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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 |

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 At the edge |

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*

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