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## Hagen-Poiseuille flowThe flow of fluid through a pipe of uniform (circular) cross-section is known as Hagen-Poiseuille flow. The Hagen-Poiseuille flow is an exact solution of the Navier-Stokes equations in fluid mechanics. The equations governing the Hagen-Poiseuille flow can be derived from the Navier-Stokes equation in cylindrical coordinates by making the following set of assumptions: - The flow is steady ( ).
- The radial and swirl components of the fluid velocity are zero (
*u*_{r}=*u*_{θ}= 0 ). - The flow is axisymmetric ( ) and fully developed ( ).
## Additional recommended knowledge
- The solution is
Since Thus we have finally the following parabolic velocity profile: The maximum velocity occurs at the pipe centerline (r=0): The average velocity can be obtained by integrating over the pipe cross-section: Internal Links: |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Hagen-Poiseuille_flow". A list of authors is available in Wikipedia. |