1919.] 
Departmental Reports. 
125 
necessary to alter the horizontal scale according 
to the value of 
CL 
A 
to 
adapt it to any area of reservoir and any length of discharge-weir : for 
instance, if the value of 
A 
CL 
be 36,000, then one horizontal division on the 
scale represents one-tenth of this, or 3,600 seconds, or 1 hour. 
If the inflow be assumed constant over any length of time, and the 
flow is such that the head on the weir is, say, 2 ft. when discharging 
the whole of the flow, then the line corresponding to H = 2 will show the 
rate at which the level of the lake rises from zero to 2 ft. to which the 
curve is asymptotic. 
If the inflow varies, a simple graphical construction wdll enable a 
curve to be drawn showing the rate at which the lake-level rises above 
the weir-level. Such a curve is shown in D 67, curve 2, which is derived 
from the inflow curve 1 by dividing the latter up into six-hour sections 
and assuming the inflow to be constant during that time at a value which 
is a mean during the interval. The curve applies to Lake Coleridge, and 
the discharge is over an assumed weir-length of 660 ft., with a weir 
coefficient of 3 ; and as the area of the lake is 400 x 10 6 square feet the 
value of A/CL becomes 400 x 10 6 /3 x 660, or 202,000. The value of 
one horizontal division in D 68 and D 69 is therefore one-tenth of this, 
or 20,200 seconds, or 5 hours 36 minutes 42 seconds. For curve¬ 
drawing purposes the time interval is taken at 6 hours, which is equal to 
1-0693 horizontal divisions of D 68 and D 69. The average flow for the 
first interval is 550 cubic feet per second, corresponding to a head of 
0 - 4258 ft. over the weir. The first portion of curve 2, D 67, consists of 
a segment for the interval 0 to 6 hours transferred from an interpolated 
curve corresponding to H = 0-4258 ft. in D 68, which brings the lake- 
level up to 0-0291 ft. The average inflow for the next six-hour interval 
is 2,050 cubic feet per second, corresponding to a head of 12315 ft. on 
the weir. The second portion of curve 2, D 67, will consist of a segment 
from an interpolated curve in D 68 corresponding to IT = 1-2315, begin¬ 
ning at a point on that curve where h = 0 0295 and ending where the 
ordinate through the six-hour interval cuts the curve — i.e ., where 
h = 0-1369 ft. Continuing this process we reach a maximum of 3 47 ft. 
in 60 hours, or 24 hours after the maximum of the flood. It will be 
noted that the flood reached a maximum of 22,000 cubic feet per second 
36 hours after the commencement, and that it had fallen to a value of 
13,500 cubic feet per second when the lake-level reached its maximum. 
The maximum discharge over the weir is 12,880 cusecs, corresponding to 
a head of 3 - 47 ft., whereas the maximum of the flood reached 22,000 
cusecs, corresponding to a head of 4-98 ft. over the weir. Curve 2, D 67, 
was actually constructed by placing tracing-paper over the chart D 68 
and transferring the segments, or rather the chords, from the various 
curves of H corresponding to the value of the inflow' so as to form a con¬ 
tinuous curve. Where the inflow does not correspond to an exact value 
of H on the chart the segment is obtained approximately by interpolation. 
The curve so obtained corresponds exactly with a calculated curve, and 
it is found that no error is introduced by assuming a position for a segment 
of an interpolated curve. 
Having reached a maximum, the lake-level will begin to fall as the 
flood continues to subside, and in order to complete the construction a 
series of descending curves has been plotted on the charts D 68 and 
D 69, derived from the following equations. 
