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The velocity of upper layer of water in a river is 36 \mathrm{kmh}^{-1}. Shearing stress between horizontal layers of water is 10^{-3} \mathrm{Nm}^{-2}. Depth of the river is__________\mathrm{m}. (Co-efficient of viscosity of water is 10^{-2} \mathrm{~Pa} . \mathrm{s} )

Option: 1

100


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{V= 36\, \frac{km}{hr}= 10\, m/s}


By Newton's law for laminar flow ,

\mathrm{F= \eta A\left ( \frac{dv}{dx} \right )}
\mathrm{Shearing\: stress= \left ( \frac{F}{A} \right )= \eta \left ( \frac{\Delta v}{\Delta x} \right )}
\mathrm{10^{-3}= 10^{-2}\frac{\left ( v-0 \right )}{\left ( Depth \right )}}

\mathrm{Depth\: of\; river= 100\, m}

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manish

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