454 APPLIED MECHANICS 
BF 
Exercises XXVIIIa. . 
1. A pipe whose axis is horizontal is full of water in motion. Ata section A 
the velocity of the water is 300 feet per minute, and the pressure is 20 De 
square inch. The pipe tapers gradually from 6 inches diameter at A to 4 inches 
diameter at B. Assuming that there is no loss of energy between A and ie 
determine the pressure of the water at B. What must be the diameter of the . 
pipe at B if the pressure there is reduced to 4 lbs, per square inch ? 1s 
2. A horizontal tube is tapered slowly from a diameter of 15 inches to a 
diameter of 6 inches. Neglecting friction, calculate the difference in the 
pressures in lbs. per square inch at the two sections when the cae is 
60,000 gallons per hour, [Inst. ie 
3. The diameter of a pipe gradually changes from 8 inches at a point A, 40 — 
feet above datum, to 5 inches at a point B, 20 feet above datum, The pressure — 
at A is 30 Ibs. per square inch, and the pipe delivers water at the rate of 5 cubic — 
feet per second. Neglecting friction, find the pressure at B. ay. 
4. A conical pipe varying in diameter from 4 feet 6 inches at the large end 
to 2 feet at the small end forms part of a horizontal water main. The pressure 
head at the large end is found to be 100 feet, and at the small end 96°5 feet. 
Find the discharge through the pipe. [Inst.C.E.] _ 
5. A Venturi water meter is 15 inches diameter in the main and 6 inches 
diameter in the throat. The difference between the pressures of the water in 
the main and in the throat is 9°2 inches of mercury. Find the discharge in 
gallons per minute. (Specific gravity of mercury, 13°56.) 
6. In a particular Venturi water meter the diameter of the main is 3 feet, — 
and .the diameter of the throat 1 foot. Q is the number of gallons of water — 
delivered per minute, and & is the effective head, in inches of mercury, in the — 
gauge showing the difference between the pressures in the main and in the 
throat. Taking the specific gravity of mercury as 13°56, find the numerical 
value of the constant ¢ in the formula Q =c,/k for this meter. 
7. Define and describe ‘‘ forced” and “‘ free” vortices. A glass tube 2 inches 
diameter, open at the top, containing a liquid, rotates about its axis, which is — 
vertical, at 700 revolutions per minute. What is the depression of the lowest — 
point of the surface below the surface of the liquid when at rest ? [U.L.] — 
8. A glass tube, internal diameter 2 inches, and length 12 inches, has its 
axis vertical; it is closed at both ends, and contains a liquid which fills three- — 
fourths of the volume of the tube. The tube is made to revolve about its axis. — 
Find the speed of the tube in revolutions per minute (1) when the top of the cup 
formed by the liquid is at the top of the tube, (2) when the bottom of the cup 
is at the bottom of the tube. Construct the speed scale, the gradations to show 
speed increments of 10 revolutions per minute. : 
9. A glass tube 3 feet long, of uniform cross section, bent into the form 
of three sides of a square (Fig. 748), and half filled with water, - 
rotates uniformly about the axis of one of the parallel limbs, 
which is vertical. Find the angular velocity if the other 
vertical limb is half full of water. 
10. Neglecting the effect of friction, with what velocity 
will water flow through an orifice in the shell of a steam i & 
boiler at a point 30 inches below the water level when the 
steam pressure gauge indicates 40 lbs. per square inch? “Faq. 748 
11. Water under a pressure of 7 lbs, per square inch is fed 7 : a 
into a tank containing water to a depth of 15 feet through an orifice in the bottom 
of the tank. Neglecting friction, find the velocity of flow through the orifice. 
12. A jet of water under a head of 3 feet enters a condenser where the 
absolute pressure is 5 Ibs. per square inch. If the pressure of the atmosphere 
is 14:7 lbs. per square inch, find the velocity of the jet, neglecting friction. _ 
13. A vertical pipe of 3 inches bore contains water which runs out through 
an orifice at the bottom of the pipe. The diameter of the issuing jet is 4 inch, r 
Neglecting friction, determine the velocity of the jet, in feet per second, when ~ 
the head of water in the pipe is 10 feet, (i.) neglecting the velocity of app } 
(ii.) taking the velocity of approach into account. Construct a curve showing 
the relation between the velocity of the jet and the head of water over it, 
