Velocity and Shear Stress Distribution of Laminar Flow between Parallel Plate by Laplace Transform Approach

Abstract

Viscosity is the property of a fluid in which an internal frictional force (viscous force) produced by intermolecular forces becomes active when the fluid is in motion and opposes the relative motion of its different layers, just as surface tension is the property of a fluid at rest. When the different layers of the fluid move at different speeds, this viscous force acts tangentially and causes a tangential (shearing) stress between the layers of the fluid in motion. In this paper, Laplace transforms approach is applied in obtaining the velocity distribution and the shear stress distribution of a unidirectional laminar flow between the stationary parallel plates as well as between the parallel plates having a relative motion by solving the differential equation describing flow characteristics of the viscous liquid via Laplace transform method. This paper shows how to use the Laplace transform to get the solution (velocity distribution and shear stress distribution) without having to find the general solution of a differential equation describing the flow characteristics equation of unidirectional laminar flow between parallel plates.