Page:Lowell Hydraulic Experiments, 4th edition.djvu/50

The latitude of Lowell, as given in the American Almanac, is 42°, 38′, 46″, and the height above the sea is known to be about 25 metres. With these data, the above formula gives, in feet,

$$g=32.1618.$$

69. Column 19. Velocity of the interior circumference of the wheel. The diameter of the circle inscribing the inner edges of the buckets, is 6.75 feet; see art. 35. Consequently the interior circumference of the wheel is 21.20575 feet. The product of this number into the number of revolutions per second, given in column 8, gives the numbers in column 19.

70. Column 20. Ratio of the velocity of- the interior circumference of the wheel, to the velocity due to the fall acting on the wheel. This column is obtained by dividing the numbers in column 19 by the corresponding numbers in column 18. This column indicates the relative velocities of the wheel, in the different experiments, eliminated from the effects of the variations in the fall acting upon the wheel.

71. Column 21. Quantity of water which passed the wheel, reduced to a uniform fall of thirteen feet. The numbers in this column are obtained from those in column 15, in the following manner.

Let H = the observed fall acting upon the wheel.

Let HQ = the observed quantity.

Let HQ′ = the quantity that would have passed the wheel, if the fall had been thirteen feet, instead of H, all other circumstances being the same.

As the quantity of water discharged by the wheel, all other things being equal, will vary as the square root of the fall acting upon the wheel, we have

$${\sqrt {H}}:Q::{\sqrt {13}}:Q\prime ,$$

therefore

$$Q\prime =Q{\sqrt {{13} \over {H}}}.$$

The quantities given in column 21, have been calculated by this formula.

72. Column 22. Ratio of the reduced quantity in column 21, to the reduced quantity in experiment 30. The numbers given in this column indicate the relative quantities discharged by the wheel in the different experiments, eliminated from the effects due to the variations in the fall acting upon the wheel; the reduced quantity in experiment 30 is taken as unity, that experiment giving the maximum coefficient of effect. It will be seen by a comparison of columns 20 and 22, that the quantity discharged by the wheel, when the gate is fully raised, diminishes regularly with the velocity. The quantity discharged is a minimum in experiment 42,