An exact solution to the rigid-plastic equations is presented, which contains inertial terms, together with a nonzero (intrinsic) cohesion, S-0. Matching the mass flow from this exact solution to that predicted in Beverloo-type equations, identifies S-0 as equal to about rho gd/2, where d is a characteristic particle diameter. This cohesion suggests the presence of dead regions about orifice boundaries, and of arching in narrow orifices. The solution is only defined beneath an elliptical arch above the outlet of the hopper orifice.