Page:Lowell Hydraulic Experiments, 4th edition.djvu/99

 The factor $c\sqrt{2g}$, being constant, can be determinea by an experiment in which $L$ and $h$  are known. To determine this constant, the following experiment was made.

The weir was closed up by the flashboards, and made tight in the usual manner, so that no appreciable quantity passed over the weir; the head gate was closed, and the small quantity leaking through it was caught in the leak box and carried over the weir in the leak pipe (art. 24). The water in the wheelpit having then no supply, its surface began to lower, in consequence of the leakage through the floor; while thus falling, the following observations were  made.

The area of the surface of the water in the wheelpit, after making the proper deductions, was about 506 square feet; consequently, $$L = { {506 \times 0.2} \over {2476} } = 0.0409 \text{ cubic feet per second.}$$

During the interval of 2476 seconds, the mean height of the water in the lower canal was 1.2316 feet below the top of the weir, and the mean height in the wheelpit, during the same period, was 0.496 feet above the top of the weir, then $$h= 1.2316 + 0.4960 = 1.7276\text{ feet}.$$ Substituting these values of $L$ and $h$  in the equation $$L=c\sqrt{2g}\sqrt{h},$$ we have $$c\sqrt{2g} = 0.03112:$$ consequently, $$L= 0.03112 \sqrt{h}.$$ To find the depth on the weir, corrected for the leakage of the wheelpit, let