Skip to main content

Differentiate GVF, RVF and SVF with sketches

Short answer

Gradually varied flow (GVF) features slow depth change, constant discharge, hydrostatic pressure; e.g., backwater behind a dam. Rapidly varied flow (RVF) has abrupt depth change, constant discharge, non-hydrostatic pressure; e.g., hydraulic jump. Spatially varied flow (SVF) involves varying discharge due to lateral addition or removal; e.g., side channel spillway.

Differentiate gradually, rapidly and spatially varied flow with neat sketches and examples.

BasisGradually varied flow (GVF)Rapidly varied flow (RVF)Spatially varied flow (SVF)
Depth changeSlow, over a long reachAbrupt, over a short reachGradual or abrupt, along the reach
DischargeConstantConstantVaries along the length
StreamlinesNearly parallelStrongly curvedDepends
PressureHydrostaticNon-hydrostaticHydrostatic (usually)
Energy lossMainly friction (distributed)Local, may be large (eddies)Friction plus mixing of the lateral flow
AnalysisEnergy equation dy/dx=(S0−Sf)/(1−Fr2)dy/dx=(S_0-S_f)/(1-Fr^2)Momentum, specific energy, empiricalMomentum equation (increasing Q) or energy equation (decreasing Q), with a dQ/dxdQ/dx term
ExamplesBackwater behind a dam, drawdown to an overfallHydraulic jump, flow over a spillway crest, flow below a sluice gateSide weir, side channel spillway, roadside gutter
GVF: backwater            RVF: hydraulic jump
     ___                   
 ~~~~    ~~~~|  dam          ~~~~\___/\~~~~~
 ___________|                 ___________

SVF: increasing Q            SVF: decreasing Q
   | | |  lateral inflow       ~~~~~~~~~~\
 ~~~~~~~~~~~~~~>                ~~~~~~~~~~~~~> 
 ___________________            _____/weir___

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Hydraulics chapter 5 questions →