Question

In a laminar flow experiment, Fluid A is pumped through a straight tube and the volumetric flow rate and pressure drop per unit length are recorded. In a second straight tube having twice the internal diameter of the first one, Fluid B records the same pressure drop per unit length at the same volumetric flow rate. Assuming fully developed flow conditions in the tubes, the ratio of the dynamic viscosity of Fluid B to that of Fluid A is

• A. 16
• B. 32
• C. 64
• D. 128

Answer 1

The correct option is A 16

$Q_A=\frac{\pi r_A^4(P_1-P_2)}{8\mu L}$

Since, $(P_1-P_2)$ is constant, and all other variables are also made constant in the second experiment.
So,

$\frac{\pi (P_1-P_2)}{8\mu L}=k\left(say\right)$

$\therefore Q_A=k{r}_A^4$

$\text{and also}{Q}_B=k{r}_B^4$

$\text{put,}{r}_B=2r_A$

$\therefore Q_B=k(2r_A{)}^4=16k{r}_A^4$

Dividing (ii) by (i) we get,

$\frac{Q_B}{Q_A}=\frac{16k{r}_A^4}{k{r}_A^4}=16$