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Question

For a flow, the velocity components are given by u=(λxy2x3y2) and v=(x2y33y3). What is the value of λ for the possible flow field which includes steady incompressible flow ?

A
3
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B
5
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C
7
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D
9
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Solution

The correct option is D 9
Data given : Velocity component :

u=λxy2x3y2

v=x2y33y3

For steady incompressible flow to exist, continuity equation must be satisfied .
ux+vy=0

(2-dimension continuity equation)

ux=λy23x2y2

vy=x2(3y2)3×3y2=3x2y29y2

ux+vy=λy23x2y2+3x2y29y2=0
λ=9

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