A small wheel, under 10 × 13.5 ft. head, would give the same power with the above 376 cubic feet of water a minute, as a large wheel would with 10 × 376 cubic feet, under a 13.5 foot head.
This is due to the acceleration of gravity on falling bodies. A rifle bullet shot into the air with a muzzle velocity of 3,000 feet a second begins to diminish its speed instantly on leaving the muzzle, and continues to diminish in speed at the fixed rate of 32.16 feet a second, until it finally comes to a stop, and starts to descend. Then, again, its speed accelerates at the rate of 32.16 feet a second, until on striking the earth it has attained the velocity at which it left the muzzle of the rifle, less loss due to friction.
The acceleration of gravity affects falling water in the same manner as it affects a falling bullet. At any one second, during its course of fall, it is traveling at a rate 32.16 feet a second in excess of its speed the previous second.
In figuring the size wheel necessary under given conditions or to determine the power of water with a given nozzle opening, it is necessary to take this into account. The table on page 51 gives velocity per second of falling water, ignoring the friction of the pipe, in heads from 5 to 1000 feet.
The scientific formula from which the table is computed is expressed as follows, for those of a mathematical turn of mind:
Velocity (ft. per sec.) = sqrt(2gh); or, velocity is equal to the square root of the product (g = 32.16,—times head in feet, multiplied by 2).
SPOUTING VELOCITY OF WATER, IN FEET PER SECOND, IN HEADS OF FROM 5 TO 1,000 FEET
| Head | Velocity |
|---|---|
| 5 | 17.9 |
| 6 | 19.7 |
| 7 | 21.2 |
| 8 | 22.7 |
| 9 | 24.1 |
| 10 | 25.4 |
| 11 | 26.6 |
| 11.5 | 27.2 |
| 12 | 27.8 |
| 12.5 | 28.4 |
| 13 | 28.9 |
| 13.5 | 29.5 |
| 14 | 30.0 |
| 14.5 | 30.5 |
| 15 | 31.3 |
| 15.5 | 31.6 |
| 16 | 32.1 |
| 16.5 | 32.6 |
| 17 | 33.1 |
| 17.5 | 33.6 |
| 18 | 34.0 |
| 18.5 | 34.5 |
| 19 | 35.0 |
| 19.5 | 35.4 |
| 20 | 35.9 |
| 20.5 | 36.3 |
| 21 | 36.8 |
| 21.5 | 37.2 |
| 22 | 37.6 |
| 22.5 | 38.1 |
| 23 | 38.5 |
| 23.5 | 38.9 |
| 24 | 39.3 |
| 24.5 | 39.7 |
| 25 | 40.1 |
| 26 | 40.9 |
| 27 | 41.7 |
| 28 | 42.5 |
| 29 | 43.2 |
| 30 | 43.9 |
| 31 | 44.7 |
| 32 | 45.4 |
| 33 | 46.1 |
| 34 | 46.7 |
| 35 | 47.4 |
| 36 | 48.1 |
| 37 | 48.8 |
| 38 | 49.5 |
| 39 | 50.1 |
| 40 | 50.7 |
| 41 | 51.3 |
| 42 | 52.0 |
| 43 | 52.6 |
| 44 | 53.2 |
| 45 | 53.8 |
| 46 | 54.4 |
| 47 | 55.0 |
| 48 | 55.6 |
| 49 | 56.2 |
| 50 | 56.7 |
| 55 | 59.5 |
| 60 | 62.1 |
| 65 | 64.7 |
| 70 | 67.1 |
| 75 | 69.5 |
| 80 | 71.8 |
| 85 | 74.0 |
| 90 | 76.1 |
| 95 | 78.2 |
| 100 | 80.3 |
| 200 | 114.0 |
| 300 | 139.0 |
| 400 | 160.0 |
| 500 | 179.0 |
| 1000 | 254.0 |