78 
The N.Z. Journal of Science and Technology. 
[Mar. 
THE SURGE-CHAMBER PROBLEM.* 
By E. Parry, Public Works Department, Wellington, N.Z. 
Inquiries are being addressed from time to time by those interested in 
hydraulics concerning the derivation of one or other of the formulae in 
use for calculating the surge manifested in a surge-chamber when the flow 
of the water is checked or impeded. The derivation of a rational formula 
if limited in its application to a surge-chamber with parallel sides presents 
no great difficulty provided certain assumptions are made which, although 
at first sight unwarrantable, are justified by the result. 
The phenomenon is analogous to that which obtains in an electrical 
circuit containing resistance, self-induction, and capacity. The frictional 
resistance of the conduit corresponds to the frictional resistance in the 
electrical circuit, the inertia of the water to the self-induction of the 
electrical circuit, and the elastic distortion of the conduit or tube to the 
electrostatic capacity. The elastic distortion of the conduit, though a 
reality, and its effect appreciable in some circumstances, does not affect 
the result appreciably in the present instance, and consequently the resist¬ 
ance and inertia are the only effects taken into account herein. The water 
problem is not so simple as the electrical problem, because the resistance 
is a function of the velocity, whilst the relationship between the various 
elements involved is a most complicated one. In the fundamental formula 
for the flow of water in pipes we have, in terms usually employed by 
engineers, 
v 2 = C- 2 rs 
where v is the velocity, r the hydraulic mean depth, s the hydraulic 
gradient, and C a coefficient. This coefficient is a complex function, and 
may be expressed approximately, according to Professor Lees,| in the form 
1 ( v\n 
c 5 = “ wj + 
where a and [3 and n are constants, v the coefficient of 
v the velocity, d the diameter of the pipe. 
If the first equation be transformed into a form 
parable though not strictly analogous with Ohm’s 
Resistance, we have 
1 1 a 
h = Tti ‘ “ • v 
C 2 r 
kinematic viscosity, 
more directly com- 
Law of Electrical 
where h is the “ head ” and l the length of the conduit or pipe ; and if 
P-Pi be the difference of total pressure on the two ends of the conduit, 
and ir the density of the water, and a the area of the conduit, we have 
P-Pi 
* Lecture delivered before the Technological Section, Wellington Philosophical 
Society, 27th November, 1918. 
t C. H. Lees, On the Flow of Viscous Fluids, Proc. Roy. Soc., A, vol. 91, pp. 46-53, 
1914. 
