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 x area, the area decreases as velocity increases.
(D). The surface tension causes the exposed surface area of the liquid to decrease continuously.

Answer 1

Hint: Before attempting this question one must have prior knowledge of gravitational force, pressure and surface tension and remember to use the equation of continuity I.e. ${A_1}{V_1} = {A_2}{V_2}$ Here A is the area of cross-section and V is the velocity, using this information will help you to approach closer towards the solution to the problem.

Complete step-by-step solution -

According to the given information water is falling from the tap vertically with respect to ground in streamline flow and as the water moves down its cross section decreases
So as we know that as the water will fall down from the tap due to the force of gravitational speed of water will increase and the pressure will decrease and as the water gets compressed by the atmospheric pressure it will try to achieve terminal velocity due to which its area of cross section decreases
So as we know that 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 x area, the area decreases as velocity increases.
Hence the option C is the correct option.

Note: The concept of continuity which we used in the above solution can be explained as the equilibrium condition of fluid in motion according to which a flowing liquid flows in such a way that its mass remain conserved and it is given by the equation of continuity which represents the product of area of cross section area of pipe through which fluid is flowing and the speed of fluid inside any point of pipe in such a way that the product of area of cross section of pipe and speed of fluid remains constant i.e. R = AV = constant.