GVF Profile (Rectangular / Trapezoidal)

Standard-step solution of gradually varied flow using dy/dx = (S₀ − S_f)/(1 − Fr²). Choose units and section type, then define a control depth and integrate along the reach.

Inputs

Current units: SI – lengths in metres, discharge in m³/s.

Section type

Bottom width Bm

Discharge Qm³/s

Manning n

Bed slope S₀dimensionless, in flow direction

Known depth y₀m

Control location

Reach length Lm

Step size Δxm (along channel)

Normal & critical conditions

Enter data and click “Compute GVF profile” to see slope type, normal depth, critical depth and control depth regime.

For mild slopes (subcritical), a downstream depth (e.g., due to a weir or backwater) is typically known (M-profiles). For steep slopes (supercritical), an upstream control depth is used (S-profiles).

Water depth vs station

Station is measured from the control section in the direction of integration. Depth is measured above the channel bed.

Station	Depth y	V	Fr	Regime
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