Solution of the Navier-Stokes: Hagen-Poiseuille Flow

MEC516/BME516 Fluid Mechanics, Chapter 4 Differential Relations for Fluid Flow, Part 6: Exact solution of the Navier-Stokes and Continuity equations for fully developed laminar flow in a round pipe (Hagen-Poiseuille Flow). The video ends with a numerical example.

Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.

#fluidmechanics #fluiddynamics

[pranavlimaye]

Slowly falling in love with the Navier-Stokes Equation. Brilliantly explained, Professor. Thank you!

[ingGS]

Thanks for the content professor. I have thoroughly enjoyed your videos.

[DonnyHadden]

At 8:54 you said that for the C1/r term that dividing by zero would make the term go singular, and the only way for the equation to be true is if C1 was equal to zero. I'm a little confused because 0/0 is still undefined?

It may be due to the fact that at r=0, polar coordinates are not able definitively specify a location. Because at r=0 any angle theta will result in the location being at the origin. However, because we know the flow is symmetric about theta, any angle theta will result in the same value at any distance r. Therefore, we can conclude C1 must be zero at r=0.

[pidgeonengineer]

Professor why don't you have more subscribers rn wow