Question

Water containing air bubbles flows without turbulence through a horizontal pipe which has a region of narrow cross-section. In this region the bubbles.

• A. Move with greater speed and are smaller than in the rest of the pipe
• B. Move with greater speed and are larger in size than in the rest of the pipe
• C. Move with lesser speed and are smaller than in the rest of the pipe
• D. Move with lesser speed and are of the same size as in the rest of the pipe

Answer 1

The correct option is B Move with greater speed and are larger in size than in the rest of the pipe

Since the water flow is assumed to be laminar, we can apply Bernoulli's equation between two points in the flow.

Bernoulli's equation is given by $P+\frac{1}{2}\rho v^2=\text{constant}$

The continuity equation is given by $Av=\text{constant}$

At the narrow section, we have $A$ to be minimum. Thus, $v$ is maximum.

So, the bubbles travel faster at the narrow section.

Since, $v$ is maximum, by Bernoulli's equation, we have $\frac{1}{2}\rho v^2$ also maximum. Thus, $P$ is minimum.

If $P$ is minimum, we have the size of the bubbles as maximum.

Hence, at the minimum cross-section, the bubbles are larger in size and move with greater speed than rest of the pipe.