Let us assume that the diameter of the wheel at the center of the blades is two feet, which would, roughly estimating, give a circumference of six feet, or a travel of each particular blade that distance at each turn of the wheel.
If the wheel turns one hundred times a minute, and this is multiplied by the circumference of the wheel (six feet), the result is 600 feet. This, again, multiplied by 432 pounds (which represents the pressure of the water on the entire discharge opening), and we have a product of 259,200, which represents foot pounds.
This means the same work as if 259,200 pounds would have been lifted through a space of one foot in one minute of time. To ascertain how much power has been developed we must know how many foot pounds there are in a horse power.
Horse Power.—It is determined in this way: any force which is capable of raising 550 pounds one foot in one second of time, is developing one horse power. A man might have sufficient strength to raise such a weight once, twice, or a dozen times in succession, but if he should try to do it sixty times a minute he would find it a trying, if not impossible task.
Foot Pounds.—If he should be able to lift 550 pounds sixty times within a minute, he would have lifted 33,000 pounds one foot in one minute of time (550 × 60), and thus have developed one horse power.
As the water wheel, in our calculations above, raised 259,200 pounds in that period of time, this figure divided by 33,000 shows that a little more than 73/4 horse power was developed, assuming, of course, that we have not taken into account any waste, or loss by friction, or otherwise.
This method of determining one horse power should be carefully studied. Always keep in mind the main factor, 33,000 pounds, and this multiplied by one foot, the result will be 33,000 foot pounds,—that is, one horse power.
It would be just the same, however, if it were possible to raise one pound 550 times in one second, or one pound 33,000 times within a minute.
Power and Time.—You are thus brought face to face with another thing which is just as important, namely, that, in considering power, time, as well as energy, must be considered. If a man, by superior strength, could be able to raise 550 pounds once within a second, then skip a few seconds, take another hold, and again raise it that distance, he would not be developing one horse power for a minute, but only for one second while he lifted the weight. For the whole minute he would only develop a certain number of foot pounds, and less than 33,000 foot pounds.
If, within a minute, he succeeded in raising it one foot for six times, this would be six times 550, equal to 3,300 foot pounds, or just one-tenth of one horse power for one minute; so time is just as important as the amount lifted at each effort.