According to Poiseuille's law for laminar flow through a cylindrical vessel (Q = pi ΔP r^4 / (8 eta L)), if vasoconstriction reduces the radius of an arteriole by 50% (r becomes r/2) while perfusion pressure remains constant, by what factor does the volumetric blood flow rate Q decrease?
Answer and explanation
Correct answer: B. It decreases by a factor of 16 (flow drops to 1/16 of its original rate)
Poiseuille's equation states that flow rate Q is directly proportional to the fourth power of the radius (r^4). When the radius is halved (r' = r/2), the new flow rate is Q' proportional to (r/2)^4 = r^4 / 16. Therefore, flow drops to 1/16 of its baseline value (a 16-fold decrease in flow), highlighting the extreme sensitivity of vascular resistance to vessel radius.
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