Computational model for speed of efflux in liquids

Abstract

We have looked at the efflux of a viscous liquid from an orifice. Assuming the steady flow of a Newtonian fluid, a model for the energy loss due to viscous shearing stress is derived, and a first-order non-linear ordinary differential equation of second degree is obtained for the speed of efflux. Numerically, the equation is quasi-stiff, due to the small value of kinematic viscosity of common liquids. We resolve the equation numerically using a modified Rosenbrock formula for the speed of efflux at different depths of the orifice, below the free surface of the liquid. Generally, the results show that the speed of efflux for a liquid with a large kinematic viscosity is lower than that for a liquid with a small kinematic viscosity at any particular depth. At a low hydrostatic pressure, the speed of efflux of a viscous liquid is less than that of an inviscid fluid. Thus there is a significant energy loss if the kinematic viscosity of a liquid is high. Also, the results suggest that liquids with a large kinematic viscosity are more likely to support steady flow if subject to a high pressure gradient.

JONAMP Vol. 11 2007: pp. 137-144