An Empirical Discharge Coefficient Model for Orifice Flow

Abstract

In fluid power systems, flow control is mainly achieved by throttling the flow across valve orifices. Lumped parameter models are generally used to model the flow in these systems. The basic orifice flow equation, derived from Bernoulli's equation of flow, is proportional to the orifice sectional area and the square root of the pressure drop and is used to model the orifice coefficient of proportionality. The discharge coefficient, Cd, is often modeled as being constant in value, independent of Reynolds number.However, for very small orifice openings, Cd varies significantly and can result in substantial error if assumed constant. In this situation, modelers usually revert to graphs or look—up tables to determine Cd. This paper provides a closed form model for Cd as a function of the Reynolds number which can be applied to different types of orifices. Based on this model, a technique to evaluate flow given an orifice area and pressure drop without having to use iteration is introduced.