GATE2016-3-41

Question

For a two-dimensional flow, the velocity field is $\overrightarrow{u}=\dfrac{x}{x^2+y^2}\hat{i}+\dfrac{y}{x^2+y^2}\hat{j}$  where$\hat{i}$ and $\hat{j}$ 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,$a_y=\dfrac{-y}{(x^2+y^2)^2} \\$
4.  x-component of acceleration,$a_x=\dfrac{-(x+y)}{(x^2+y^2)^2}$

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