Estimation of velocity profiles of flow in a slot subjected to oscillating pressure gradient

In this work velocity profiles have been calculated for a flow in a slot with a pressure gradient subjected to oscillations using a computer program. From previous work and findings, it is known that the flow in a slot with a constant pressure gradient has a velocity profile which forms a parabolic shape. In this work we add an vibratory component to the steady gradient under consideration. Moreover, the changes in velocities and changes in dimensional parameters of the slot has been analyzed. Graphs of velocity changes are captured for various time and slot stations in order to fully understand the flow when a pressure gradient of vibratory nature is applied. The Navier — Stokes and continuity equations in are used and are kept in the Cartesian coordinates. Changes in velocity profiles for various kinematic viscosity of the fluids are also taken into consideration. The establishment of the viscous region within the slot and its variation with respect to viscosity of the fluid is studied. Moreover, the variation in velocity profile with changing dimensions of the slot is also taken into consideration. The proposed algorithm formulated during the course of this research will enable and aid scientific investigators and academics to accomplish calculations to design various slots according to situational requirements. The results achieved will help in designing slots and channels which experience oscillation in pressure gradients and can also be used to predict the of nature of gradient at work.