Three capillary tubes of same length but internal radii 0.3 mm .0 .45 and 0.6 mm are connected in se

Question

Three capillary tubes of same length but internal radii 0.3 mm .0 .45 and 0.6 mm are connected in series and liquid flows steadily through them. If the pressure difference across the third capillary is 8.1 mm of mercury, the pressure difference across the first capillary (in mm of mercury) is\

Professor PC Thomas Classes · Answer

The rate of flow of liquid through capillary tube is\ $\mathrm{V}=\frac{\pi \mathrm{Pr}^{4}}{8 \eta \ell}$\ Here, volume of liquid flow per second is constant all of tubes\ $	herefore \mathrm{P} \propto \frac{1}{\mathrm{r}^{4}}$\ $	herefore \frac{\mathrm{P}_{3}}{\mathrm{P}_{1}}=\left(\frac{\mathrm{r}_{1}}{\mathrm{r}_{3}}ight)^{4}$\ $\frac{8.1}{\mathrm{P}_{1}}=\left(\frac{0.3}{0.6}ight)^{4}$\ $\Rightarrow \mathrm{P}_{1}=16 	imes 8.1=129.6 \mathrm{~mm}$ of mercury\