Answer: Decreases by factor 16.
- A Decreases by factor 16
- B Decreases by factor 2
- C Increases by factor 16
- D Decreases by factor 4
Correct answer: A. Decreases by factor 16
Explanation: Q ∝ r⁴. If r halves (r/2), Q = (r/2)⁴ × (original Q/r⁴) = Q/16. The flow rate decreases by factor 16.
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.