| Abstract: | The creeping flow of a highly viscous incompressible fluid through a circular aperture located in an infinitely wide horizontal plate is analyzed by solving Navier-Stokes equations without inertia terms. Solutions for vertical and radial velocities as well as pressure have been obtained in terms of integral equations with an undetermined Kernal function. This function has been evaluated by assuming several different velocity distributions at the aperture, and the corresponding pressure drop for each case has been calculated. The results show that the pressure loss for a given flow rate goes through a minimum as the assumed velocity profile changes from flat to parabolic. Based on the minimum energy dissipation theorem of Helmholtz, the most appropriate velocity distribution is discussed. Experimental data obtained using sharp-edged orifices are compared with theoretical predictions. |
