In this paper an attempt has been made to find the solution of the Navier-Stokes equations for the flow of a viscous incompressible fluid between two plates, one at rest and the other in uniform motion, with small uniform suction at the stationary plate. A solution has been obtained under the assumption that the pressure between the two plates is uniform. It has been shown that due to suction a linear transverse velocity is superimposed over the longitudinal velocity. With suction, the longitudinal velocity distribution between the plates becomes parabolic and decreases along the length of the plate.
The longitudinal velocity, the shearing stress at the stationary plate, and the volume rate of flow increase withσ(=v0y0/v), the suction parameter defined with reference to the suction velocity, and the distance between the two plates. Forσ=0 the results transform to the known results for plane Coutte flow without suction.