A hump reduces available specific energy. If it would fall below Emin, the model raises upstream head until the crest is critical. With sufficient approach energy, flow stays on the subcritical branch.
Equations and boundaries
E=y+Q²/(2gb²y²); yc=[Q²/(gb²)]⅓; Emin=1.5yc. Total head H=z+E is constant in this lossless short-reach model. H=max(initial approach head, max bed elevation + Emin). Depth is found on the appropriate E–y branch at each section.
Assumed subcritical approach, alpha=1, hydrostatic sections, no friction/local losses and free downstream discharge. Initial approach depth comes from n=0.010 Manning depth plus the extra-depth control, bounded above critical depth. No submerged-weir, tailwater-control, hydraulic-jump, separation or jet solver is included. Sharp-corner energy predictions are idealized; actual edge losses need measurements.
Rounded shoulders use an illustrative 0.08 m cosine transition, not manufacturer geometry. Default insert heights and length come from manual pp.25–26. The inlet U/S station is x=0; crest station is the highest bed point; D/S is x=3.30 m. The manual’s later profile distances extend beyond its stated 4.30 m flume, so they are not used as physical coordinates here.
Predicted water is shown in 3D. Entered readings overlay the chart but do not calibrate the solver. Depths are measured from the local bed or hump crest, not the original bed datum. The manual does not clearly resolve the reference datum of its crest sample readings; those samples are not used as calibration targets.