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Define gradually varied flow

Short answer

Gradually varied flow is steady non-uniform flow with slowly changing depth, nearly parallel streamlines and hydrostatic pressure. Discharge is constant. Profile given by dy/dx = (S0 - Sf)/(1 - Fr^2). Examples: backwater behind a dam, drawdown to an overfall.

Define gradually varied flow.

Gradually varied flow (GVF) is steady non-uniform flow in which the depth changes gradually along the channel length, so that streamlines are almost parallel and the pressure distribution is hydrostatic. The discharge is constant.

Examples: the backwater curve upstream of a weir or dam, drawdown curve approaching a free overfall, and flow in a canal where the slope changes from mild to steep.

        ______ GVF (backwater) 
   ~~~~~~          ~~~~~~|
   _____________________| dam

Its profile is governed by the dynamic equation

dydx=S0−Sf1−Fr2\frac{dy}{dx}=\frac{S_0-S_f}{1-Fr^2}

It is different from rapidly varied flow, in which the depth changes abruptly over a short length (for example, a hydraulic jump).

✓ Answer checked by Claude Opus 5.5 (high effort)

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