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The velocity of water in a river is $18 k m / h r$ at the surface. If the river is $5 m$ deep and the flow is streamlined, find the shearing stress between the horizontal layers of water assuming uniform veloicty gradient. Viscosity of water is $10^{- 3}$ poiseuille.

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$1 x 10^{- 3} N / m^{3}$

$10^{- 3} N / m^{3}$

$2 x 10^{- 3} N / m^{2}$

$4$

answer is A.

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Detailed Solution

$\frac{d v}{d y} = \frac{18 x 10^{3}}{60 x 60 x 5} = 1 s^{- 1} \frac{F}{A} = η \frac{d v}{d y} = 10^{- 3} x 1 = 1 x 10^{- 3} N / m^{2}$

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