20 In which H ?= R φ = LOSS OF HEAD BY BENDS. the head due to change of direction, in inches. radius of the bore of the pipe, in inches. radius of the centre line of the bend, in inches. = angle of bend, in degrees. V = velocity of discharge, in feet per second. Thus, say we require the loss of head by a bend of 9 inches radius in a 6-inch pipe, discharging 800 gallons per minute, with an angle of 55°. A 6-inch pipe containing roughly gallon per foot run, the velocity of discharge will be 62 30 = 1.2 800 1.2 x 60 Table 4 has been calculated by the second formula. The first part is adapted to bends of the radius usually met with in practice; this may vary slightly with different makers, but not so much as to affect the result seriously. Fig. 6 gives the proportions of the 8-inch bend as an illustration. The second part of the Table gives the loss by quick bends of the proportions given by Fig 7, which are sometimes necessary in special cases; they are commonly named "elbows." Table 4 requires but little explanation; it shows, for instance, that an ordinary 8-inch bend, with 18 inches radius, consumes 3 inches head when passing 1970 gallons per minute; but a quick 8-inch bend with 6 inches radius consumes 12 inches TABLE 4.-TABLE for BENDS in WATER PIPES, showing the Loss of HEAD DUE to CHANGE of DIRECTION by ONE BEND of 90°. HEAD OF WATER IN INCHES LOST BY ONE BEND OF 900. Inches. GALLONS DISCHARGED PER MINUTE. 81 103 126 146 163 179 219 252 309 358 58 83 117 144 166 203 235 288 332 371 407 498 576 795 814 102 145 205 252 291 356 411 504 582 650 713 873 1008 1233 1426 1070 1236 1514 1748 1954 2141 2622 3028 3708 4282 3940 4824 5572 4912 6015 6948 136 172 333 385 472 544 608 666 816 944 1155 1332 2345678 head when passing nearly the same quantity, or 1950 gallons, and these, it should be observed, are the heads due simply to change of direction, and do not include the head due to velocity or to friction. Thus, for instance, if the quick 8-inch bend had a length of one yard, the head for friction by Table 3 (say for 2000 gallons) would be 5 foot, and the head for velocity at entry by the rule in (3), namely (13) 2 = : H is = 5.48 feet. Thus we have a total for such a Again, in a 6-inch pipe carrying 800 gallons, the Table shows that each common bend causes a loss of 11⁄2 inches head, and each quick bend a loss of 5 inches, &c. The Table is arranged for bends of 90°, or quarter bends, as they are technically named, but it is applicable to any other angle, for the loss of head is simply proportional to the angle, the radius being the same; thus, a half-quarter bend of 45°, or one-eighth part of a circle, consumes half the head of a bend of 90°, and a bend of 180°, or half a circle, takes double, &c., &c. (15.) "Discharge of Compound Water-mains."-When a long main is composed of pipes of different sizes, as is very frequently the case, the head for each must be separately calculated, and the sum total taken. Thus, if we required 300 gallons per minute through a main 1200 yards long, composed of 800 yards of 7-inch, 300 yards of 6-inch, and 100 yards of 5-inch pipe, the head would be If there were bends in the pipes we must add the head for them from Table 4, but it will be found, as in the case of head for velocity, see (12), that with long mains the effect of bends is very small. Say we had 4 common bends in the 7-inch, each 1-inch head 18131+ دو 36 4 2 دو 39 2 وو دو دو Total 10 inches. Thus, even for such a large number of bends, the loss of head is only 10 inches, or 875 of a foot; so that the total loss is 43.73+ ·875 = 44.605 feet. (16.) When, with such a series of pipes the head is given, and the discharge has to be determined, the case does not admit of a direct solution, because we cannot tell beforehand in what proportions the given head must be divided among the different pipes. We must in that case follow the course explained in (13): thus, say we required the discharge with 30 feet head by a main 2000 yards long, composed of 1200 yards of 8-inch pipe with four common bends in it; 700 yards of 6-inch pipe and three bends; and 100 yards of 5-inch pipe, with two common and two quick bends. The first thing to be done is to assume a discharge, and calculate the head for that, as was done in the last example; it is unimportant whether the assumed discharge is near the true quantity or not. Say in our case we take it at 400 gallons. Then Thus we find that for 400 gallons we require 105.3 feet head instead of 30 feet, the head given; then by the rule in (13) (17.) "Effect of Contour of Section.”—The contour of the section of the line of pipes is a matter of some importance. The best condition, when the pipe is of uniform diameter from end to end, is, of course, a uniform slope throughout. This, however, can rarely be obtained, the pipe having to follow the contour of the ground, as in Fig 9. If a number of open-topped pipes were inserted anywhere along the main, as at A, B, C, D, &c., the water would rise in them to the level of the oblique line J K, which in the case of a pipe of the same bore from end to end, would be a straight line as shown; this line is termed the hydraulic mean gradient. Now, the vertical distance from any point in that line (say the top of E) to the level line K M, will give the head for friction between E and K, and the vertical distance from the same point to the level line J L will give the friction between E and J: we have here supposed, of course, that the figure is correctly drawn to scale. (18.) When, as in Fig. 11, the pipes are of different diameters, then each would have its own gradient, showing at every point the loss of head due to that particular pipe as in the figure. No loss of effect will arise from the pipe following the section of the ground, so long as the contour of the pipe does not anywhere along the line rise above the hydraulic mean gradient. Thus, in |