Continuity equation: velocity in a narrowed vessel
Blood flows steadily through a vessel that narrows to half its original radius. Assuming incompressible flow, the velocity in the narrow segment is:
Answer B: explanation for every choice
A
This scales velocity with radius instead of cross-sectional area.
B
Correct. Continuity: A₁v₁ = A₂v₂. Area ∝ r², so halving r reduces A to ¼ and velocity rises 4×.
C
This inverts the relationship. Narrower segments carry faster flow at constant flow rate.
D
The r⁴ dependence comes from Poiseuille's law, which relates flow rate to the pressure gradient and resistance. It does not set velocity at constant flow.
TakeawayConstant Q = Av. Velocity scales with 1/r², not 1/r or 1/r⁴.
Equation usedContinuity equation
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