Question

A fluid of density \( 800 \, \text{kg/m}^3 \) is flowing through a pipe of varying cross-sectional area. The velocity of the fluid at point A is \( 2 \, \text{m/s} \), and the velocity at point B is \( 4 \, \text{m/s} \). If the cross-sectional area at point A is \( 1 \, \text{m}^2 \), find the cross-sectional area at point B.

• A. \( 0.5 \, \text{m}^2 \)
• B. \( 1.5 \, \text{m}^2 \)
• C. \( 2.0 \, \text{m}^2 \)
• D. \( 4.0 \, \text{m}^2 \)

Hint:

In fluid dynamics, the principle of continuity ensures that the mass flow rate remains constant in an incompressible fluid. This means that if the velocity of the fluid increases, the cross-sectional area must decrease.