimals, constant to the ratio of the versed sine, divided by the diameter. The formula is — Diameter^ x C (as per table); XX = the versed sine (GH) divided by the diameter of the circle; and C = the constant number or co-efficient placed opposite in table. If we have a 36 - inch sewer running three-quarters full, we find the sectional area thus : Measure the 136 DOMESTIC SANITARY DRAINAGE AND PLUMBING. versed sine (GH), which is the greatest depth of the water, 225 feet, and divide it by the diameter, 3 feet; we have then '75; opposite '75 in table we find the co-efficient '632; now square the diameter, 3 feet = 3x3 = 9, and multiply 9x632; the result is 5688 square feet, which is the sectional area of water flowing. 3« X -632 = 5-688 square feet. When the sectional area of water flowing has b^n thus obtained, divide into it the length of the wetted perimeter in feet, and the quotient will be the hydraulic mean depth. To find the hydraulic mean depth of a 6-inch circular drain-pipe running half full the sectional area is first found thus : — Divide the versed sine (GH = 3 inches) by the diameter 6 inches, = in decimal fractions of a foot '25 and '5 respec- tively- :^=.25^.5 = -5. '5 The constant C (in table) opposite "5 = 3927 ; now square the diameter in feet = -5^ = '25, and multiply '25 x -3927, and the product gives the sectional area of water flowing, viz. 098175. Now proceed to find the length of the wetted perimeter in feet, which, in the case of drains running half full, is equal to half the circumference. The circumference of any circle is found by multiplying the diameter by 3'1416; therefore -5 x 31416 = 1-5708 -2 = 7854, the length of the wetted perimeter in feet. Now, having found the sectional area = -098175, and the length of the wetted perimeter = -7854, divide the area by the perimeter — •098175 ^ -7854= -125 = hydraulic mean depth. The same when the drain is flowing full and half full SEWERAGE AND DRAINAGE. 137 USBFTTL TABLB OF HtDRAULIO MkAK DePTH OF ClKCULAR DrAIN. PttlL Three-qiur- t«T8fo]l. Two-thirda fell. HalffaU. One-third Aill. Quarter foil. 4-inch •0835 •1006 •0970 •0835 •0621 •0489 5-iiich . •1042 •1315 •1216 •1042 •078 •064 • 6-inch . •125 •1508 •1466 •125 •0931 •0788 9-inch . •1876 •2268 •2188 •1875 •1396 •11 12-inch . •26 •3017 •2911 •26 •1862 •1466 15.inch . •3125 •3771 •3639 •3125 •2327 •1833 18.inch . •875 •4525 •4367 •375 •2793 •2199 Useful Table of Sectional Area ik Square Feet of Water in Circular Drain. Full, Three-quar- ters nilL Two-thirds ftiU. Half ftill. One-third full. Quarter full. 4.inch . •0878 •0762 •0618 •0436 •0255 •017 5-inch . •1363 •1096 •0972 •0681 •0391 •0267 6-inch . •19634 •158 •139 •09817 •0673 •0384 9-inch . •4418 •3554 •318 •2209 •1289 •0864 12-inch . •7854 -6318 •556 •8927 •2292 •1635 15-inch . 1^227 •9878 •869 •6185 •3581 •24 18inch . 1767 1-422 1^25 •884 •5167 -3455 Useful Table of Internal Circumferences of Circular Drains in Feet. 4-inch 0-333 1-0471 6-inch 0^4166 6-inch 06 1-5708 9-inch 0-75 23562 12-inch 3-1416 16 -inch 1^25 3-927 1^-4°^^ [diameter. 4 -712 = circumference. Useful Table giving Inches in Decimals of One Foot. 12 inches . 1-0 5 inches . ^4166 i inch . ^0104 11 inches . •9166 4 inches . -333 finch •0208 10 inches . -8333 3 inches . -25 i inch -0312 9 inches . •75 2 inches . -1666 f inch •0416 8 inches . -666 1 inch . •0833 linch •0521 7 inches . •5833 finch •0625 6 inches . -5 iinch . ^0729 With this table, if we measure a versed sine or a peri- 138 DOMESTIC SANITARY DRAINAGE AND PLUMBING. meter in inches — say, nine and a quarter inches — we find the corresponding decimal fraction of a foot at once :— 9 inches = 75, and i inch = '0208 ; •75+0208-7708 feet = 9i inches. Mr. Griffiths, a well-known London sanitary engineer, recommended and adopted, wherever he was able to do so, unusually steep