Question

A fluid flows through a pipe with varying cross-section. If the velocity at the narrow section is 3 m/s and the cross-sectional area is half of the wider section, what is the velocity in the wider section?

• A. 1.5 m/s
• B. 6 m/s
• C. 0.5 m/s
• D. 3 m/s

Hint:

In fluid flow, the equation of continuity ensures that \( A_1 v_1 = A_2 v_2 \) when the fluid is incompressible and steady.

Answer 1

The Correct Option is A

Apply the principle of continuity.
The continuity equation is expressed as: \[ A_1 v_1 = A_2 v_2 \] If the wider section's area is denoted by \( A \), then the narrow section's area is \( \frac{A}{2} \). The velocity in the narrow section is \( v_1 = 3 \, \text{m/s} \) with an area \( A_1 = \frac{A}{2} \). For the wider section, the area is \( A_2 = A \), and the velocity is \( v_2 = ? \). Substituting these values into the equation: \[ \frac{A}{2} \cdot 3 = A \cdot v_2 \Rightarrow \frac{3A}{2} = Av_2 \Rightarrow v_2 = \frac{3}{2} = 1.5 \, \text{m/s} \]