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
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:
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