The 'gradually varied flow' (GVF) equation in open channels is derived from:
Choose the correct answer
Continuity equation alone
Energy equation for non-uniform flow: dy/dx = (So−Sf)/(1−Fr²) — slope of water surface depends on bed slope, friction, and Fr
Bernoulli equation between two fixed points
Momentum equation ignoring friction
Correct Answer
B. Energy equation for non-uniform flow: dy/dx = (So−Sf)/(1−Fr²) — slope of water surface depends on bed slope, friction, and Fr
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GVF equation: dy/dx = (So − Sf)/(1 − Fr²) where So = bed slope, Sf = friction slope (energy gradient), Fr = Froude number = V/√(gD). Derived from energy equation for non-uniform flow. If So > Sf and Fr < 1: backwater curve (M1 or S1); if So < Sf: drawdown. Critical depth occurs at Fr=1. Numerical integration (standard step method or direct step method) solves GVF profile.
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