I know that when modeling incompressible flow in a pipe, it is common practice that when you have a velocity inlet, there should be a zero pressure gradient at the inlet as well.  Also, when you have a pressure outlet, you should set the velocity gradient to zero at the outlet.  But when you have both a pressure inlet and pressure outlet, should one set the velocity gradients at both inlet and outlet to zero?  Would this lead to a stable solution for pipe flow?
How should I set the velocity conditions when you have a pressure inlet and pressure outlet?
fluid dynamics