STUDY OF UNSTEADY INCOMPRESSIBLE FLOW OF A VISCOUS FLUID IN A PLANE CHANNEL

This paper presents an analytical solution to the problem of unsteady oscillatory fluid flow in a plane channel under the action of a constant pressure gradient. The problem is solved using the Laplace transform, and analytical expressions are derived for determining the velocity distribution and volumetric flow rate of the fluid. The transient processes associated with the transition from unsteady oscillatory flow to steady-state viscous fluid flow in a plane channel are analyzed. The results show that, at low values of the oscillation frequency parameter, the amplitudes of velocity and volumetric flow rate oscillations reach their maximum values and oscillate in phase with the pressure gradient. At high values of the oscillation frequency parameter, the amplitudes of velocity and volumetric flow rate oscillations decrease, while their oscillation phases lead the phase of the pressure gradient oscillations by 90 degrees.