GENERAL PRINCIPLES OF HYDRAULICS 473 
____ 8. Find the head lost in friction in a pipe 15 inches in diameter and 4 miles 
cop, Benen the discharge is 2,000,000 gallons in twenty-four hours. Take 0-0054 
_ as the coefficient of friction. : 
9. A set of pumping engines has to force 3,000,000 gallons of water per day 
through a pipe 18 inches in diameter and 5 miles long to a height of 210 feet. 
Taking “v4 coeflicient friction as 0°0053, what is the effective horse-power of the 
nes 
10. Two reservoirs, 10 miles apart, are connected by a pipe 3 feet in 
_ diameter, the difference in their water levels being 40 feet. If the inlet valve 
to the lower reservoir is partially closed, so that the water rises in a vertical 
tube let into the pipe on the inlet side of the valve 20 feet above the level of the 
water in the reservoir, what would be the discharge of the pipe? [Inst.C.E.] 
11. Assuming a coefficient of friction equal to 0°006, what must be the 
diameter of a pipe 12 miles long to discharge 40,000 gallons of water per hour, 
the available head being 600 feet ? 
12. A Pipe, 9 inches diameter and 1 mile long, connects two reservoirs. The 
pipe has a slope of | in 80. The level of the water is 25 feet above the inlet 
end, and 6 feet above the outlet end. Neglecting all losses except skin friction, 
find the discharge, and draw the hydraulic gradient. Determine the pressure 
head in the pipe at a distance of half a mile from the inlet. The coefficient of 
friction may be taken as 0-007. [Inst.C.E.] 
13. A pipe 30 inches in diameter branches into two pipes of equal diameter 
J 
whose combined area equals that of the 30-inch pipe. Compare the loss of head 
in a mile of the latter Pipe with that in a mile of the two pipes, the rate of flow 
being 4 feet per second. [Inst.C.E.] 
fi _ 14. Two reservoirs are connected by a pipe 1 mile long and 10 inches 
_ diameter, the difference in the water surface levels being 25 feet. The value of 
¢e in the formula v=c,/mi is 120, feet and seconds being the units. Determine 
the flow det the pipe in gallons per hour, and find by how much the 
discharge would be increased if for the last 2000 feet a second pipe 10 inches 
diameter is laid alongside the first and coupled to it so that the water flows 
equally along the two pipes. [U.L.] 
15. A pipe consists of half a mile of 12-inch and half a mile of 6-inch pipe, 
and slopes at 1 in 100, The discharge is 2 cubic feet per second. Find the 
difference in pressure head at the two ends of the pipe. [Inst.C.E.} 
16. A line of piping has, in the upper portion of its length, a diameter of 15 
inches for a length of 5000 feet, sat an inclination of 4 per 1000. A tapering 
pipe then reduces the diameter to 12 inches, which remains constant for a length 
of 2000 feet, throughout which length the inclination is 3 per 1000. Find the 
' rate of discharge in cubic feet per second when the pipe is fully charged and is 
_ delivering freely at its termination. The equation of discharge may be assumed 
as Q=42 a fl where Q denotes cubic feet per second, h the head lost in 
length 7, and d the diameter in feet. [Inst.C.E.] 
17. A pipe AB is fully charged with water at A. ‘Two smaller pipes BC and 
BD convey the water from B to two points C and D. The length and diameter 
respectively of AB are 10,000 feet and 15 inches; of BC, 10,000 feet and 12 
inches; of BD, 10,000 feet and 9 inches: Points Cand D are respectively 50 feet 
and 80 feet below A. At all points the piping is under pressure except at C and 
D, where the water issues freely. Find the discharge at C and D, using the 
equation of discharge in the preceding exercise. [Inst.C.E.] 
18. A reservoir A supplies water to two other reservoirs B and C (Fig. 768). 
The difference of level between the surfaces of A and B is 75 feet, and between 
A and C 97°5 feet. A common 8-inch cast-iron main 
supplies for the first 850 feet to the point D. A 6-inch A 
main of length 1400 feet is then carried on in the same 
straight line to B, and a 5-inch main of Jength 630 feet B 
branches off at D and goes to C. The entrance to the C 
8-inch main is bell-mouthed, and losses at the pipe 
exits to the reservoirs and at the junction of the Fia. 768. 
pipes may be neglected. Find the quantity of water 
discharged per minute into the reservoirs Band C. Take the coefficient of fric- 
tion as 0°01. [U.L.] 
