Uploaded December 2017 | Updated September 2026, 3 weeks ago
In this video, I use the Navier-Stokes Equations to derive Poiseuille's Law (aka. The Hagen-Poiseuille Equation). This is a rather simple derivation carried out by simplifying Navier-Stokes in cylindrical coordinates, making some substitutions, and determining the solution of the resulting ODE. The end result is a parabolic velocity profile for laminar flow of an incompressible, Newtonian fluid in a cylindrical pipe.
This velocity profile is then used to deduce the relationship between the pressure difference and the radius of the cylindrical pipe (it turns out to be a 1/R^4 dependence). Once Poiseuille's Law is derived, I use it to discuss the significance of the pressure-flow rate-radius relationship in the clinical context.
Questions/requests? Let me know in the comments!
Prerequisites: Basic knowledge of Fluid Mechanics and the Navier-Stokes equations. I plan on adding to this playlist in the future so hopefully I can replace this line by actual video links some day.
Lecture Notes: drive.google.com/open?id=1i_MFl_Em7466GrhRYLPfOkP_t-LbLNn4
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons:
- Jennifer Helfman
- Justin Hill
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
In this video, I use the Navier-Stokes Equations to derive Poiseuille's Law (aka. The Hagen-Poiseuille Equation). This is a rather simple derivation carried out by simplifying Navier-Stokes in cylindrical coordinates, making some substitutions, and determining the solution of the resulting ODE. The end result is a parabolic velocity profile for laminar flow of an incompressible, Newtonian fluid in a cylindrical pipe.
This velocity profile is then used to deduce the relationship between the pressure difference and the radius of the cylindrical pipe (it turns out to be a 1/R^4 dependence). Once Poiseuille's Law is derived, I use it to discuss the significance of the pressure-flow rate-radius relationship in the clinical context.
Questions/requests? Let me know in the comments!
Prerequisites: Basic knowledge of Fluid Mechanics and the Navier-Stokes equations. I plan on adding to this playlist in the future so hopefully I can replace this line by actual video links some day.
Lecture Notes: drive.google.com/open?id=1i_MFl_Em7466GrhRYLPfOkP_t-LbLNn4
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons:
- Jennifer Helfman
- Justin Hill
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
