The capacity or power of a steam engine is rated in horsepower, one horsepower (H. P.) being the equivalent of 33,000 foot-pounds of work done per minute. The horsepower of a given engine may be computed by the formula:
| APLN | |
| H. P. = | ——— |
| 33,000 |
in which
| A | = | area of piston, in square inches, |
| P | = | mean effective pressure per square inch, |
| L | = | length of stroke, in feet, |
| N | = | number of strokes per minute = number of revolutions × 2. |
The derivation of the above formula is easily explained, as follows: The area of the piston, in square inches, multiplied by the mean effective pressure, in pounds per square inch, gives the total force acting on the piston, in pounds. The length of stroke, in feet, times the number of strokes per minute gives the distance the piston moves through, in feet per minute. It has already been shown that the pressure in pounds multiplied by the distance moved through in feet, gives the foot-pounds of work done. Hence, A × P × L × N gives the foot-pounds of work done per minute by a steam engine. If one horsepower is represented by 33,000 foot-pounds per minute, the power or rating of the engine will be obtained by dividing the total foot-pounds of work done per minute by 33,000. For ease in remembering the formula given, it is commonly written
| PLAN | |
| H. P. = | ——— |
| 33,000 |
in which the symbols in the numerator of the second member spell the word “Plan.”
Example:—Find the horsepower of the following engine, working under the conditions stated below:
- Diameter of cylinder, 12 inches.
- Length of stroke, 18 inches.
- Revolutions per minute, 300.
- Mean effective pressure (M. E. P.), 40 pounds.
In this problem, then, A = 113 square inches; P = 40 pounds; L = 1.5 feet; and N = 600 strokes.