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Fluid Mechanics

Model Analysis

In a 1/50 mod...

Question

In a 1/50 model of a spillway, the discharge was measured to be $0.3 m^{3} / s e c .$ The corresponding prototype discharge in $m^{3} / s e c$ is

A

2.0

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B

15.0

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C

106.0

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D

5303.0

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Solution

The correct option is D 5303.0
$Q_{r} = L_{r}^{2.5}$

$\frac{Q_{p}}{Q_{m}} = {(\frac{L_{p}}{L_{m}})}^{2.5}$
$= (50)^{2.5}$
$∴ Q_{p} = 0.3 \times (50)^{2.5} = 5303.3 m^{3} / s$

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