gradients for house drains, in consequence of the intermittent and restricted flow of house drainage. He gave 4-inch drains a fall of 1 in 30 feet; 6-inch, 1 in 40 feet; and 9-inch, 1 in 60 feet; and if these falls could not be obtained he used automatic flushing arrangements. These steep gradients involve deep excavations and specifid provisions at the higher levels furthest from outfall, which considerably add to expense; but, without further questioning such skilled recommendations, the writer must state that his practice in many hundreds of houses has fully confirmed a theory he adopted many years ago, that to determine the maximum fall required for house drains we need only multiply the diameter of the drain in inches by 10. This rule cannot very easily be forgotten. Thus, for a 4-inch drain give a fall of 1 in 40 ; for a 5-inch drain, 1 in 50; for a 6-inch drain, 1 in 60; for a 9-inch drain, 1 in 90. It is a remarkable fact, which the writer has not seen pointed out elsewhere, that this ratio holds good in all sizes from three inches to a hundred and twenty inches in diameter; but, unfortunately, such good gradients and velocity cannot always be obtained either in town sewers or in house drains. This decimal system of gradients yields in circular drains a velocity of over four and a half feet per second running two-thirds full, and of over three feet per second running SEWERAGE AND DRAINAGE. 139 only one quarter full — amply sufficient for all house-drain work. In order more clearly to show the effect of decimal gradients we have calculated the velocities in this table by Beardmore's formula: — Fall JUL Gradient. Iin40 linSO 1 in 60 lin70 lin80 linOO 1 in 100 1 in 120 Velocity in Feet per Minute. Diameter. Full Three- quarters mil. Two- tbinls Ml. Half mil. One- thini full. Quarter tull. 4 inches . 5 inches 6 inches 7 inches 8 inches 9 inches 10 inches 12 inches . Feet. 182 106 88 75 66 58 52 44 256 258 258 258 258 256 256 258 282 280 283 283 283 281 280 288 278 277 278 277 277 277 277 277 256 258 258 258 258 256 256 258 222 222 222 222 222 222 222 222 198 198 198 198 198 195 195 198 Mr. Baldwin Latham, calculating from Weisbach's more elaborate formula, gives a somewhat higher velocity in his valuable work on Sanitary Engineering, but the ratio of the velocity to the decimal gradients is shown to be the same throughout : — Feet. Feet. 4 inches lin 40=278 16 inches 1 in 160=278 6 inches lin 60=279 18 inches lin 180 = 278 8 inches lin 80=278 20 inches lin 200=278 9 inches lin 90=279 25 inches lin 250=278 10 inches lin 100=279 30 inches 1 in 300=278 12 inches 1 in 120=278 86 inches lin 860-278 14 inches lin 140=271 40 inches lin 400=278 15 inches 1 in 150=278 60 inches . lin 600-278 We shall be on the safe side, therefore, in following Beardmore's simple formula and the decimal gradients for house drains as the maximum fall. 140 DOMESTIC SANITARY DRAINAGE AND PLUMBING. Various Tables of Discharges, Velocities, and Falls. Mr. Bailey Denton, C.B., in his advanced work on Sanitary Engineering, gives the following figures, which appear very simple and clear: — Viiinoff* ■ '••t P*' Second. ik Feet per Second. 270 Feet per Minute. 6 Feet per Second. 860 Feet per Minute. DUmetar. Fkll. GaIIoiu per Mlnate. P-„ Gftllonsper '^*"- j MinutT FWl. Gsllonsper Minute. 4 inches . 6 inches . 9 inches . 12 inches . lin 92 1 in 180 1 in 207 1 in 276 96 216 495 876 lin 40 lin 61 1 in 92 lin 122 144 824 742 1814 lin 28 lin 84 lin 51 lin 69 192 482 990 1752 Mr. Baldwin Latham, CE., represents the velocities in house drains, calculated by Weisbach's formula, to be as follows in feet per minute with various given falls : — RuNNiKo Full and Half Full. Falls of 1 Foot in- SO 80 40 60 00 70 80 M 100 Diameter. 