In all these cases the quantity of water actually delivered is less than As c. ft. per stroke,—A = area of piston, S= stroke, because of the leakage back past the valves, the loss or slip varies from 8 or 10 per cent up to 25 or even more; it is least in vertical pumps, in which the bucket is used, and greatest, so far as the types we have considered are concerned, in horizontal plunger, or solid piston, pumps.

EXAMPLES.

1. A breast wheel 50 feet diameter receives 5000 gallons per minute, total fall 48 feet. Find the revolutions in order that the velocity of periphery may be 5 f.s., and if the H.P. be 52, find the efficiency. Ans. 1.91; .715.

2. If the preceding were replaced by an overshot wheel in which the buckets commenced to empty themselves at 5 ft. from the bottom, what H.P. would be lost from this cause?

Ans. 7.6.

3. The ram of an accumulator is 8 ins. diameter, and is loaded with 20 tons. To what head is the pressure equivalent? If the stroke be 8 feet, how much energy is accumulated when the ram is right up? Ans. 2050 ft., 160 ft.-tons.

4. The diameter of the large part of the spindle of a differential accumulator is 8 ins. Find the diameter of the small part so that a load of 12 tons may be equivalent to a head of 1800 feet. Ans. 10 ins.

5. The accumulator in the last question is connected to a hydraulic cylinder 8 ins. diameter by a 2-inch pipe 50 feet long. Find the speed of steady motion when the total resistance of load and solid friction is 1 ton. Ans. 6.9 f.s.

6. A load of 5 tons is to be lifted 20 feet by a hydraulic crane. The water pressure is 700 lbs. per square inch, and the total efficiency one-half. Find the necessary volume of the ram.

Ans. 4 c. ft.

7. If the ram in (6) be differential, with area of rod half that of piston, find the saving of energy when lifting 2 tons, assuming the same efficiency. By how much would the coefficient of resistance referred to the velocity of lifting require to be increased if the ram were not differential?

Ans. 100 ft.-tons per lift; trebled.

8. A lift is required to raise 2 tons at 5 f.s.; the diameter of the supply pipe is 4 ins., length 200 feet. Find the head required, the ram being 18 ins. diameter, and its stroke half the rise of the lift. Ans. 680 ft. diameter, 9 ins. stroke; it pumps pressure, through a 4-inch pipe, 30 Find the necessary steam pressure 40 revolutions per minute.

9. A pump piston is 6 ins. into a boiler against 135 lbs. feet long, with three bends. on a 10-inch piston to run at

Ans. 52 lbs. per square inch.

10. Prove that the tension of the rod in a common pump is Awh, where A is the area of piston, w the weight of a c. ft. of water, and the height of the water-level in the pumps, whether above or below the bucket, above the surface of the water outside.

11. The length of the cylinder of a hydraulic brake is 3 ft., diameter 12 ins., diameter of pipe connecting the ends 2 ins., length 3 ft. 8 ins. Find the force necessary to move the piston at 4 f.s. when the cock is wide open, and half shut, respectively. Ans. 15.3 tons; 54.3 tons.

12. In (10) find the delivery, allowing 20 per cent slip. Ans. 59 galls. per min.

THE END

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