Approximate wall shear equation for unsteady laminar pipe flows

An approximate equation is derived for wall shear stress in unsteady laminar pipe flows in terms of the instantaneous section mean velocity and acceleration. The equation, which is exact for a constantly accelerating or decelerating flow, is applied to solve for two types of pressure gradient functions, a transient start-up flow and a linearly reversing pressure gradient. Comparison with exact analytical solutions verifies that the equation is adequate for the two types of transient flows investigated, and for low frequency oscillating flows.