Hagen-Poiseuille equation for laminar flow of a viscous fluid (11-30)
Question
Volume flow rate of fluid through a pipe
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Review
Figure 11-36 shows the laminar flow of fluid within a circular pipe seen in cross section. Due to friction, the fluid that’s right up against the inside walls of the pipe doesn’t move at all. This is the no-slip condition that we described in Section 11-9. (The fluid in contact with the lower plate in Figure 11-34 behaved the same way.) The fluid a small distance from the walls moves a little, the fluid a bit farther away moves a bit faster, and so on. The fastest flow is at the very center of the pipe. This flow pattern is called parabolic (since the dashed curve in Figure 11-36 is a parabola lying on its side). A derivation using calculus gives the following expression, called the Hagen-Poiseuille equation, relating the pressure difference between the two ends of the pipe to the resulting flow rate. (Non-French speakers can pronounce Poiseuille as “pwa-zoo-yah.”)
