Poiseuille's Flow (conceptual)

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Volumetric flow rate through capillary depends most strongly on radius as?

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1. **Context**: Poiseuille's Law describes the steady, laminar flow of a viscous liquid through a cylindrical tube.
2. **Formula**: $Q = \frac{\pi r^4 (P_1 - P_2)}{8 \eta L}$.
3. **Analysis**: $Q$ is proportional to the **fourth power of the radius** ($Q \propto r^4$).
4. **Practical meaning**: Doubling the radius of a tube (while keeping pressure and length constant) increases the flow rate by a factor of $2^4 = 16$. This makes flow extremely sensitive to small changes in vessel width (critical in biology/arteries).

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Poiseuille's Flow (conceptual)

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