
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
164.1k+ views
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.
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.
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