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Question

The velocity of water in a river is 18 kmh1 near the surface. If the river is 5 m deep, then the shearing stress between the surface layer and the bottom layer is:
(Given - coefficient of viscosity of water, η=103 Pa.s)

A
102 Nm2
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B
103 Nm2
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C
104 Nm2
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D
105 Nm2
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Solution

The correct option is B 103 Nm2
Since the velocity of water in contact with the bottom of the river is zero,
Δv=18 kmh1=18×518=5 ms1
Also, Δz=5 m,η=103 Pa.s
Velocity gradient is given as,
ΔvΔz=55=1 s1
Viscous force is,
Fv=ηAdvdz
Shearing stress will be,
σs=FvA=ηdvdz=ηΔvΔz
σs=103×1=103 Nm2

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