Question

A tube of radius R and length L is connected in series with another tube of radius $\frac{R}{2}$ and length $\frac{L}{8}$. If the pressure across the tubes taken together is P, the pressure across the two tubes separately are:

• A. $\frac{P}{2}$ and $\frac{P}{2}$
• B. $\frac{P}{3}$ and $\frac{3P}{2}$
• C. $\frac{P}{4}$ and $\frac{3P}{2}$
• D. $\frac{P}{3}$ and $\frac{2P}{3}$

Answer 1

The correct option is D $\frac{P}{3}$ and $\frac{2P}{3}$

Flow rate = $\frac{\pi \Delta P{r}^4}{8\eta L}$

Let pressure drop across tube 1 be $P_1$ and tube 2 be$P_2$

Then $P_1+P_2=P$ eq(1)

Also flow rate should be equal in both tube

=>$\frac{\pi P_1{R}^4}{8\eta L}=\frac{\pi P_2{R}^{4}8}{8\eta L\times 16}$

=>$2P_1=P_2$

Replacing in eq(1)

=> $P_1=\frac{P}{3}$

$P_2=\frac{2P}{3}$

Answer. D