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For an incompressible flow field, V which one of the following conditions must be satisfied?

1. ∇ · V = 0
2. ∇ × V = 0
3. (V · ∇)V = 0
4. ∂V/∂t + (V · ∇)V = 0

Correct answer: ∇ · V = 0

Solution

For an incompressible flow, the divergence of the velocity field must be zero, indicating that the fluid density remains constant and there is no net flow of fluid into or out of any infinitesimal volume.

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