alleryPoiseuille's law gives the volume flow rate Q of a viscous fluid through a horizontal pipe of length L and radius r under pressure difference ΔP as:
AQ = π ΔP r⁴ / (8 η L)
BQ = π ΔP r² / (η L)
CQ = π ΔP r / (η L)
DQ = 8 η L / (π ΔP r⁴)
Answer & Solution
Correct answer: A. Q = π ΔP r⁴ / (8 η L)
1. For laminar (Re ≪ 2000) viscous flow in a cylindrical pipe, Q = π ΔP r⁴ / (8 η L) — the Hagen–Poiseuille equation.
2. The fourth-power dependence on r is striking — halving the radius cuts Q by a factor of 16.
3. Explains why even a slight constriction in an artery causes a huge drop in blood flow.
4. Option (D) is the resistance R_viscous = 8ηL/(πr⁴), the reciprocal relation.
_Source: syllabus Physics Ch 9 §9.7 Stokes + Poiseuille (extension)_
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