A laboratory model of a river is built to a geometric scale of 1 : 100. The fluid used in the model is oil of mass density $900 k g / m^{3}$ . The highest flood in the river is $10000 m^{3} / s$ . The corresponding discharge in the model shall be

0.095 m^{3} / s

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0.100 m^{3} / s

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0.105 m^{3} / s

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10.5 m^{3} / s

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Solution

The correct option is B $0.100 m^{3} / s$
Froude model law will be applicable in this case.

$\frac{Q_{m}}{Q_{p}} = \frac{(L_{m})^{3} / T_{m}}{(L_{p})^{3} / T_{p}}$ $[∴ \frac{L_{m}}{T_{m}} = V_{m}]$
$\Rightarrow \frac{Q_{m}}{Q_{p}} = \frac{V_{m} (L_{m})^{2}}{V_{p} (L_{p})^{2}}$ $[∴ V_{r} = \sqrt{L_{r}}]$
$\Rightarrow \frac{Q_{m}}{Q_{p}} = (\frac{L_{m}}{L_{p}})^{5 / 2}$
$\Rightarrow Q_{m} = Q_{p} \times (\frac{L_{m}}{L_{p}})^{5 / 2}$
$\Rightarrow Q_{m} = 10000 \times (\frac{1}{100})^{5 / 2}$

$= 0.1 m^{3} / s$

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