1919.] 
Parry.—The Surge-chamber Problem. 
85 
balance in gates and screens. The amount of the latter was abnormal 
at the time of the observation, for reasons which need not be entered into 
here. 
The general arrangement of the Lake Coleridge works is shown in 
fig. 1, and the dimensions of the elements affecting the result are shown 
in fig. 1 and also in fig. 2. Referring to fig. 1, it will be seen that the 
works consist of a tunnel, &c., with inlet work at A and terminating in a 
surge-chamber at B, from which pipes are led down to the power-house 
at C. The crown of the tunnel is 12 ft. below normal lake-level at the 
inlet, and 19 ft. below at the surge-chamber. The net length of tunnel 
is 6,952 ft., the cross-sectional area 50-745 square feet, hydraulic mean 
depth 1-946. The area of the surge-chamber is 975 square feet in the clear, 
to which has to be added the area of one or more screen-chambers which 
may be in communication with the main chamber at the time of the 
experiment. The coefficient C in Chezy’s formula is found by test to have 
a value of 110 at a velocity of 3J ft. per second. Assuming this to be a 
constant for the sake of simplicity we have, on collecting the values of 
the different symbols, l = 6,952 ft., a — 50-745 sq. ft., A = 1,050 sq. ft., 
A/a = 20-7, C = 110, r = 1-946. From the foregoing dimensions and 
from the fact that the flow at the beginning of the operation was 61 cusecs 
and the corresponding velocity 1-2 ft. per second, we obtain the following- 
derived quantities: The total inclusive friction-head was 0-5 ft., of which 
0-425 ft. is in surface friction and 0-075 ft. in gates and screens ; the value 
of l/C 2 r is 0-295, and of k 0-052 ; the value of K corresponding to velocity 
V is (0-295 + 0-052) V = 0-347 x 1*2 = 0-417, whence a = — 0-000963, 
fj — 0-015, and the periodic time 420 seconds. 
If the above values be substituted in equation (3) or (4) and the value 
of t varied, a series of values is obtained which when plotted yield the result 
shown in the upper portion of fig. 2, and on comparing this with the 
observed values plotted in the lower portion of fig. 2 we see that the first 
calculated surge is over twice the first observed surge, because the calculated 
value is for sudden closure, whilst the observed value is for a gradual 
closure during which the flow was reduced. It will be noted that the 
periodicity is the same, whilst the attenuation or damping is slightly greater 
at the same amplitude for the calculated than for the observed result, 
whereas it should be less, because in the experiment the closure was not 
complete, there being a leakage of 7 cusecs, which would intensify the 
damping effect due to resistance of the conduit, gates, and screens. The 
greater attenuation shown on the calculated curve is due to the fact that 
the frictional resistance is assumed to be constant and at a value corre¬ 
sponding to the velocity at the instant of closure, whereas the resistance 
is a function of the velocity, as already explained. Closer results 
between the calculated and observed curves would be obtained by 
adjusting the value of C to the velocity, and by adjusting the resistance 
to the velocity of the water in the conduit at the corresponding time 
intervals selected for calculating the height of the water in the surge- 
chamber. This involves considerable extra labour not justifiable by the 
result. Equation (3) may be regarded as a first approximation, and the 
variation of the resistance with velocity a second approximation. This 
degree of approximation is unnecessary in practice, as the main object 
in view is to obtain the value of the periodic time and the first positive 
and negative surges, which values are not greatly affected by the present 
considerations. 
