Hello,
I understand that your upstream boundary will be supercritical, and the downstream boundary subcritical with depth imposed. So you will get probably a hydraulic jump in between. It seems to me that in this configuration the conservation of water mass and of momentum between upstream and downstream can give the head loss, it is a classical problem of Saint-Venant equations, at least in 1D on flat bottom. So you might be right, though at first sight we are tempted to think that the complexity of the energy loss is beyond reach.
You can look at the case hydraulic_jump, which is similar to what you want to do.
With best regards,
Jean-Michel Hervouet