Question 11: When water falls from a tap, its cross-sectional area decreases as it comes down. Explain why?

ANSWER

When water emerges from the mouth of the tap, it falls down under the action of gravity (apart from the pressure of water behind). The acceleration of downward motion of water is equal to the gravitational acceleration, g. Therefore, while falling vertically down, the velocity of water increases every moment. Therefore, the velocity of water at the starting point is less as compared to the velocity near the ground.

Water is incompressible fluid. Therefore, it follows the equation of continuity.

Where A₁ and v₁ are the cross-section and velocity of water at the start and A₂ and v₂ are the corresponding values near the ground.

Therefore, the cross-sectional area of water is inversely proportional to the velocity of water at any instant. When water comes down, its velocity increases and correspondingly, the cross-sectional area decreases.