Question

A pipe network consists of a pipe of 60 cm diameter and branches out at a point T into two branches, one of 30 cm diameter and the other of 45 cm diameter. These branch pipes rejoin at a point B. The velocity in the first branch (of 45 cm diameter) is 1.5 m/sec. Which one of the following statements is true?

• A. The velocity in the second branch is 1.0 m/sec.
• B. The velocity in the second branch is 2.25 m/sec.
• C. The velocity in the second branch is $\frac{2}{3}=0.667m/sec$.
• D. The potential drop between T and B in both branches is the same.

Answer 1

The correct option is D The potential drop between T and B in both branches is the same.

From T to B the branches are parallel to each other. Therefore head loss in both pipes will be same.

$h_f=f\frac{L}{d_1}\frac{V_1^2}{2g}=f\frac{L}{d_2}\frac{V_2^2}{2g}$

$\therefore \text{Velocity in second branch,}$

$V_2=V_1\sqrt{\frac{d_2}{d_1}}=1.5\times \sqrt{\frac{30}{45}}=1.23\text{m/s}$