Velocity of a Water-Hammer Wave in an Elastic Pipe

The general expression for the velocity of a water-hammer wave through a fluid in an elastic pipeline is evaluated. This result is applied to the following common practical cases: A rigid pipeline; thick-walled and thin-walled elastic pipelines with various longitudinal constraints; rock tunnels; and tunnels having a steel, or concrete, or steel and concrete lining. The results obtained are compared with those given in several standard reference books. It is shown that certain errors do exist, and considerable confusion does arise with these texts due to the fact that the assumptions made by the authors have not been clearly stated. Most of the confusion and errors in the texts are concerned with the effect of the external constraints or of Poisson's ratio, and the error involved is, in general, small (less than 10%). Nevertheless, this error may be important, and textbooks should make quite clear any assumptions made in deriving their results.