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Q.

Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as $v = k (\frac{2 y^{2}}{a^{2}} - \frac{y^{2}}{a^{2}})$ . If coefficient of viscosity of water is $η$ . What will be the force per unit area along the layers acting between layers of water at y = a.

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a

$\frac{η a}{k}$

b

$\frac{2 η k}{a}$

c

$\frac{η k}{a}$

d

$\frac{η k}{2 a}$

answer is A.

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Detailed Solution

Newton’s law of velocity, $F = η A \frac{d v}{d y}$
$S t r e s s = F = η (\frac{d v}{d y}) = η k (\frac{4 y}{a^{2}} - \frac{3 y^{2}}{a^{3}})$
At Y = a, stress = $η k (\frac{4}{a} - \frac{3}{a}) = \frac{η k}{a}$

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Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as v=k(2y2a2−y2a2) . If coefficient of viscosity of water is η. What will be the force per unit area along the layers acting between layers of water at y = a.