Answer: r⁴/L (fourth power of radius divided by length).
- A r⁴/L (fourth power of radius divided by length)
- B r²/L, as if flow rate scaled only with cross-sectional area
- C r/L, a linear dependence on radius alone
- D r³/L, an intermediate power between area and the true relation
Correct answer: A. r⁴/L (fourth power of radius divided by length)
Explanation: Poiseuille's law: Q = πr⁴ΔP/(8ηL). Doubling the tube radius increases flow rate 16 times. This explains why even small arterial narrowing severely reduces blood flow.
Since the same volume of fluid must pass every cross-section per second (continuity), the fluid speeds up where the pipe narrows; Bernoulli's equation then says this faster-moving fluid has lower pressure - the principle behind a venturi meter and an aircraft wing's lift.
Concept context
Pressure, buoyancy, Bernoulli equation, viscosity, and surface tension.