Upon evaluating the integration constants, K and K2, with the boundary conditions, the final expression for the velocity profile, Eq. (7), is obtained: u = { [(c/vRe) 1]/[1 e*]} (e*y e*) + (c/vRe)[y 1] + 1 (7) r For the case of c = 0 and b = 0, Eq. (7) reduces to the well known linear velocity profile for plane Couette flow. Also, the linear velocity profile is obtained when c = vRe, and this is the case where the streamwise velocity gradient is equal to the suction or blowing velocity. Pig. 1 presents several velocity profiles, and it can be seen that the combined effect of the velocity gradient and suction or blowing velocity can produce velocities greater than the plate velocity, or reverse flow. In general, adverse pressure gradients retard the velocity profile in the vicinity of the fixed surface, and, for the particular pressure gradient shown, a value of vRe = —1.594 produces the separation velocity profile—i.e., the velocity gradient at y = 0 is zero. As Schlichting stated, the analysis of Couette flow with a pressure gradient can be applied in the hydrodynamic theory of bearing lubrication.