We consider fully discrete approximations to solutions of the inhomogeneous boundary value for the incompressible Navier-Stokes eqns. The approximations are constructed via a discontinuous Galerkin method and Runge-Kutta methods. The velocity field is approximated using piecewise polynomial functions that are totaly discontinuous across interelement boundaries and which are pointwise divergence free on each element(locally solenoidal). The pressure is approximated by standard continuous piecewise polynomial functions. Numerical results on standard benchmark problems will be presented.