Techniques of analysis for nonlinear transient flow in a pipe

Analytical solutions to the time-dependent, nonlinear equation governing incompressible, one dimensional flow in a pipe are presented. The flow is pressure-driven, and a valve on the pipe controls the flow rate. Power-law losses and an exponential closing action of a valve are assumed. Four different approximation methods are used. Of these, perturbation and Adomian's decomposition are seen to be valid only for small time. The WKB approximation works only for a quadratic loss term. Homotopy analysis is broadly applicable but needs parameter tuning, optimal values of which have been determined.

► Analytical solutions time-dependent, nonlinear equation governing incompressible, one dimensional flow in pipe are presented.
► Four different approximation methods are used.
► Homotopy analysis is broadly applicable but needs parameter tuning.