A fluid element has a velocity V = -y2. xi + 2yx2 . j. The motion at (x, y) = (1/√2, 1) is_________________?
Correct answer: B. Rotational and compressible
- A. Rotational and incompressible
- B. Rotational and compressible
- C. Irrotational and compressible
- D. Irrotational and incompressible
Explanation
With u = -xy^2 and v = 2x^2y, the divergence at the stated point is -y^2 + 2x^2 = -1 + 1 = 0, so the flow is incompressible. The vorticity component is ∂v/∂x - ∂u/∂y = 6xy, which is nonzero, making it rotational.
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