474 APPLIED MECHANICS 
19. A 4-inch fire main is connected to a storage tank, the length of the pipe 
being 800 feet. If the main ends in a nozzle 14 inches in diameter, and if ee 
head of water in the storage tank is 150 feet above the nozzle, to what height 
will the nozzle be able to deliver water? The coefficient of friction is 0006. _ 
[U.L.] 
20. A pipe 8 inches in diameter and 1000 feet long leads from a reservoir, 
terminates in a nozzle open to the atmosphere. The nozzle is 600 feet below 
the free surface of the water in the reservoir. Determine the diameter of the — 
nozzle when the kinetic energy of the jet is a maximum. ‘Take the coefficient — 
of friction as 0°006. 
21. Referring to the preceding exercise, calculate the velocity of the water in 
the pipe and in the jet, also the horse-power of the jet and the efficiency, for 
nozzles of 1, 2, 3, 4, 5, 6, 7, and 8 inches diameter, and plot the results on a base — 
representing the diameters of the nozzles. it 
22. Prove that when power is transmitted hydraulically through a pipe the 
maximum horse-power is transmitted when one-third of the original head is 
wasted in friction. You may assume that the loss of head due to friction is — 
proportional to the square of the velocity. - 
What will the maximum horse-power be if the diameter of the pipe is 6 
inches, its length 1200 feet, the original pressure 700 lbs. per square inch, and — 
the coefficient of friction 0°0075 ? ([U.L.] 
23. Calculate the percentage loss of horse-power per mile, when power is 
hydraulically transmitted in cast-iron pipes, 6 inches in diameter, for velocities 
of flow of 120, 150, and 180 feet per minute, and for pressures of 250, 750, and — 
1250 lbs, per square inch, 
Draw curves to show the results of your calculations, and from your curves 
obtain the total loss of horse-power when the 6-inch pipe is 4500 yards inlength, 
the velocity of flow 175 feet per minute, and the pressure 1000 lbs. per square 
inch. Use the formula—tloss of head =0:03lv?/2gd (feet second units). [B.E.] 
24. One hundred horse-power is to be transmitted to a distance of 5 miles 
with a loss of 15 per cent. of the head due to an accumulator pressure of 750 Ibs, 
per square inch. The beginning and end of the pipe are at the same elevation. 
Find the diameter of the pipe. The equation of discharge in Exercise 16 may 
be used in this case, but with a coefficient of 36 instead of 42. [Inst.C.E.] 
25. Some hydraulic machines are served with water under pressure by a pi 
1000 feet long, the pressure at the machines being 600 lbs. per square inch. 
The horse-power developed by the machines is 300, and the friction horse-power 
in the pipes 120, Find the necessary diameter of the pipe, taking the loss 
of head in feet as oros! : i and 0°43 lb. per square inch as equivalent to 1 foot 
head. Also determine the pressure at which the water is delivered by the pump, 
What is the maximum horse-power at which it would be possible to work the 
machines, the pump pressure remaining the same ? [U.L. 
26. The cross sections of four channels are shown in Fig. 769. They are al 
Fie. 769. 
equally smooth, they have the same slope and the same rate of discharge. Find 
the dimensions s, d, and b. 
27. If the faces of an open channel are plane and they are tangential to 
the surface of a cylinder whose axis is in the free surface of the water in the 
channel, show that the hydraulic mean depth is equal to half the radius of the 
cylinder. 
: 28. A semicircular channel 10 feet in diameter flows full of water. Compare 
its discharge with that of a rectangular channel of the same cross sectional area 
9 feet wide, lined with the same material, and having the same inclination. 
. [Inst.C.E.] 
