What is gradually varied flow and how is it computed?

Gradually varied flow (GVF) has gradual depth changes along channel with constant discharge. The GVF equation: dy/dx = (S0 - Sf)/(1 - Fr^2), where S0 = bed slope, Sf = friction slope, Fr = Froude number. Flow profile types depend on bed slope (mild, steep, critical, adverse, horizontal) and depth relative to normal and critical depths. Computation uses standard step method (known sections) or direct step method (known depths). Profiles predict water surface through channel transitions, over weirs, and approaching controls.