1919.] 
Parry.—The Surge-chamber Problem. 
79 
and substituting a/p for r where p is the periphery, and Q /a for v where Q 
is the flow in units of volume per unit-time, we have 
p-Pi = *- £- |- Q = b .-Q 
where S is the total area of contact. 
By analogy with Ohm’s Law of E-E, = RI, where E—E : is the difference 
of potential, R the resistance, and I the current, and on comparing the 
two forms of resistance, we have in the electrical case 
R = P . - 
a 
where l is the length of the circuit, a the cross-sectional area of the con¬ 
ductor, and p the specific resistance, which is practically a constant for 
low frequencies and a small area of conductor, and varies only with the 
nature of the conductor ; likewise in the case of fluid friction we have 
i.e., the resistance varies directly as the total surface, and the velocity 
inversely as the cross-sectional area, and directly with ^ 2 , which is a 
function involving the viscosity, the velocity of flow, and the diameter. 
It will be realized that a rigorous solution of any problem in hydraulics 
which is at the same time suitable for use is impossible, and the device 
herein adopted in order to obtain a practical result is to express the 
friction-head in the form kv, and to adopt in the application of the solution 
a value of k which contains the value of the velocity at the instant the flow 
is interrupted. Let this latter be denoted by Y, then the surface resistance 
during the remainder cf the movement will be denoted by . Account 
must also be taken of the head absorbed in the gates and screens, and for 
the same reason as before it is necessary to cast the resistance into the 
form kY. The total frictional resistance is then 7^- kY. Let this be 
C V 
denoted by K. The total frictional head for any value of v after the flow 
of water is checked is then Kv. 
This device is a crude one, but its adoption reduces the differential equa¬ 
tion between the quantities involved to a standard form, and is, moreover, 
justified by comparison with experiment. The departure from accuracy 
consists in making the resistance constant and dependent on the velocity 
at the moment of closure, whereas, as already shown, the resistance varies 
as the velocity varies, a condition which is impossible to embody in an 
equation of any manageable form. The use of Chezy’s formula with a 
constant coefficient, although simpler than the more rigorous form, is 
inexact, and also leads to difficulties. 
Fig. 1 represents a typical arrangement of conduit, surge-chamber, 
and pipes, and the problem is to determine the nature of the oscillations 
in the surge-chamber when the flow out of the chamber is suddenly inter¬ 
rupted. Using the same symbols as before, let the velocity of flow in the 
conduit be constant and equal to V, the head is entirely absorbed by 
friction, its value being KY, which is manifested by a difference in level — H 
