Answer: rnew = r × 21/3 ≈ 1.26r.
- A rnew = r × 21/3 ≈ 1.26r
- B rnew = 2r, as if the radii generally added together
- C rnew = r√2, as if the surface areas generally added
- D rnew = r/√2, shrinking instead of growing on merging
Correct answer: A. rnew = r × 21/3 ≈ 1.26r
Explanation: Volume is conserved: (4/3)π rnew³ = 2 × (4/3)π r³. rnew = r × 21/3 ≈ 1.26r.
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.