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Consider a velocity vector, V in (x, y, z) coordinates given below. Pick one or more CORRECT statement(s) from the choices given below. V = ux̂ + vŷ

1. z-component of Curl of velocity: ∇ × V = ((∂ v)/(∂ x) - (∂ u)/(∂ y))ẑ
2. z-component of Curl of velocity: ∇ × V = ((∂ u)/(∂ x) - (∂ v)/(∂ y))ẑ
3. Divergence of velocity: ∇ · V = ((∂ u)/(∂ x) + (∂ v)/(∂ y))
4. Divergence of velocity: ∇ · V = ((∂ u)/(∂ y) + (∂ v)/(∂ x))

Correct answer: z-component of Curl of velocity: ∇ × V = ((∂ v)/(∂ x) - (∂ u)/(∂ y))ẑ

Solution

The correct option accurately represents the z-component of the curl of a two-dimensional velocity vector field, which is defined as the difference between the partial derivative of the y-component with respect to x and the partial derivative of the x-component with respect to y.

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