Question

Two capillaries of same length and radii in the ratio 1: 2 are.connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is 1 m of water, the pressure difference across first capillary is

• A. 9.4 m
• B. 4.9 m
• C. 0.49 m
• D. 0.94 m

Answer 1

The correct option is D 0.94 m

Here, $l_1=l_2=1m$ and $\frac{r_1}{r_2}=\frac{1}{2}$

As $V=\frac{\pi P_1{r}_1^4}{8\eta l}=\frac{\pi P_2{r}_2^4}{8\eta l}$ or $\frac{P_1}{P_2}={\left(\frac{r_2}{r_1}\right)}^4=16$

$\therefore P_1=16P_2$

Since, both tubes are connected in series, hence pressure difference across the combination is

$P=P_1+P_2$ $\Rightarrow$ $1=P_1+\frac{P_1}{16}$

or $P_1=\frac{16}{17}=0.94m$