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Two pipes are smoothly connected together without leaks. One has a diameter of 3 cm and the other has a diameter of 5 cm. Water flows through the pipes. In which pipe is the flow speed the greatest? in which pipe is the volume flow rate the greatest?

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Answer:

  1. The speed will be the greatest in the smaller pipe
  2. The volume flow rate is the same in both pipes

Explanation:

This question can be answered using the equation of continuity. Which is

V = A1v1 = A2v2

where V is the volume flow rate

           A is the cross sectional area of the pipe at that position

           v is the velocity of the flow at that point.

From the equation we can see the volume flow rate does not change even as the area and flow speed change. Which is consistent with the assumptions used in this equation which is that

  • The tube must one entry and one exit.
  • The fluid in question is non-viscous.
  • The fluid is incompressible.
  • The flow is steady.  

If the temperature does not change, meaning there is not expansion/contraction and it is incompressible then the volume flow rate does not change.

And the speed will be higher in the pipe with the smaller diameter because area and speed are inversely related.

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