Question

Water flows through a horizontal pipe with a velocity of 2 m/s. The cross-sectional area of the pipe reduces to half. What is the velocity of water in the narrower section?

• A. 1 m/s
• B. 2 m/s
• C. 4 m/s
• D. 8 m/s

Hint:

Use the continuity equation $A_1v_1 = A_2v_2$ to relate flow speeds in pipes of varying cross-section. If area halves, velocity doubles.

Answer 1

The Correct Option is C

The continuity equation for an incompressible fluid, also known as the principle of conservation of mass, states that \[ A_1 v_1 = A_2 v_2 \]. With the given values \( v_1 = 2 \, \text{m/s} \) and \( A_2 = \frac{1}{2}A_1 \), substituting into the equation yields \( A_1 \cdot 2 = \frac{1}{2}A_1 \cdot v_2 \). Simplifying this equation results in \( 2 = \frac{1}{2} v_2 \), which further simplifies to \( v_2 = 4 \, \text{m/s} \).