While the velocity of a pipe should not be less than 180 feet per minute, it is not an advantage to have excessive gradients, especially in branch drains, because the excessive velocity so produced would, in times of light discharge of wastes from the house, cause the liquids in the sewage to part from the solids, and these would be left behind, decomposing in the pipe until the stream was sufficiently strong to carry them along. There is no reason why steep gradients should be adopted, as, by laying the pipes in the manner which will be hereafter pointed out as necessary to effect a change of level, it is very simple indeed to adhere to the self-cleansing gradients. These may be very easily rememliered by means of Maguire's decimal rule. For 4-inch, 6-inch, and 9- inch pipes, tin-figure of the diameter multiplied by 10 gives the gradient, thus: -

Fig. 309 - Section of Drain, Illustrating the "Hydraulic Mean Depth.

 A drain 4 inches in diameter must have a gradient of 1 in 40. " 6 . „ 1 in 60. "9 " " 1 in 90.

For good materials and workmanship these are approximately correct, as will be seen by reference to Table XXVI., bat when greater accuracy is important, resort must be had to a selected formula.

In order to ascertain the velocity of the flow of water through pipes, numerous experiments have been made in all countries under all .sorts of conditions, from which formulas have been compiled and published, many of which are very well known to engineers. That of Weisbach is the one used in tip-tables published by The Surveyor and almost all that are recorded will In-found in the little pocket-book issued by Mr. Albert Wollheim, A.M.I.C.E., called The Sewerage Engineer's Note-book. For a long time past the one moat generally used in this country has been Eytelwein's, which has the merit at any rate of being easily remembered, and not demanding to., great a mathematical strain in its solution, as will be readily gathered; it iwhere V = velocity in feet per minute. R = hydraulic mean depth in feet H = fall in feet per mile. 55 =a constant.

A Swiss engineer, Kutter, has introduced a formula which includes a coefficient for roughness, varying according to the nature of the materials used in the channel, and this has been somewhat reduced and simplified by an American engineer, P. J. Flynn. Mr. Wollheim in his Note-book adopts Chezy and Eytelwein's formula where V = velocity in feet per second.

R = hydraulic mean depth in feet.

S= inclination of water surface length of channel

C = a co-efficient determined by experiment

The value of will vary according to the co-efficient of roughness which is adopted, and for glazed stoneware pipes where the condition of the surface is fair, this will be .013, and then the values of C√R will be for 6-inch pipes flowing full, 24.60, for 9-inch pipes flowing full, 34.00, and the value of √S may be ascertained from the following table (P. J. Flynn) according to the gradient required. S = sine of angle of inclination = fall of water-surface in any distance divided by that distance.

### Table XXV. Values Of √S For All Gradients From 1 In 4 To 1 In 90

 slop √s slope √s Slope. √s Slope. √s 1 in 4 •500000 1 in 26 .196116 1 in 48 .144337 1 in 70 •119524 "5 •447214 "27 .192450 „ 49 .142857 „ 71 .118678 6 •408248 . 28 •188982 „ 50 .141421 „ 72 .117851 ,. 7 .377978 .29 •185695 „ 51 .140028 „ 73 .117041 " 8 .353553 „ 30 .182574 "52 •138676 „ 74 .116248 "9 •333333 „ 31 •179605 " 53 .137361 „ 75 .115470 ., 10 •316228 „ 32 •176777 „ 54 .136085 „ 76 •114708 11 .301511 . 33 174077 „ 55 .134839 n 77 .113961 . 12 288675 „ 34 •171499 „ 56 .133630 „ 78 .113228 . 13 •277350 „ 35 •169031 „ 57 .132453 „ 79 .112509 "14 .267261 „ 36 •166667 „ 58 .131305 „ 80 .111803 " 15 •258199 „ 37 •164399 „ 59 .130189 „ 81 .111111 . 16 .250000 „ 38 •162221 „ 60 .129100 „ 82 .110431 . 17 .242536 „ 39 •160125 „ 61 .128037 „ 83 .109764 "18 •235702 . 40 .158114 „ 62 .127000 " 84 .109109 . 19 •229416 . 41 •156174 „ 63 .125988 „ 85 .108465 "20 •223607 „ 42 •154303 „ 64 • 125000 „ 86 .107833 "21 •218218 „ 43 •152499 „ 65 .124035 » 87 .107211 •"22 .213200 „ 44 •150756 „ 66 .123091 n 88 .106600 . 23 •208514 . 45 .149071 „ 67 .122169 „ 89 .106000 . 24 •204124 „ 46 .147444 „ 68 .121268 „ 90 .105409 " 25 •200000 "47 .145865 „ 69 .120386

The solution of Sutter's original formula, or of the modification introduced by r= hydraulic mean depth in feet s= fall divided by the length.

Flynn, is rather too complicated and intricate a process for ordinary application, and the formula recently devised by Mr. Santo Crimp, M.I.C.E., is much more simple for general use. It is the outcome of a long series of experiments, and approximates in its results very closely to Kutter's when the co-efticient of roughness in that formula lies between .012 and .013. Crimp's formula is as follows: v=124 2√r^2 √s where v - velocity in feet per second.

For cicular pipes running full or half-full this is equivalent to -

V-velocity in feet per minute. D - diameter in inches - 48r. I -inclination, or length divided by the fall- 1/4 Q - cubic feet discharged per minute when running full.

In the Tables and Diagrams for use in Designing Sewers, by \V. Santo Crimp,.

M.I.C.E., and C. E. Bruges, A.M.I.C.K., will he found the velocities of all sizes of pipes for every gradient required, together with a table for calculating their values, and the use of these tables will be found of great service.

On reference to Table XXVI., it will be noticed that the hydraulic mean depth of a circular pipe is the same when the pipe is flowing full and half-full, being equal to one-fourth the diameter of the pipe, and that it is greater when flowing three-quarters full, but, as already pointed out, it will be greatest when the pipe is thirteen - sixteenths full.

The discharge of water through pipes is calculated by multiplying the velocity in feet per second by the sectional area of the stream, thus-

D = VxA, where D = discharge in cubic Gael per second

On p. 150 of Slagg's book on "Sanitary Work", figures are given showing the carrying rapacity of a circular sewer when running full, half-full, two-thirds, and one-third full, and the information is here exhibited in Fig. 310.

2/3 c.c. occurs at 61 H.

1/2 c.c. occurs at .5 H.

1/3 c.c. occurs at .39 H.