# 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.

## Abstract

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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