If the radius is halved and ΔP remains constant, Flow becomes

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Multiple Choice

If the radius is halved and ΔP remains constant, Flow becomes

The key idea is how radius affects flow in a tube when the pressure drop is fixed. Poiseuille’s law shows that flow Q is proportional to the fourth power of the radius (Q ∝ r^4) for laminar flow with constant ΔP, viscosity, and length. If the radius is halved, the flow becomes (1/2)^4 = 1/16 of its original value. So the flow is sixteen times smaller. In respiratory terms, even a modest reduction in airway radius greatly lowers flow due to this fourth-power relationship.

The key idea is how radius affects flow in a tube when the pressure drop is fixed. Poiseuille’s law shows that flow Q is proportional to the fourth power of the radius (Q ∝ r^4) for laminar flow with constant ΔP, viscosity, and length. If the radius is halved, the flow becomes (1/2)^4 = 1/16 of its original value. So the flow is sixteen times smaller. In respiratory terms, even a modest reduction in airway radius greatly lowers flow due to this fourth-power relationship.

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