Topic: Fluid Mechanics
Which of the following flow is rotational (where u and v are velocity components in x and y directions respectively)
- A. $u=y; v=(\frac{3}{2}x)$
- B. $u=xy^{2} ; v=x^{2}y$
- C. Both (a) and (b)
- D. None of these
Answer: A. $u=y; v=(\frac{3}{2}x)$
Explanation: A flow is rotational if the angular velocity component $\omega_{z} = \frac{1}{2}\left(\frac{\partial v}{\partial x} - \frac{\partial u}{\partial y}\right)$ is non-zero. For option (a), $\omega_{z} = \frac{1}{2}\left(\frac{3}{2} - 1\right) = \frac{1}{4} \neq 0$, making it rotational. For option (b), $\omega_{z} = \frac{1}{2}(2xy - 2xy) = 0$, making it irrotational.