Adding gravity term to Navier Stokes equation

We are trying to solve the channel flow problem with gravity effects. Modified the Lid driven cavity problem to a 2D channel flow problem and added gravity term into the momentum_x equation.

Without the gravity term, the results are looking good and comparable with openfoam results.

But when added gravity (- rho * 9.81) to the momentum_x equation, the results are exactly same as without gravity. With the gravity term added in the direction of the flow and the gravity term added in the direction opposite to the flow (same magnitude), we observe no change in the max centerline velocity.

Is this related to the unit of gravity used, I have seen in the this post this that the density need to be non-dimensionalised.