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Mechanical Properties of Fluids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMechanical Properties of Fluids2 Marks
Question
The velocity of water in a river is $18 \mathrm{~km} \mathrm{~h}^{-1}$ near the surface. If the river is 5 m deep, find the shearing stress between horizontal layers of water. The coefficient of viscosity of water $10^{-2}$ poise.
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Answer

As the velocity of water at the bottom of the river is zero,$\text{dv}=18\text{km h}^{-1}$
$=18\times\frac{5}{18}=5\text{ms}^{-1}$
Also, dx = 5m, $\eta=10^{-2}\text{poise}=10^{-3}\text{Pa-s}$ Force of viscosity $\text{F}=\eta\text{A}\frac{\text{dv}}{\text{dx}}$ We know that, shering strees $=\frac{\text{F}}{\text{A}}$$\Rightarrow\frac{\text{F}}{\text{A}}=\eta\frac{\text{dv}}{\text{dx}}$
$=\frac{10^{-3}\times5}{5}=10^{-3}\text{Nm}^{-2}$

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