Compensating for a narrowed vessel
A blood vessel's radius decreases by 10%. By about how much must the pressure difference increase to keep the flow rate the same?
Answer D: explanation for every choice
A
This assumes flow is proportional to r.
B
This assumes flow is proportional to r²: 1/0.9² ≈ 1.23.
C
This calculates 1 − 0.9⁴, the fractional drop in flow at constant pressure, instead of the pressure increase needed.
D
Correct. Flow ∝ r⁴ΔP, so ΔP must rise by a factor of 1/0.9⁴ ≈ 1/0.656 ≈ 1.52, about 52%.
TakeawayQ ∝ r⁴ΔP. Small changes in radius require large changes in pressure.
Equation usedPoiseuille's law
Next question →Reviewed 2026-11-05 by a medical student. Spot an error? Report it with question ID cp117.