Topic: Fluid Mechanics
For solid sphere falling vertically downwards under gravity in a viscous fluid, the terminal velocity V varies with diameter D of the sphere as :
- A. $V \propto D^{\frac{1}{2}}$
- B. $V \propto D^2$
- C. $V \propto D$
- D. $V \propto \frac{1}{D}$
Answer: B. $V \propto D^2$
Explanation: According to Stokes' Law, the terminal velocity of a sphere falling in a viscous fluid is given by $V = \frac{(\rho_s - \rho_f) g D^2}{18\mu}$, where $\rho_s$ and $\rho_f$ are the densities of the sphere and fluid, respectively, and $\mu$ is the dynamic viscosity. Therefore, $V$ is directly proportional to the square of the diameter ($D^2$).