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For a two-dimensional flow, the velocity field is u = (x)/(x²+y²)î + (y)/(x²+y²)ĵ, where î and ĵ are the basis vectors in the x-y Cartesian coordinate system. Identify the CORRECT statements from below. (1) The flow is incompressible. (2) The flow is unsteady. (3) y-component of acceleration, a_y = (y)/(x²+y²) (4) x-component of acceleration, aₓ = (x+y)/(x²+y²)

1. (A) (2) and (3)
2. (B) (1) and (3)
3. (C) (1) and (2)
4. (D) (3) and (4)

Correct answer: (B) (1) and (3)

Solution

The flow is incompressible because the divergence of the velocity field is zero, indicating that the density remains constant. The y-component of acceleration is correctly derived from the velocity field, confirming that statement (3) is accurate.

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