484 APPLIED MECHANICS 
8. A jet of water 1 inch in diameter, coming from a reservoir at a hei 
200 feet, strikes a fixed hemispherical cup so that the direction of its motion 
reversed. Find the force it exerts upon the cup, assuming that the jet ha 
90 per cent. of the full velocity due to its head. 
9. A jet of water 2 inches in diameter, moving with a velocity of 40 feet 
second, strikes the interior of a cup. The axis of the jet coincides with the 
of the cup. The interior surface of the cup is part of the surface of a sp 
whose radius is 6 inches, and the depth of the cup is 3 inches. Find the ' 
pressure on the cup, (a) when the cup is fixed, (6) when the cup is movin 
the same direction as the jet with a velocity which makes the work done pe 
second on the cup a maximum. “4 
10. Taking the data of the preceding exercise, except that there is a succes 
sion of cups instead of one cup. Find the work done on the cups in ft.-lbs. pe 
second when the efficiency is a maximum, and determine the maximum efficient 
11. A small steam-boat is provided with two jet propellers, one on each 
of the vessel. The combined area of the two jets is 2 square feet. The 
for the jets is taken from the sea and driven astern, below the water line, by 
centrifugal pump. ‘The velocity of the jets in relation to the vessel is 25 fe 
per second, and the speed of the vessel is 9 knots. Determine the resistance | 
the motion of the vessel, also the horse-power developed in the cylinders of f 
engine, assuming that the useful work done by the jets in propelling the vess: 
is 40 per cent, of the work done in the cylinders. Take the weight of 1 c 
foot of sea water =64 lbs., and 1 knot =6080 feet per hour. ‘ 
12. The cross section of a jet of water is a rectangle 6 inches wide and 1 ine 
deep. This jet impinges upon a vane without shock. The cross section of 
vane is a quadrant of a circle. The velocity of the jet is 30 feet per seconc 
Find the component of the total pressure on the vane in the direction of th 
motion of the jet, (a) when the vane is fixed, (b) when the vane is moving in th 
same direction as the jet with a velocity of 15 feet per second, ‘= 
13. AB and AC are two lines inclined at 30°. A jet of water moves in th 
direction AC with a velocity of 24 feet per second, and a vane in the directio 
AB with a velocity of 12 feet per second. Show how to find the form of a ya 
so that the water may come on it tangentially, and leave it in a direction per 
pendicular to the direction of motion of the vane. Determine the pressure ¢ 
the vane in the direction of motion due to each pound of water striking th 
vane, [Inst.C. oF 
14. Indicate how a vane, moving with a velocity of 25 feet per second in ¢ 
horizontal direction, must be shaped in order to abstract the maximum amoun 
of energy from a jet of water impinging upon it at an angle of 45° to the 
horizontal with double the above velocity. What pressure would be exerte 
on the vane per cubic foot of water impinging per second ? {Inst.C. E. 
15. A jet of water, area 1 square inch, velocity 160 feet per second, has it 
axis inclined at 15° to the direction of motion of a bucket upon which | 
impinges, the velocity of the bucket being 70 feet per second. Find the 
direction and magnitude of the total pressure and the pressure in the direction 
of motion, if there is no loss due to shock at entrance, and no velocity of whi 
at exit from the bucket. Find the maximum possible hydraulic efficiency of | 
wheel provided with such buckets, and find also the speed corresponding. ‘tu de 
16. The rim of a turbine is going at 50 feet per second; 100 Ibs. of fiuic 
enter the wheel each second, with a velocity in the direction of the rim’s mo ate 
of 60 feet per second, leaving it with no velocity in the direction of the wh 
motion, What work is done per second upon the wheel ? [B 
17. A wheel having curved vanes is driven by a jet of water delivered 
to the vanes, as shown in Fig. 780, p. 482. 7,=2 feet, 72=2} feet. The 
delivers 2 cubic feet of water per second. The absolute velocities of the w 
at entrance and exit are 100 feet per second and 10 feet per second respective! 
If 0,=20°, and #,=85°, what tangential resistance will this wheel overcom 
at uniform speed and at a radius of 10 inches, neglecting friction? 7 
18. A locomotive going at 40 miles per hour scoops up water from a trough 
The outlet to the tank is 8 feet above the mouth of the scoop, and the deliver 
pipe has an area of 150 square inches. If half the available head at entrant 
is wasted, find the velocity at which the water is delivered into the tank, am 
the number of tons lifted in a trench 500 yards long. What, under these cot 
ditions, is the increased resistance to the motion of the train; and what is th 
minimum speed of the train at which water can be delivered to the tank ? 
