The 'nappe formula' for discharge over a sharp-crested weir is based on:
Choose the correct answer
Uniform pressure distribution
Integration of velocity √(2gh) over the full head H for each horizontal strip — gives Q ∝ H^(3/2)
Bernoulli equation at midspan only
Continuity at inlet and outlet
Correct Answer
B. Integration of velocity √(2gh) over the full head H for each horizontal strip — gives Q ∝ H^(3/2)
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Sharp-crested weir (Francis formula for rectangular): Q = (2/3)Cd√(2g)L(H^(3/2)−h^(3/2)) where h = height of velocity head. For low approach velocity: Q ≈ 1.84L(H^(3/2)) (Cd≈0.62). The formula is derived by integrating elemental discharges dQ = Cd×b×√(2gh)×dh from 0 to H. Nappe = free-falling sheet of water over weir crest.
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