A variational method is used to derive numerical models for transient flow simulation in fluid transmission lines. These are generalizations of models derived using the more traditional modal method. Three different transient compressible laminar pipe flow models are considered (inviscous, one-dimensional linear viscous, and two-dimensional dissipative viscous flow), and a model for transient turbulent pipe flow is given. The (model) equations in the laminar case are given in the form of a set of constant coefficient ordinary differential equations, and for the turbulent case (model) in the form of a set of nonlinear ordinary differential equations. Explicit equations are given for various end conditions. Attenuation factors, similar to the window functions used in spectral analysis, are used to attenuate Gibbs phenomenon oscillations. [S0022-0434(00)03201-9]

Because the conventional formula for turbulent orifice flow rate has an infinite derivative when the pressure difference is zero, ODE solvers may fail during numerical simulation of fluid power circuits. To remedy this, a two-regime orifice flow formula is proposed in which an empirical polynomial laminar flow function is used for small pressure differences. The proposed formula has a smooth transition between laminar and turbulent regimes, and its derivative does not have any singularities.

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