Page:Lowell Hydraulic Experiments, 4th edition.djvu/95

${\textstyle n=}$	the number of end contractions. In a single weir having complete contraction, ${\textstyle n}$ always equals 2, and when the length of the weir is equal to the width of the canal leading to it, ${\textstyle n=0}$.
${\textstyle h=}$	the depth of water flowing over the weir, taken far enough upstream from the weir, to be unaffected by the curvature in the surface caused by the discharge.
${\textstyle a=}$	a constant power.

The coefficient ${\textstyle C}$ can be determined only from experiments in which the actual discharge is known; the constants, ${\textstyle a}$ and ${\textstyle b}$ can, however, be determined without knowing the actual discharge in any particular case.

It has been stated that the proposed formula is applicable only to weirs having a considerable length in proportion to the depth of water running over them. It is found by experiment that, when the length equals or exceeds three times the depth, the formula applies; but in lengths less than this in proportion to the depth, the formula cannot be used with safety; the error increasing as the relative length of the weir diminishes.

It is evident, from the construction of the formula, that it cannot be of general application. The factor ${\textstyle l-bnh}$ represents the effective length of the weir; if ${\textstyle l=bnh}$ this effective length becomes 0, and the formula would give 0 for the discharge, which is absurd; similarly, if ${\textstyle bnh>l}$, the discharge given by the formula would be negative. In weirs of very short length in proportion to the depth, the effect of the end contraction cannot be considered as independent of the length. The end contraction influences the discharge to a certain distance, ${\textstyle A}$, from the end of a weir; if the whole length of the weir is greater than ${\textstyle 2A}$, the effect of the end contraction is independent of the length; but if the length is less than ${\textstyle 2A}$, the whole breadth of the stream is affected in its flow by the end contractions, and, consequently, the proposed formula would not apply.

In practical applications, this will seldom be an inconvenience, as it is nearly always practicable so to proportion the weir, that the length may not be less than three times the depth upon it; if, however, there is no end contraction, the proportion of the length to the depth is not material.

125. The author has made numerous experiments on the discharge of water over weirs, according to each of the methods described above.

First, those at the Tremont Turbine, and at the centre-vent water-wheel for moving the guard gates of the Northern Canal. In none of these experiments has any attempt been made to measure the absolute quantities flowing over the weirs; but simply to cause quantities of water known to be equal, to pass over