In Poiseuille's Law, Change in Pressure is calculated as

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In Poiseuille's Law, Change in Pressure is calculated as

Poiseuille's law shows how pressure difference driving flow through a cylindrical tube depends on flow, viscosity, length, and radius. The pressure change ΔP is proportional to the flow rate Q times the viscosity μ and the tube length L, divided by the radius to the fourth power: ΔP ∝ (μ L Q) / (π r^4). The key idea is that radius has a powerful inverse effect: as the radius increases, ΔP drops rapidly (r^4 in the denominator); as the radius decreases, ΔP rises steeply. The flow rate sits in the numerator, so for a given tube, increasing flow increases the pressure drop. Therefore, the correct way to think about the relationship is Flow divided by r^4. The option that multiplies flow by r^4 would imply the opposite behavior and is not the correct form. This radius sensitivity helps explain why even small changes in airway radius dramatically affect the pressure required to maintain flow.

Poiseuille's law shows how pressure difference driving flow through a cylindrical tube depends on flow, viscosity, length, and radius. The pressure change ΔP is proportional to the flow rate Q times the viscosity μ and the tube length L, divided by the radius to the fourth power: ΔP ∝ (μ L Q) / (π r^4). The key idea is that radius has a powerful inverse effect: as the radius increases, ΔP drops rapidly (r^4 in the denominator); as the radius decreases, ΔP rises steeply. The flow rate sits in the numerator, so for a given tube, increasing flow increases the pressure drop. Therefore, the correct way to think about the relationship is Flow divided by r^4. The option that multiplies flow by r^4 would imply the opposite behavior and is not the correct form. This radius sensitivity helps explain why even small changes in airway radius dramatically affect the pressure required to maintain flow.

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