Question

A liquid flows through two capillary tubes A and B connected in series. The length and radius of B are twice that of A. The ratio of pressure difference across A and across B is:

• A. 4
• B. 2
• C. 1
• D. 8

Answer 1

The correct option is D 8

By poiseuille's equation,

$\Delta P=\frac{8\mu LQ}{\pi r^4}$

where

$\Delta P:$ Pressure Difference

$\mu :$ Viscosity

$L:$ Length of the tube

$Q:$ Volumetric flow rate

$r:$ Radius

Since, the tubes are in series flow rate ($Q$) is same.
Given $L_B=2L_{A}and{r}_B=2r_A$

$\frac{\Delta P_A}{\Delta P_B}=\frac{L_A{r}_B^4}{r_A^4{L}_B}=\frac{2^4}{2}=8$