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Formation of a Differential Equation from a General Solution

The stage in ...

Question

The stage in a river is 4.8 m, the water surface slope is 1 in 10,000 and the discharge in the stream is $600 m^{3} / S$ . If the stage remains the same and the water surface slope is 1 in 14,400 then the discharge in the stream will be

A

500 m^{3} / S

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B

$400 m^{3} / S$

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C

$300 m^{3} / S$

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D

600 m^{3} / S

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Solution

The correct option is A $500 m^{3} / S$
$\frac{Q_{2}}{Q_{1}} = \sqrt{\frac{S_{2}}{S_{1}}}$

$∴ Q_{2} = 6000 \times \sqrt{\frac{10, 000}{14, 400}} = 500 m^{3} / s$

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