518 APPLIED MECHANICS 
Exercises XXX. 
1. The diameter of the barrel of a simple bucket pump is 9 inches, and 
stroke of the bucket is 2 feet. The bucket-rod is driven through a connecti 
rod coupled to a crank which makes 25 revolutions per minute, The total h 
of water is 40 feet. How many cubic feet of water are raised per minute, 2 
what horse-power must be delivered to the crank if the efficiency of the pump i 
50 per cent, ? ; 
2. A bucket pump works under a mean suction head of 20 feet and a mean — 
delivery head of 40 feet of water. The diameters of the bucket and pump-rod — 
are 12 inches and 23 inches respectively, and the stroke is 3 feet. Taking into 
account the influence of the pump-rod, what is the pull on the rod during the — 
up stroke? Also, what is the volume of water discharged during (a) one up 
stroke, (b) one down stroke ? ; 2 . 
3. The suction and delivery heads of a plunger pump are 20 feet and 50 — 
feet respectively. The diameter of the plunger is 6 inches, and its stroke 10 — 
inches. The plunger makes 48 double strokes per minute. Calculate the force — 
required to work the plunger (a) during the suction stroke, (6) during the delivery — 
stroke, assuming that the efficiency of the pump is 50 percent. for the suction 
stroke, and 70 per cent. for the delivery stroke. Find also the horse-power 
required to work this pump. J 
4. In a shale mine, in order to drain one of the pits a treble-ram pump, — 
driven by an electric motor, is employed. ‘The rams are 94 inches in diameter 
by 12-inch stroke, they each make 34°75 double strokes per minute, the height to — 
which the water is lifted is 393 feet, and the total length of the 6-inch discharge 
pipe is 700 feet. Find: (i.) How many gallons of water are lifted per minute. — 
(ii.) The useful horse-power when the pumps are running steadily. (iii) The 
efficiency of the pumps if the B,H.P. of the motor is 50, (iv.) How many foot- 
pounds of work are done per minute in overcoming the friction in the pipe (the 
coefficient of friction is 0°0975). (v.) The B.H.P. required to lift the water and 
overcome the pipe friction, [B.E.] 
' 6. The cylinder of a double-acting piston pump has a diameter of 9 inches, 
and the piston-rod has a diameter of 2 inches, The piston-rod goes through one __ 
end of the cylinder only. The suction and delivery heads are 10 feet and 50 
feet respectively. Neglecting friction, calculate the force necessary to work the 
piston during the “tin” and ‘‘out”’ strokes. If the mean speed of the piston 
is 90 feet per minute, how many gallons of water does this pump deliver per hour, 
6. In a duplex Worthington pumping engine (see Fig. 818, p. 510) each of the 
two pump-pistonsis10}inches diameter, and the pump-rodsare3} inches diameter. __ 
The rate of pumping is 1,442,312 gallons per 24 hours. What is the mean speed ~ 
of the pistons in feet per‘minute? The head is 648 feet, including friction. 
What is the pump horse-power? The duty of the engine is 183,300,000 ft.-Ibs. 
per cwt. of coal, and the steam consumption is 12°1 lbs. per pump horse-power 
per hour. What is the weight of steam produced per lb, of coal used ? j 
7. Reproduce the indicator diagrams given in Fig. 820, p. 511, enlarging them 
to, say, twice the size shown, ‘Then, taking the particulars of the Worthington 
pumping engine given in Art. 441, construct, on a stroke base, the diagram 
whose ordinates show the effective driving force on the pump piston as described 
in Art. 441, but allow for the effect of the various piston-rods on the areas 
of the pistons, All the steam piston-rods are 24 inches diameter. On the final 
diagram add a horizontal line whose height above the base is the mean height of __ 
the diagram. Also add the line whose height above the base shows the resistance 
of the pump obtained from the particulars given in the preceding exercise.. If 
several students in a class should work this exercise, a number of them should 
et the diagram for the forward stroke, and the others for the return 
stroke. ar 
8. Show, by drawing the rate of delivery curves, that the fluctuation of 
delivery from a pump having two single-acting plungers driven through two 
cranks at right angles to one another is considerably greater than for one 
plunger only, : ty 
9. Draw the rate of delivery diagram for a pump of the type shown in Fig, 
