Question

When Water falls from a tap, down the streamline
A. Area decreases
B. Area increases
C. Velocity remains the same
D. Area remains the same

Answer 1

Hint:Before solving this question one should know about gravitational force, pressure, and surface tension and we need to use the equation of continuity that is, \[{A_1}{v_1} = {A_2}{v_2}\]. Here A is the area of cross-section and V is the velocity, using this formula we are going to find the solution to the problem.

Formula Used:
From the principle of continuity, the formula is,
\[{A_1}{v_1} = {A_2}{v_2}\]
Where, \[{A_1},{A_2}\] is the area and \[{v_1},{v_2}\] is the speed of water.

Complete step by step solution:
Consider the water falling from a tap, down the streamline. We need to find what happens to the velocity and area. If we consider a tap, at the starting point we have \[{{\rm{A}}_{\rm{1}}}\] flowing with a velocity \[{{\rm{v}}_{\rm{1}}}\]. As we go down the area becomes \[{{\rm{A}}_{\rm{2}}}\] flowing with a velocity \[{{\rm{v}}_{\rm{2}}}\].

As the water falls from a tap, down the streamline, the area starts decrease due to the increase in velocity of water as it experiences gravity, that is, by the equation of continuity, we have
\[{{\rm{A}}_1}{{\rm{v}}_1}{\rm{ = }}{{\rm{A}}_2}{{\rm{v}}_{\rm{2}}}\]
Therefore, when water falls from a tap, down the streamline the area decreases.

Hence, option A is the correct answer.

Note:The concept of continuity used in the above solution is applied to a flowing fluid in terms of mass conservation, that is, assume that a certain mass of fluid ‘m’ enters a pipe (domain) from one end and exits at the other end. According to the equation of continuity, the mass (m) entering the system should match the mass exiting the system.