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The 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:
Additional recommended knowledge
Since uz needs to be finite at r = 0, c1 = 0. The no slip boundary condition at the pipe wall requires that uz = 0 at r = R (radius of the pipe), which yields
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:
|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.|