Abstract
In this paper, the velocity profile and pressure gradient of the unsteady state unidirectional flow of Bingham fluid between parallel plates are solved by the Laplace transform method. The flow motion between the plates is induced by a prescribed arbitrary inlet volume flow rate which varies with time. Based on the flow conditions described, two basic flow situations are solved; these are a suddenly started, and a constant acceleration, flow respectively. These two results are then applied to a practical case that is a trapezoidal piston motion which contains three phases of piston motion, the constant acceleration from the rest to a fixed velocity, then keeping at this velocity, following with the constant deceleration to a stop. In addition, oscillatory flow is also considered. The result indicates when the yield stress τ 0 is equal to zero, the solution to the problem reduces to that of a Newtonian fluid.
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