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Poiseuille's equation
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Flow rate through a pipe depends on the fourth power of radius.
Q = πr⁴ΔP/8ηLVolume flow rate through a pipe is Q = πr⁴ΔP/(8ηL): very sensitive to radius. Halving the radius reduces flow by 16.
Narrowed arteries raise blood pressure significantly.
Valid for laminar flow only.
In more detail
Poiseuille's equation gives the flow rate through a long narrow tube, Q = πr⁴ΔP/(8ηL). Flow depends strongly on the radius, which is raised to the fourth power.
Real-world uses
- Blood flow through arteries is analysed using Poiseuille's equation.
- Designers of drug delivery systems use it to set flow rates.
- Doctors and engineers use Poiseuille's equation to estimate blood flow in arteries and the flow through narrow tubes.
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Frequently asked questions
Why does radius matter so much?
Because flow depends on the fourth power, so doubling the radius increases flow sixteen times.
Does it need laminar flow?
Yes. It applies to smooth, streamline flow in long straight tubes.
Why does the radius matter so much?
Flow depends on the fourth power of the radius, so halving the radius reduces the flow sixteen-fold.
Related topics in Fluids & Elasticity
Lift on a wing · Magnus effect · Viscosity · Stokes' law · Terminal velocity in fluids · Reynolds number