MEASUREMENT AND DIVISION OF WATER. 
11 
If two chambers are connected, as in the diagram, the 
water in the second chamber will be lower than that in 
the first by an amount depending on the size of the ori¬ 
fices. But the amount the water in the first is above that 
in the second bears a constant ratio to the depth in the 
second. Thus, if the depth in B is 6 inches and the 
water in A is 12 inches deeper, if the water in B becomes 6 
inches deeper the excess of A over B would increase by 
twice 12, or 24 inches. Its depth would then be 36, while 
before it was 18 inches. Under these circumstances an 
increase of depth of 18 inches in A causes one-third as 
much in B. 
By means of such a regulating chamber, therefore, the 
variations in the height of the water in the canal are les¬ 
sened in the regulating chamber,which is intended to fur¬ 
nish the water under constant pressure. While apparently 
avoiding the difficulty, this really does not do so. As a mat¬ 
ter of fact, the flow will increase in the same ratio for a given 
increase in depth of the main channel , whether the orifice comes 
direct from the mam channel or from, the regulating chamber , 
provided it be at the same level. 
The reason is this; The velocity of water flowing 
from an orifice varies with the square root of the depth, 
and consequently the discharge for the same opening will 
vary with the square root of the depth or pressure. While 
the variation in the regulating chamber is less by consid¬ 
erable than in the main canal, the head is less than it 
would be if the orifice were pierced at the same level in 
the canal, in the same ratio. As in the numerical ex¬ 
ample given, while the pressure in the regulating box 
doubles, or changes from 6 to 12 inches, that in the canal 
changes from 18 to 36 inches. In consequence, an orifice 
in the main canal, at the same level, would change its dis¬ 
charge in the same ratio as one at the lower end of a reg¬ 
ulating box. 
