Peter's Physics Pages

An introduction to Electricity and Strength of Materials with Peter Eyland

Poiseuille's Law Derivation

Consider a solid cylinder of fluid, of radius r inside a hollow cylindrical pipe of radius R. The driving force on the cylinder due to the pressure difference is: The viscous drag force opposing motion depends on the surface area of the cylinder (length L and radius r): In an equilibrium condition of constant speed, where the net force goes to zero. We know empirically that the velocity gradient should look like this: At the centre • r=0 • • v is at its maximum. At the edge • r=R • v=0

From the velocity gradient equation above, and using the empirical velocity gradient limits, an integration can be made to get an expression for the velocity. Which has a parabolic form as expected.

Now the equation of continuity giving the volume flux for a variable speed is: Substituting the velocity profile equation and the surface area of the moving cylinder: Poiseuille's equation  email me a note if you found this useful
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