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Siphon spillway: discharge–head relation Let a be the flow area at the throat and H be the effective head. Cd denotes the coefficient of discharge and g is gravitational acceleration. Choose the correct proportional form for the discharge through a siphon spillway.

Difficulty: Medium

Cd × a × √(2g) × H
Cd × a × √(2g) × H^(3/2)
Cd × a × √(2g) × H^2
Cd × a × √(2g) × H^(5/2)

Correct Answer: Cd × a × √(2g) × H^(3/2)

Explanation:

Concept/Approach

For free-flow (weir-like) siphon action, discharge varies as area × velocity with velocity ≈ √(2gH) and effective head dependence H^(3/2) for weir-type flow.

Relation
Q = C_d × a × √(2g) × H^(3/2) (up to geometry-dependent constants).

Final Answer
Cd × a × √(2g) × H^(3/2)

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