Poiseuille's Law

Q = \frac{\pi r^4 \Delta P}{8 \mu L}

Blood or fluid flow through a tube depends strongly on radius to the fourth power.

By Jean Léonard Marie Poiseuille

Medical Sciences

Poiseuille's Law

1840 · Jean Léonard Marie Poiseuille

Why it matters: Explains why small artery narrowing dramatically reduces blood flow.

Discoverers: Jean Léonard Marie Poiseuille (1840)

What does it mean?

Blood or fluid flow through a tube depends strongly on radius to the fourth power.

Explains why small artery narrowing dramatically reduces blood flow.

Symbol	Name	Unit	Meaning
$Q$	Flow rate	—	m³/s
$r$	Radius	m	Tube radius
$ΔP$	Pressure drop	—	Pa
$μ$	Viscosity	—	Pa·s
$L$	Length	m	Tube length

Halve radius → flow drops 16×.

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Equation Universe

Q = \frac{\pi r^4 \Delta P}{8 \mu L}

Real-world impact

Modern electronics

Electrostatic design at nanometer scales.

Photo: Unsplash — microchip

Blood or fluid flow through a tube depends strongly on radius to the fourth power.

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