A very small particle of diameter $d_{p}$ and density $\rho_{p}$ freely settles at constant velocity in a tank of depth $L$ containing liquid of viscosity $\mu_{l}$. The density of the liquid is $\rho_{l}$ where $\rho_{l}<\rho_{p}$. The velocity of particle in the liquid can be expressed as

(A) $\frac{g L\left(\rho_{p}-\rho_{l}\right) d_{p}}{18 \mu_{l}}$

(B) $\frac{g\left(\rho_{p}-\rho_{l}\right) d_{p}^{3}}{18 L \mu_{l}}$

(C) $\frac{g\left(\rho_{p}-\rho_{l}\right) d_{p}^{2}}{18 \mu_{l}}$

(D) $\frac{g\left(\rho_{p}-\rho_{l}\right) L^{2}}{18 \mu_{l}}$

A very small particle of diameter $d_{p}$ and density $\rho_{p}$ freely settles at constant velocity in a tank of depth $L$ containing liquid of viscosity $\mu_{l}$. The density of the liquid is $\rho_{l}$ where $\rho_{l}<\rho_{p}$. The velocity of particle in the liquid can be expressed as

(A) $\frac{g L\left(\rho_{p}-\rho_{l}\right) d_{p}}{18 \mu_{l}}$

(B) $\frac{g\left(\rho_{p}-\rho_{l}\right) d_{p}^{3}}{18 L \mu_{l}}$

(C) $\frac{g\left(\rho_{p}-\rho_{l}\right) d_{p}^{2}}{18 \mu_{l}}$

(D) $\frac{g\left(\rho_{p}-\rho_{l}\right) L^{2}}{18 \mu_{l}}$

1 Answer

127 votes

(C) $\frac{g\left(\rho_{p}-\rho_{l}\right) d_{p}^{2}}{18 \mu_{l}}$

127 votes

127