A hydraulic model of a spillway is constructed with a scale \(1:16.\) If the prototype discharge is 2048 cumec, then the corresponding discharge for which the model should be tested is

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JKSSB JE (Civil) Official Paper (Held On: 19 Nov, 2023)

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Answer 1

Concept:

When working with a hydraulic model of a spillway:

For flow modeling, based on Froude similarity (since free surface flow is governed by gravity):\(\frac{Q_{model}}{Q_{prototype}}=L_r^{\frac{5}{2}}\)
where, L_r= linear scale ratio

Calculation:

Given: Prototype discharge = 2048m³/s

Linear scale ratio = 1:16

\(\frac{Q_{model}}{Q_{prototype}}=\frac{1}{16}^{\frac{5}{2}}\)

\(Q_{model}=2048\times\frac{1}{16}^{\frac{5}{2}}\)

\(Q_{model}=2cumec\)