Question

In a laminar flow experiment two fluid A and B are flowing into two identical pipes at the same Reynolds number and at the same volumetric flow rate. The densities of fluid A and B are same but the pressure drop per unit length is 2 times in case of B than that of A. The ratio of dynamic viscosity of fluid A to B is

• A. $\frac{1}{4}$
• B. $4$
• C. $\frac{1}{2}$
• D. 2

Answer 1

The correct option is C $\frac{1}{2}$

For laminar flow, dynamic viscosity is given by

$\mu =\frac{\pi D^4\Delta P}{128QL}$

$\text{Where, D = diameter of pipe}$

$\Delta \text{P = pressure drop per unit length}$

$\text{Q = discharge flow rate}$

$\text{L = length of pipe}$

$\text{From equation (i),}\mu \propto \Delta P$

$\frac{{\mu }_A}{{\mu }_B}=\frac{\Delta P_A}{\Delta P_B}=\frac{1}{2}$