Question

If $V_1$ and $V_2$ be the volume of two liquids flowing out of the same tube in the same interval of time and ${\eta }_1$ & ${\eta }_2$ are their coefficients of viscosity, then

• A. $\frac{{\eta }_1}{{\eta }_2}=\frac{V_2}{V_1}$
• B. $\frac{{\eta }_1}{{\eta }_2}=\frac{V_1}{V_2}$
• C. $\frac{{\eta }_1}{{\eta }_2}=\frac{V_1^2}{V_2^2}$
• D. $\frac{{\eta }_1}{{\eta }_2}=\frac{V_2^2}{V_1^2}$

Answer 1

The correct option is A $\frac{{\eta }_1}{{\eta }_2}=\frac{V_2}{V_1}$

According to Poiseuille’s equation volumetric flow rate under same pressure gradient in same tube is inversely proportional to the viscosity of the liquid given by $\frac{\partial V}{\partial t}=\frac{\pi R^4\Delta P}{8\eta L}$

Therefore $\frac{{\eta }_1}{{\eta }_2}=\frac{V_2}{V_1}$

Answer. A