4 inches 895 322 278 246 226 209 194 162 172 6 inches 481 895 342 307 279 257 289 225 218 9 inches 582 481 418 875 343 317 296 279 264 12 inches 664 551 481 432 895 366 842 322 806 But as house drains frequently run only quarter full, with greatly reduced velocity and scouring effect, the following table will afford a safer indication of the best falls to provide :- RuNNrNo Quarter Full. Fslla of 1 Foot In- 20 80 40 60 60 70 80 00 100 DUmeter. 4 inches 280 280 198 176 160 150 188 126 112 5 inches 366 255 221 198 180 166 155 146 187 6 inches 280 240 215 198 180 170 160 150 9 inches 296 264 242 220 209 195 185 12 inches ... ... ... 800 275 250 240 225 212 SEWERAGE AND DRAINAGE. 141 The depths of water flowing quarter full in 4-inch, 6-inch, 9-inch, and 12-inch drains are respectively one inch, one and a half inch, two and a half inches, and three inches, which explains differences in velocities. A gradient of 1 in 35 gives a velocity, according to Weisbach's formula, of 298 feet per minute in 4-inch diameter pipe flowing full or half full ; 1 in 60 = 279 feet, in 6-inch pipe; 1 in 100 = 264 feet, in 9-inch pipe; 1 in 250 = 213 feet, in 15-inch pipe; 1 in 300 = 213 feet, in 18-inch pipe. To obtain a velocity of three feet per second in circular sewers the following falls should be given, according to the same formula : — 15 in. 18 in. 21 in. 24 in. 80 in. 86 in. 48 in. diameter. 1 in 350 400 500 550 700 750 1,000 gradient. The following faUs given to 4-inch, 6-inch, 9-inch, and 12-inch circular drain-pipes, running full or half full, being ordinary sizes in use, will produce the following velocities in feet per second : — ♦.inch . 1 in 200=2 ft. ; 1 in 90=8 ft. ; 1 in 60-4 ft. ; 1 in 80=5 ft. Cinch . 1 in 300=2 ft. ; 1 in 130=3 ft. ; 1 in 70 = 4 ft. ; 1 in 60=5 ft. 9-inch . 1 in 450=2 ft. ; 1 in 200=3 ft ; 1 in 120 = 4 ft. ; 1 in 76=6 ft. 12.inch . 1 in 600=2 ft. ; 1 in 260=8 ft. ; 1 in 160 = 4 ft. ; 1 in 100=6 ft The length of drain to which this calculation applies cojrrectly can be found by multiplying the velocity by the fall. Thus, the calculation for a 9-inch sewer with a fall of 1 in 200 and a velocity of 3 feet applies to a length of 600 feet — 200 x 3 « 600 ; the calculation for a 6-inch sewer with a fall of 1 in 50 and a velocity of 5 feet applies to a length of 250 feet— 50x5 = 250. As to the proper size of drains for dwelling-houses there still exists much misapprehension. It is commonly held 142 DOMESTIC SANITARY DRAINAGE AND PLUMBING. that the larger the drain the better. Let us consider the question. Take full-sized models in zinc of 4-inch, 6-inch, 9-inch, and 12-inch drains, about two feet long each, and closed staunchly at each end with sheet glass. Pour an equal quantity of water — say two gallons — ^into each, and the varying depth of water in each will show conclusively that any ordinary water-flush must carry soUds better, and clear out a drain of small diameter with more power, than when it is spread across the shallow section of a large drain. The power of carrying off solids with equal amounts of water is evidently much greater in a 4-inch than in a 6-inch drain, and in a 6-inch than in a 9-inch drain, because the water is deeper and the friction surface is less extended in the smaller drains. Private house drains in towns usually consist of two sections quite distinct. The first section is that generally provided, laid by, and under the direct control of the sanitary authority, from the public sewer across under the roadway and up to the outermost wall of the premises, inside which Umit the sanitary authority does not usually carry the drain. The second section is that laid by and under the control of the occupier or owner of the houses and premises, beside, aroimd, or under the houses, as circum- stances require. Under section one it is very important that the proper size of house drains should be determined and adopted in towns and cities under local authority. In one city, containing more than 25,000 houses in about 130 miles of streets, with a population over 250,000, there are about 100 miles of 9-inch diameter connecting house drains (exclusive of main sewers) laid by and under the SEWERAGE AND DRAINAGE. 