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Define GVF, RVF and spatially varied flow

Short answer

Gradually varied flow: depth changes slowly over long distance, pressure hydrostatic; e.g., backwater behind dam, drawdown to fall. Rapidly varied flow: depth changes abruptly over short distance, pressure non-hydrostatic; e.g., hydraulic jump, flow over weir. Spatially varied flow: discharge varies along channel due to lateral inflow/outflow; e.g., side weir, roadside gutter.

Define gradually varied, rapidly varied and spatially varied flow with examples (sketches).

Gradually varied flow (GVF)

Steady non-uniform flow in which the depth changes slowly over a long distance, so the streamlines are nearly parallel and the pressure is hydrostatic. Examples: the backwater curve upstream of a dam or weir, and the drawdown curve towards a free fall.

Rapidly varied flow (RVF)

Steady non-uniform flow in which the depth changes abruptly over a short distance; the streamlines are strongly curved and the pressure is not hydrostatic. The energy loss is local and may be large (as in a hydraulic jump). Examples: a hydraulic jump, flow over a weir or spillway crest, and flow below a sluice gate.

Spatially varied flow (SVF)

Flow in which the discharge changes along the channel due to lateral inflow or outflow. Examples: a side channel spillway, side weir, roadside gutter, or a drain with lateral inflow.

 GVF (backwater)      RVF (jump)          SVF (side weir)
   ____                 ___                 ~~~~~~~\ 
 ~~~     ~~~~            \_/\___            ~~~~~~~~~~>
 ~~~~~~~~~~~~~~        ~~~~~\_ ____        ____/weir____
  dam |                    jump
FlowDepth changeLengthDischarge
GVFgraduallongconstant
RVFabruptshortconstant
SVFgradual or abruptanyvaries along the length

✓ Answer checked by Claude Opus 5.5 (high effort)

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