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You are studying the laminar flow of water in a pipe at 20˚C. The pipe is...

You are studying the laminar flow of water in a pipe at 20˚C. The pipe is 2 cm in diameter, and the pressure gradient driving the flow is 0.8 Pa/m.

  1. Find the x-sectional average velocity (Poiseuille’s Law) and the maximum velocity achieved at the centerline of the pipe (use the equation for Umax presented in the alternative derivation of Poiseuille’s Law). How many times greater is the maximum velocity compared to the average velocity?
  2. Is this ū/umax ratio constant or does it vary with some other parameter? Prove your answer by deriving an equation for ū/umax from the equations used in part.
  3. Verify that the flow is laminar.

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