Question

Two capillary tubes of same radius but lengths $l$ and $2l$ are connected in series to the bottom of a vessel containing water. The length of a single tube of same radius that can replace the two tubes so that pressure difference across the single tube is equal to total pressure difference across the combination is :

• A. $3l$
• B. $\frac{2l}{3}$
• C. $1.5l$
• D. $\frac{l}{3}$

Answer 1

The correct option is A $3l$

So, $P$ be pressure difference across the combination of according to Question,

Let $P_1$ be pressure at function,

$\frac{(P-P_1)}{L}=\frac{P_1}{2L}$ [from poiseulli's equation]

$\Rightarrow 2P-2P_1=P_1$

$\Rightarrow \frac{2P}{3}=P_1$------------(1)

So,

$\Rightarrow \frac{\pi P{r}^4}{8\eta L_1}=8Q_{in}\left(1\right)=\frac{\pi 2P{r}^4}{8\eta 32L}$

$\Rightarrow \frac{P}{L_1}=\frac{P}{3L}$

$\Rightarrow L_1=3L$