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A plane flow has velocity components u = x/T₁, v = -y/T₂ and w = 0 along x, y and z directions respectively, where T₁ (≠ 0) and T₂ (≠ 0) are constants having the dimension of time. The given flow is incompressible if

1. T₁ = -T₂
2. T₁ = -T₂/2
3. T₁ = T₂/2
4. T₁ = T₂

Correct answer: T₁ = T₂

Solution

The flow is incompressible if the divergence of the velocity field is zero. In this case, setting T₁ equal to T₂ ensures that the contributions from the x and y components of velocity balance out, resulting in a divergence of zero.

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