1919.J 
Departmental Reports. 
123 
normal lake-level, which begins at A and terminates in a surge-chamber 
at B, from which pipes are led down to a power-house at C. A section 
to scale is shown in the article on <; The Surge-chamber Problem” in 
this number (p. 80). 
It is desirable for several reasons that the lake-level should not rise 
more than 4 ft. above a predetermined datum-level, to be maintained by 
a weir of the proper length and height situated at the effluent. 
Curve 1, D 67, shows a flood characteristic in the Harper which is of 
a normal type and occurs some three or four times in the year. The 
flow rises to a maximum of 22,000 cubic feet per second in thirty-six 
hours, and then subsides at a slower rate. The total volume reckoned 
over eight days is 4,7 64 x 10 6 cubic feet, and as the lake area is 400 x 10° 
square feet the volume of water mentioned would occupy a depth of 
11-9 ft. if it were all impounded. 
Let A denote the area of the lake, h the level or the head on the weir 
at any instant, q the rate of flow in the river at any instant during the 
flood, and H the head corresponding to a particular flow Q, whilst L is 
the length of the weir, C a coefficient in the formula for a discharge over 
the weir, viz. : 
q = CL^/2 
When the rate of inflow is on the increase we have—Rate of inflow = 
rate of storage -f rate of discharge, or 
q = + CLW* 
1 dt 
qdt — A dh + Chh‘ 6 l 2 dt 
7, A dh 
dt — - . 
{q - CL/13/8) 
Let H be the head of the weir when discharging at the rate q ; then 
CL 
X 
. dt 
dh 
H 3 / 2 - /i 3 / 2 
the integral for which is 
CL 
A 
x 1 - 7i I ~ i los (‘ - Vi) + s ‘° g t + + h) 
Vs 
h 
H 
V 3 
+ V3f (1) 
This solution was first given by GoulcL in a slightly different form, 
and a table of the function as adopted by Gould appears in Morley 
Parker’s treatise on the Control of Water .f These tables are very con¬ 
venient but entail a considerable amount of interpolating, and the device 
CT 
is here adopted of charting the value of h in terms of t x for different 
A 
values of H. D 68 and D 69 give the value of h in feet for H = 0 to 
H = 6 feet, with intervals of 0-2 of a foot corresponding to values of 
t x — in seconds. The diagram is universal in character, for it is only 
* Gould, Engineering News, 5th December, 1901. 
f Morley Parker, Control of Water. 
