If the diameter of the piston then be 24 inches, its surface will consist of a number of circular inches expressed by the square of 24, or 24 × 24 = 576; and, as upon each of these circular inches there is an effective pressure of 7 lbs., we shall find the total pressure in pounds by multiplying 576 by 7, which gives 4032 lbs.
We shall find the space through which this force works per minute, by knowing the length of the cylinder and the number of strokes per minute. Suppose the length of the cylinder to be 5 feet, and the number of strokes per minute 21-1/2. In each stroke[51] the piston will, therefore, move through 10 feet, and in one minute it will move through 215 feet. The moving force, therefore, is 4032 lbs. moved through 215 feet per minute, which is equivalent to 215 times 4032 lbs., or 866,880 lbs., raised one foot per minute.
[Footnote 51: By a stroke of the piston is meant its motion from one end of the cylinder and back again.]
For every 33,000 lbs. contained in this, the engine has a horse-power. To find the horse-power, then, of the engine, we have only to divide 866,880 by 33,000; the quotient is 26 nearly, and, therefore, the engine is one of 26 horse power.
Let it be required to determine the quantity of water which a boiler must evaporate per hour, for each horse-power of the engine which it works.
It has been already explained that one horse-power expresses 33,000 lbs. raised one foot high per minute, or, 1,980,000 lbs. raised one foot high per hour. The quantity of water necessary to produce this mechanical effect by evaporation, will be found by considering that a cubic inch of water, being evaporated, will produce a mechanical force equivalent to 2160 lbs. raised a foot high. If we divide 1,980,000, therefore, by 2160, we shall find the number of cubic inches of water which must be evaporated per hour, in order to produce the mechanical effect expressed by one horse-power; the result of this division will be 916,6, which is therefore the number of cubic inches of water per hour, whose evaporation is equivalent to one horse-power. But it has been shown that, for every 6 cubic inches of water evaporated in the boiler which are available as a moving power, there will be 4 cubic inches intercepted by the engine. To find, then, the quantity of waste corresponding to 916 cubic inches of water, it will be necessary to divide that number by 6, and to multiply the result by 4: this process will give 610 as the number of cubic inches of water wasted. The total quantity of water, therefore, which must be evaporated per hour, to produce the effect of one horse-power, will be found by adding 610 to 916, which gives 1526.
