Accurate inflow/outflow calculation

Hi, I'm using the Free&Porous workflow, but the question is also applicable to Navier-Stokes.

I have an inlet and use NormalVelocity boundary condition which, it seems sets up a Lagrange multiplier to enforce u = u_0. No problem.

But when I do an integral over the inlet surface to check that total fluid-in matches the desired actual fluid in, then I have a big error (>20%). Yes, I could mesh more finely....

But I thought I remember a "trick" for accurate calculations of flow across a surface. Isn't this equal to a Lagrange multiplier or something? Maybe I am misremembering.

Does this ring a bell with anyone??

Thanks, John