143 control of the sanitary authority across under the roadways from the main sewers to the houses. The length of private house drains and branches beside, under and around houses, extends to many hundred miles in addition ; but we are now only dealing with the section imder the control of the sanitary authority. Now, the internal surface area of this 100 miles of 9-inch drain amounts to 4,188,000 square feet; it is coated with foul matters and constantly giving off exhalations to the air in the drain. If instead of 9-inch diameter drains the authorities had adopted 6-inch diameter, which would be even larger than necessary, the internal surface area would be reduced to 792,000 square feet, and that smaller surface would be less foul, owing to the more effectual changing thereof by the water flushing more com- pletely. By using 9-inch (which gives 50 per cent, too large a diameter) instead of 6-inch drain an unnecessary and mischievous excess is added of 400,000 square feet of foul surface, seldom, if ever, properly flushed and scoured on the upper section, and constantly giving off foul exhalations to the air in the drain. Again, the manipulation of 100 miles of 9-inch drains is very much more laborious than with 6-inch drains. Nine-iach drain weighs about ninety pounds per yard, and 6-inch drain fifty-six pounds, giving a total difference in favour of using 6-inch drain of 2,670 tons dead weight — absolutely a useless and mischievous waste of energy. One man can lay as much 6-inch drain as two men can lay 9-inch drain. The difference in cost of 100 miles of 6-inch and 9-inch drain is well worth attention also. The first cost of the drains — sea freight, land cartage, warehousing, accidental breakage, workmen's time handling 144 DOMESTIC SANITARY DRAINAGE AND PLUMBING. and laying, excavation of trenches, refilling and packing trenches, cement concrete foundations, cement joints — all cost much less for 6-inch than for 9-inch drains. An estimate shows that the saving effected in 100 miles of drain would be a capital sum of £25,000, besides the more important saving of human life and health. The importance of forming a hard, unyielding founda- tion for the drain should never be forgotten. Concrete formed of one part Portland cement to six parts clean coarse gravel, laid in a layer at the bottom of trench Fio. 19. — Drain pipe resting, supported throughout, on foundation. (between two boards afterwards removed), three inches deep by nine inches wide on ordinary ground, or six inches deep by nine inches wide on soft, yielding ground, will form a sound foundation. In the latter case the concrete is laid in two layers each three inches deep. It should be given the proper fall equally throughout, as carefully determined beforehand. The drain should not be laid until the concrete has set hard. As the laying of drain proceeds, cuts or hollows, partly across concrete, are sometimes made about two inches deep, and only sufficiently wide to receive the sockets of the pipe drain in such a manner that they shall lie over and in the hollows without touching any part, thus distributing the weight on each length of drain resting SEWERAGE AND DRAINAGE. 145 on the hard foundation, instead of allowing the whole weight of drain to press on the sockets, while from socket to socket the drain hangs unsupported, pressed on by the weight of earth above. Where the drain is laid with its sockets only resting on the concrete foundation, which is the usual course adopted, it becomes necessary to pack concrete between the under portion