Question

Water coming out of the mouth of a tap and falling vertically in streamline flow forms a tapering column, i.e., the area of cross-section of the liquid column decreases as it moves down. Which of the following is the most accurate explanation?

• A. As the water moves down, its speed increases and hence, its pressure decreases. It is then compressed by the atmosphere.
• B. Falling water tries to reach a terminal velocity and hence, reduces the area of cross section to balance upward and downward forces.
• C. The mass of water flowing past any cross-section must remain constant. Also, water is almost incompressible. Hence, the rate of volume flow must remain constant. As this is equal to velocity $\times$ area, the area decreases as velocity increases.
• D. The surface tension causes the exposed surface area of the liquid to decrease continuously.

Answer 1

Answer: (C)

The mass of water flowing past any cross-section must remain constant. Also, water is almost incompressible. Hence, the rate of volume flow must remain constant. As this is equal to velocity $\times$ area, the area decreases as velocity increases.

For the water flowing from tap, using equation of continuity- $A_1{V}_1=A_2{V}_2$

where $A$ = cross-section area of water

$V$ = velocity of water

As water goes down its velocity increases due to gravitational force so cross-sectional area will decrease as velocity increases.