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 ______ m. (Co-efficiency of viscosity of water is $10^{-2} \mathrm{~Pa.s}$)

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Fluid Mechanics

The velocity of upper layer of water in a river is

36 kmh^{- 1}

. Shearing stress between horizontal layers of water is

1 0^{- 3} Nm^{- 2}

. Depth of the river is ______ m. (Co-efficiency of viscosity of water is

1 0^{- 2} Pa.s

)

Answer: 100

Solution

The shearing stress in a viscous fluid is given by:

\frac{F}{A} = η \frac{d v}{d y}

where

η

is the coefficient of viscosity and

\frac{d v}{d y}

is the velocity gradient.

Converting velocity:

v = 36 km/h = 36 \times \frac{1000}{3600} = 10 m/s

Substituting:

1 0^{- 3} = 1 0^{- 2} \times \frac{10}{h}

h = \frac{10 \times 1 0 ^{- 2}}{1 0 ^{- 3}} = 100 m

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Integer answer

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