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The Quarterly Journal of Mechanics and Applied Mathematics 1951 4(3):330-343; doi:10.1093/qjmam/4.3.330
© 1951 by Oxford University Press
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THE EFFECT OF FRICTION ON SURGES IN LONG PIPE-LINES

A. M. BINNIE

( Trinity College Cambridge )

A pressure fluctuation occurs in a pipe-line when the velocity of the liquid in it is altered by means of a valve. A method of calculating these surges in a gravity pipeline is described for the two cases when the exit velocity is reduced to zero (i) instantaneously and (ii) at a uniform rate. Allowance is made for the effect of friction, which is assumed to be proportional to the velocity, but the method may be used to provide an approximate result when the friction loss follows some other relation. Dimensionless quantities are employed, and the working is expressed in terms of a single characteristic number k, which depends upon the properties of the pipe-line and of the liquid in it. The method holds good unless k is too large. For the two cases, numerical results are given for a small and a large value of k, and they are compared with those derived by the graphical method of solution.


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