Question

Two capillary tubes A and B are arranged in parallel. A liquid flows through these capillary tubes under the same pressure head. Both the tubes have the same length. The radii of A and B are $r$ and $\frac{r}{2}$ respectively. If the rate of flow of liquid through A is $8{cm}^3/s$, then the rate of flow through the combination of A and B is:

• A. $8.0{cm}^3/s$
• B. $8.5{cm}^3/s$
• C. $12.75{cm}^3/s$
• D. $16{cm}^3/s$

Answer 1

The correct option is B $8.5{cm}^3/s$

From Poiseuille equation, flow rate is given by:

$\Phi =\frac{\pi R^4\Delta P}{8\eta L}$

Given, $\Delta P$ and $L$ are same for both.

Hence, $\Phi \propto R^4$

$R_2=r/2=R_1/2$

$⟹{\Phi }_2={\Phi }_1/16=8/16=0.5{cm}^3/s$

Pipes are in parallel, hence total flow rate is sum of the two flow rates.

$\Phi ={\Phi }_1+{\Phi }_2=8.5{cm}^3/s$