Orifice Contraction Coefficient for Inviscid Incompressible Flow

Abstract

The theory for steady flow of an incompressible fluid through an orifice has been semi-empirically established for only certain flow conditions. In this paper, the development of a more rigorous theory for the prediction of the orifice flow contraction effect is presented. This theory is based on the conservation of momentum and mass principles applied to global control volumes for continuum flow. The control volumes are chosen to have a particular geometric construction which is based on certain characteristics of the Navier-Stokes equations for incompressible and, in the limit, inviscid flow. The treatment is restricted to steady incompressible, single phase, single component, inviscid Newtonian flow, but the principles that are developed hold for more general conditions. The resultant equations predict the orifice contraction coefficient as a function of the upstream geometry ratio for both axisymmetric and two-dimensional flow fields. The predicted contraction coefficient values agree with experimental orifice discharge coefficient data without the need for empirical adjustment.