Page:Lowell Hydraulic Experiments, 4th edition.djvu/98

the columns are sufficiently explained by the respective headings; several of them, however, require further explanation.

129. Column 11. Fall affecting the leakage of the wheelpit. This is obtained by adding together the corresponding numbers in columns 9 and 10.

130. Column 12. Depth of water on the weir corrected for the leakage of the wheelpit. This is obtained in the following manner.

It was clear, from the construction of the wheelpit, (art. 23,) that nearly the whole of the leakage passed through the wooden flooring, and that all the orifices through which it passed were constantly below the surface of the lower canal. In the construction of the wheelpit, no particular precautions were taken to prevent a free communication from the bottom of the wooden flooring to the lower canal; and as the amount of the leakage was very small, and the material, fine sand free from large springs, it is clear that the water could have had no appreciable obstruction after passing through the flooring, except from the pressure of the water in the lower canal. This being the case, the amount of the leakage would depend upon the head; or, in other words, upon the height from the surface of the water in the wheelpit, to the surface of the water in the lower canal. Let

${\textstyle L=}$	the quantity of water leaking out of the wheelpit, in cubic feet per second.
${\textstyle A,A',A'',etc.=}$	the areas of the several orifices through which the water passed.
${\textstyle C,C',C'',etc.=}$	the corresponding coefficients of contraction.
${\textstyle h=}$	the head, or the height from the surface of the water in the wheelpit, to the surface of the water in the lower canal. This head applies to all the orifices, as they are all below the surface of the water in the lower canal.

$$L=CA{\sqrt {2gh}}+C'A'{\sqrt {2gh}}+C''A''{\sqrt {2gh}}+{\text{etc.}};$$

$$L=(CA+C'A'+C''A''+{\text{etc.,}}){\sqrt {2gh}}$$

The areas ${\textstyle A,A',A'',etc,}$ are constant, as are also the coefficients ${\textstyle C,C',C'',etc.}$, the variations in the head not being very great. Let

$$c=CA+C'A'+C''A''+{\text{etc.}}:$$

then

$$L=c{\sqrt {2gh}}=c{\sqrt {2g}}{\sqrt {h}}.$$