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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(2y2a2y2a2) . 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

ηak

b

2ηka

c

ηka

d

ηk2a

answer is A.

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Detailed Solution

Newton’s law of velocity,  F=ηAdvdy
Stress=F=η(dvdy)=ηk(4ya23y2a3)
At Y = a, stress =  ηk(4a3a)=ηka
 

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