A Modified Orifice Flow Formula for Numerical Simulation

Ellman, A. U. and Piché, R. A.
Tampere University of Technology

Journal of Dynamic Systems, Measurement, and Control,121 (4), 721-724. also in Fluid Power Systems and Technology Collected Papers 1996, S. S. Nair and R. S. Chandran (eds.), ASME Press, 1996, pp. 59-62.


The conventional turbulent orifice flow formula has an infinite derivative when the pressure drop is zero. This can cause ODE solvers to crash during numerical simulation of fluid power circuits. A two-regime orifice flow formula is proposed in which an empirical polynomial laminar flow formula is used for small pressure differences. The proposed formula has a smooth transition between laminar and turbulent regimes and does not have a singular derivative, and so is well-suited for accurate and trouble-free simulation.

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