1. From the measurements given in the diagram, Fig. 5, find the average length of the pressure lines.Answer, 1.01 inch. The mean effective pressure is the average length of the pressure lines multiplied by the scale of the spring.

2. Find the mean effective pressure, supposing a 40-pound spring to have been used.-Answer, 40.4 pounds.

3. From the measurements given for Fig. 6, find the mean effective pressure for the crank end.-Answer, 0.42 inch.

4. From the same figure, find the mean effective pressure for the head end. Answer, 0.46 inch.

5. We have now for Fig. 6 the average pressure for the crank end, and the average pressure for the head end. The average of these two results is the average pressure for a double stroke. Find this average.—Answer, 0.44 inch.

6. The scale of the indicator used for Fig. 6 is 40. Find the mean mean effective pressure.- Answer, 17.6 pounds. It will be noticed that in Fig. 6 twenty pressure lines are used. This gives a closer average than ten lines.

7. Fig. 5 is the indicator card for an engine having a piston of 11 inches diameter. What is the area of the piston?-Answer, 95 square inches.

8. What is the average total pressure on the piston of Example 7? The mean effective pressure has been found in Example 2. This is the average pressure per square inch. The average total pressure is the mean effective pressure multiplied by the area of the piston. Assume that pressures for head end and crank end are the same.-Answer, 3,838 pounds.

9. Fig. 6 is the indicator card for an engine having a piston of 24 inches diameter. What is the area of the piston?- Answer, 452.4 square inches.

INDICATOR DIAGRAM TAKEN FROM A CORLISS ENGINE.

10. What is the average total pressure on the piston of Example 7?-Answer, 7,962.3 pounds.

Now, to find the amount of work done by the steam in one stroke of the piston, we must multiply the average total pressure in pounds by the distance in feet which the piston travels in one stroke. For example,

suppose the average total pressure is 6,000 pounds and the length of the stroke is 16 inches. Now, in one double stroke, that is during one revolution of the flywheel, the piston travels twice the length of the soke, or 32 inches, which equals 23 feet. Multiplying 6,000 by 23 we have 16,000. The work done is 16,000 footpounds.

11. If the piston stroke for Fig. 5 is 16 inches, how many foot-pounds of work are done in one revolution of the fly-wheel, that is in a double stroke of the piston? Take the average total pressure as found in Example 8. -Answer, 10,234 foot-pounds.

12. The piston stroke for Fig. 6 is 42 inches. How much work is done in one revolution of the fly-wheel? -Answer, 55,736 foot-pounds.

To find the work done in one minute we must multiply the work done in one revolution of the fly-wheel by the number of revolutions per minute.

13. How much work is done in one minute by the engine of Example 11, if the fly-wheel makes 110 revolutions per minute?-Answer, 1,125,740 foot-pounds per minute. To find the horse-power divide footpounds per minute by 33,000.

14. Find the horse-power of the engine of Example 13. Answer, 34.1 horse-power.

15. How much work is done in one minute by the engine of Example 12, the fly-wheel making 78 r. p. m. -Answer, 4,347,408 foot-pounds per minute.

16. Find the horse-power of the engine of Example 15.-Answer 131.7 horse-power.

We can sum up the method of finding the horsepower of an engine in the following rule:

Horse-power

mean effective pressure X area of piston X stroke in feet X 2 X r. p. m.

33000

17. Using this rule, find the horse-power of an engine if the mean effective pressure is 15 pounds,

diameter of piston 22 inches, stroke 40 inches, and r. p. m. 80.-Answer, 92.1 horse-power.

18. If 25 per cent of the power of the engine in Example 17 is lost in transmission, that is if its efficiency is 75 per cent, what power is transmitted to the machinery that is driven by the engine?-Answer, 69 horse-power.

Finding the Capacity of Tanks and Boilers.

Suppose we have a circular tank 8 feet in diameter and 6 feet in height, how many gallons of water will it hold? A gallon equals 231 cubic inches. We must, therefore, find how many cubic inches there are in the tank and divide this number by 231.

To find the number of cubic inches, we must first find the number of square inches in the bottom of the tank and multiply this by the height of the tank. The bottom of this tank is a circle. Its diameter is 8 feet. Its radius is 4 feet. To find the area of a circle we square the radius, that is, multiply the radius by itself and multiply the result by 3.1416.

The square of the radius is 2,304 square inches.

3.1416

2,304

12.5664

942.48

6,283.2

7,238.2464

There are 7,238 square inches in the bottom of the tank. The decimal is less than 1/4 of a square inch, and is so small that it may be dropped.

Multiplying the area of the bottom by the height of the tank, 72 inches, we have

7,238

72

14,476

50,666

521,136 cubic inches.

Dividing by 231 to reduce to gallons, we have

231) 521,136 (2,256

462

591

462

1,293

1,155

1,386

1,386

The tank holds 2,256 gallons.

The same method is used in finding the capacity of a boiler. Find the area of the end of the boiler by the rule for area of a circle and multiply this area by the length of the boiler. For a fire-tube boiler, first find the capacity of the boiler as though it had no tubes, then find the capacity of the tubes and subtract from the capacity of the boiler. To find capacity of tubes multiply the area of the end of a tube by its length and this product by the number of tubes.