Vertical pipe flow

Saud

I have this modeling question: I am trying to understand the effect of that will result in a body-like force in the axial direction (only) downward due to a magnetic field on a steady state vertical pipe flow. What would be the most appropriate inlet and boundary conditions That will lead for the exit flow rate as part of the solution.

I thought of prescribed inlet and boundary pressure condition defined as the head (rho*g*h)