Modelling of Orifice Flow Rate at Very Small Openings

Modelling hydraulic control systems that contain flow modulation valves is highly influenced by the accuracy of the equation describing flow through an orifice. Classically, the basic orifice flow equation is expressed as the product of cross-sectional area, the square root of the pressure drop across the orifice and a “flow discharge coefficient”, which is often assumed constant. However, at small Reynolds numbers (such the case of valve pilot stage orifices), the discharge coefficient of the flow equation is not constant. Further, the relationship between the flow cross-sectional area and the orifice opening are extremely complex due to clearances, chamfers, and other factors as a result of machining limitations. In this work, a novel modification to the flow cross-sectional area is introduced and the resulting closed form of the flow equation is presented. As a secondary benefit, an analytical form of the orifice flow gain and flow pressure coefficient can be obtained. This closed form equation greatly facilitates the transient and steady state analysis of low flow regions at small or null point operating regions of spool valve.