Question

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

Answer 1

The rate of flow of liquid through both tubes are same.
$\therefore Q=\frac{\pi p_1{r}_1^4}{8\eta l_2}=\frac{\pi p_2{r}_2^4}{8\eta l_2}$
$\therefore \frac{p_1}{p_2}={\left(\begin{array}{c}\frac{r_2}{r_1}\end{array}\right)}^4\times \frac{l_1}{l_2}$
$={\left(\begin{array}{c}\frac{2r}{r}\end{array}\right)}^4\times \frac{l}{2l}$
$=16\times \frac{1}{2}=8$