Question

Two different liquids are flowing in two tubes of equal radius. The ratio of coefficient of viscosity of liquids is $52:49$ and the ratio of their densities is $15.6:1,$ then the ratio of their critical velocities will be:

• A. 0.068
• B. 0.68
• C. 6.8
• D. 68

Answer 1

Answer: (A)

0.068

The critical velocity depends on coefficient of viscosity $\eta$, density of the liquid $\rho$, and radius of the tube $r$ as given by:

$v_c=\frac{K\eta }{\rho r}$ where $K$ is the constant of proportionality
$\Rightarrow \frac{v_{c_1}}{v_{c_2}}=\frac{\frac{K{\eta }_1}{{\rho }_1{r}_1}}{\frac{K{\eta }_2}{{\rho }_2{r}_2}}=\frac{{\eta }_1}{{\eta }_2}\times \frac{{\rho }_2}{{\rho }_1}\times \frac{r_2}{r_1}\Rightarrow \frac{v_{c_1}}{v_{c_2}}=\frac{52}{49}\times \frac{1}{15.6}\times 1=0.068$