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.
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.
This result, however, being calculated upon a supposition of a degree of efficiency in the engines which is, perhaps, somewhat above their average state, it has been customary with engineers to allow a cubic foot of water per hour for each horse-power, a cubic foot being 1728 cubic inches, or above 11 per cent. more than the above estimate.
(137.) It has been stated, that to evaporate a cubic foot of water per hour requires 9 square feet of surface exposed to the action of the fire and heated air. This, therefore, is the quantity of surface necessary for each horse-power, and we shall find the total quantity of fire and flue surface necessary for a boiler of a given power, by multiplying the number of horses in the power by 9; the product will express, in square feet, the quantity of boiler surface which must be exposed to the fire, one half of this being fire surface and the other half flue surface.
Since the supply of heat to the boiler must be proportionate to the quantity of fuel maintained in combustion, and the quantity of that fuel must depend on the extent of grate surface, it is clear that a determinate proportion must exist between the power of the boiler, and the extent of grating in the fire place. The quantity of oxygen which combines with the fuel varies with the quality of that fuel; for different kinds of coal it varies from two to three pounds for each pound of coal.
We shall take it an average of 2-1/2 pounds. Now 2-1/2 pounds of oxygen will measure 30 cubic feet; also 5 cubic feet of atmospheric air contain 1 cubic foot of oxygen; and consequently 150 cubic feet of atmospheric air will be necessary for the combustion of 1 pound of average coals. At least one third of the air, which passes through a fire, escapes uncombined into the chimney. We must, therefore, allow 220 cubic feet of atmospheric air to pass through the grate-bars for every pound of fuel which is consumed. Now since land boilers will consume 15 pounds, and marine boilers 10 pounds, per hour per horse-power, it follows that the spaces between the grate-bars, and the extent of grate surface, must be sufficient to allow 3000 cubic feet of air per hour in land boilers, and 2000 cubic feet in marine boilers, to pass through them for each horse-power, or, what is the same, for each foot of water converted into steam per hour. The quantity of grate surface necessary for this does not seem to be ascertained with precision; but, perhaps, we may take as an approximate estimate for land boilers one square foot of grate surface per horse-power, and for marine boilers two thirds of a square foot, the spaces between the grate-bars being equal to their breadth.
It is evident that the capacity of a boiler for water and steam must have a determinate relation to the power of the engine it is intended to supply. For each horse-power of the engine, it has been shown that a cubic foot of water must pass from the boiler in the form of steam per hour. Now, it is evident that the steam could not be supplied of a uniform force, if the quantity of steam contained at any moment in the boiler were not considerably greater than the contents of the cylinder. For example, if the volume of steam in the boiler were precisely equal to the capacity of the cylinder, then one measure of the cylinder would for the moment cause the steam to expand into double its bulk and to lose half its force, supposing it to pass freely from the boiler to the cylinder. In the same manner, if the volume of steam contained in the boiler were twice the contents of the cylinder, the steam would for a moment lose a third of its force, and so on. It is clear, therefore, that the space allotted to steam in the boiler must be so many times greater than the magnitude of the cylinder, that the abstraction of a cylinder full of steam from it shall cause a very trifling diminution of its force.
In the same manner, we may perceive the necessity of maintaining a large proportion between the total quantity of water in the boiler, and the quantity supplied in the form of steam to the cylinder. If, for example (taking as before an extreme case,) the quantity of water in the boiler were only equal to the quantity supplied in the form of steam to the cylinder in a minute, it would be necessary that the contents of the boiler should be replaced by cold water once in each minute: and, under such circumstances, it is evident that the action of the heat upon the water would be quite unmanageable. But, independent of this, the quantity of water must be sufficient to fill the boiler above the point at which the flue surface terminates, otherwise the heat of the fuel would act upon the part of the boiler containing steam and not water; and, steam receiving heat sluggishly, the metal of the boiler would be gradually destroyed by undue temperature.