Boussinesq-type equations should be employed in which the water surface profile is considerably steep or the bottom topography is abruptly changed. The primary reason is that the pressure deviates significantly from the hydrostatic pressure distribution due to the large curvature of the stream lines. It is shown that such a Boussinesq type equation can be also derived by making use of the concept of the averaged flow description for specifying the turbulence effects. In addition, a numerical scheme is developed to solve the equations and the effects of the Boussinesq term is briefly investigated.