1919 .] 
Parry.—The Surge-chamber Problem. 
83 
is less than unity, a condition which is not always fulfilled, the exceptions 
being long tunnels and rough surfaces ; however, in the majority of cases 
we may take it that at is less than unity, in which case we may take the 
first two terms of the expansion of e at without much error. Sin (fit — <£) 
may for the present purpose be taken as unity, because fit — <f> approxi¬ 
mates near enough^ generally speaking, to tt/2 to enable this assumption 
to be made. Subject to these limitations, we obtain an equation of the 
form 
h = 
max. 
\J — . ? . y s 
V A l 
T 
+ H- - 5 
H 
u 
K 2 g 2 
~T~ 
where T is the period of maximum amplitude determined by the condi¬ 
tion that the maximum occurs when fit = tan -1 fi/a. 
The second term under the second root is practically equivalent to 
JH 6t, and as the value of fit depends on a function containing fi the 
range of variation of fit is not great. An examination of the value of fit 
under a wide range of conditions justifies the adoption of a mean value 
of about 1-7, so that the equation finally reduces to the following terms, 
viz. : — 
n = V t ' ~ ' V 2 + H 2 - 0-85H .(5) 
max. A g 
which gives the amplitude of the first surge, or its height above static level, 
and which agrees with one of the numerous formulae in use, except that 
the coefficient in the second term is 0-85 instead of unity. 
The surge obtained by means of the formulae will be quite 40 per cent, 
greater than the liability under practical conditions because of the time 
element and the effect of elasticity. 
In ordinary operation the relief-valve connected with the turbine- 
governor serves to minimize the surge and to damp it down, and even under 
emergency conditions the closure takes time, so that it is not necessary 
to provide in all cases for the maximum surge above calculated except by 
affording means of discharging the same by overflow as a matter of con¬ 
tingency. 
The foregoing formulae apply only in case of sudden closure, which 
can only occur in rare emergencies ; and, as already explained, it is not 
always feasible to apply sudden closure to a flow, but it is quite possible 
to test the applicability of the theory by applying a gradual closure, for 
although in such an event the amplitude of the first surge will not be so 
great, the periodic time and the attenuation, depending as they do on the 
dimensions of the conduit and surge-chamber and upon the coefficient of 
friction, will be the same whether the closure is sudden or gradual. 
An opportunity was seized on the 5th April, 1915, by Mr. L. Birks and 
Mr. T. McLennan of making a test on the surge-chamber of the Lake 
Coleridge works. The results of the observations are shown in the lower 
half of fig. 2. The flow of water was 61 cubic feet per second at the 
commencement of closure, and ten minutes was occupied in reducing the 
flow from 61 cubic feet per second to 7 cubic feet per second. It will be 
seen that towards the end of the closing-movement an oscillation was set 
up, the amplitude of the first positive surge being 1 ft. 8Jin., and that the 
oscillations continued with a diminishing amplitude and with a periodicity 
of seven minutes. The frictional head at the outset was about 6 in., of 
which about 5T in. was absorbed by surface friction in the tunnel and the 
