Water flowing in a vertical pipe

Classical Mechanics Level 1

A tap is opened to fill a bucket, and water flows from the tank through a pipe.

Now, as shown in the diagram, consider two points A A and B B on the vertical part of the pipe which has a uniform cross section.

If the pipe is completely filled with water and the water flows steadily, then at which point is the speed of the water flow greater?

A B Equal at both the points

Rohit Gupta by Rohit Gupta , 34, India

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4 solutions

Maximos Stratis
Jun 11, 2017

Relevant wiki: Continuity Equation (Fluids)

By continuity equation, we know that for incompressible fluids, the volume of liquid entering per second at one end equals the volume of liquid exiting from the other end. Thus, we have:
A 1 v 1 = A 2 v 2 A_{1}v_{1}=A_{2}v_{2}
Since A and B belong in the same pipe we know that : A 1 = A 2 A_{1}=A_{2}
Thus:
v 1 = v 2 v_{1}=v_{2}
So, the speed of the water flow is the same in A and B.

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Chew-Seong Cheong
Jun 13, 2017

Note that water is imcompressible. At a steady state the flowrate throughout the pipe is constant. Since the cross-sectional area of the pipe is constant, the speed of flow is also constant throughout the pipe. Therefore the speed of flow are equal at both the points A A and B B .

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No sir , your answer is NOT OK ، the friction factor will be increased during the length of the pipe so the average speed of the flow through the pipe section will be decreased as the thickness of the attached water film will become bigger and bigger because of the friction to reduce the discharge of flow ، your answer will be OK only if you notice that the pipe is 100% smooth ,

Mahmood. msabtyg@gmail.com

Mahmood Alsaad - 3 years, 11 months ago

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Water is not air. It is practically imcompressible. The flow rate (volume/time) throughout the pipe has to be constant if there is deceleration of flow rate then compression occurs. Friction will affect the overall pressure (head) and reduce the overall flow rate. Notice the other solutions are the same as mine. Pick up a fluid mechanics book and you will find out.

Chew-Seong Cheong - 3 years, 11 months ago

Since the cross-section of the pipe is uniform, the speed at point A is equal to the speed at point B.

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Vinay Shankar
Jun 18, 2017

By the equation of continuity for incompressible fluids, A 1 v 1 = A 2 v 2 A_1 v_1 = A_2 v_2 . Since the pipe is of uniform cross section, A 1 = A 2 A_1 = A_2

⟹ v 1 = v 2 \implies v_1 = v_2 .

Speed of water flow is the same at both points A A and B B .

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