Abstract : A particular form for an effective or eddy viscosity is hypothesized and considered in conjunction with the boundary layer equations for cases where the pressure gradient parameter is held constant. Precise solutions are obtained for accelerating and decelerating flows in the range, beta infinity; the solutions span the complete boundary layer profile with the exception of the small viscous sublayer region. Comparison of the calculated velocity profiles with zero pressure gradient data and Clauser's and Stratford's decelerating flow data is excellent. For large values of beta the influence of the pressure gradient dominates the influence of the wall shear stress; defect profiles should then be presented in the form, U sub p, instead of U sub tau where U sub p is a pressure velocity and U sub tau is the conventional skin function velocity. (Author)