A Bayesian analysis of fluid flow in pipe-lines

The waterhammer equations are a pair of partial differential equations that describe the behaviour of an incompressible fluid in a pipe-line. We generalize these equations to account for uncertainty in the description of the liquid and the pipe-line, the behaviour of the boundaries of the pipe-line and the method of solution. We illustrate applications of our model to pipe-line design and to realtime pipe-line monitoring, e.g. for detecting leaks, and discuss the general features of our approach to the careful sourcing of uncertainty in deterministic models.