Water is flowing on a horizontal fixed surface, such that its flo… - Vidyadip

MCQ

Water is flowing on a horizontal fixed surface, such that its flow velocity varies with $y$ (vertical direction) as $v=k\left(\frac{2 y^2}{a^2}-\frac{y^3}{a^3}\right)$. If coefficient of viscosity for water is $\eta$, what will be shear stress between layers of water at $y=a$.

✓
$\frac{\eta k}{a}$
B
$\frac{\eta}{k a}$
C
$\frac{\eta a}{k}$
D
None of these

✓

Answer

Correct option: A.

$\frac{\eta k}{a}$

a
(a)

Newton's law of viscosity, $F=\eta A \frac{d v}{d y}$

$\text { Stress }=\frac{F}{A}=\eta\left(\frac{d v}{d y}\right)=\eta k\left(\frac{4 y}{a^2}-\frac{3 y^2}{a^3}\right)$

$\text { At } y=a, \text { stress }=\eta k\left(\frac{4}{a}-\frac{3}{a}\right)=\frac{\eta k}{a}$

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