Answer: r new = r × 2 1/3 ≈ 1.26r.
- A r<sub>new</sub> = r × 2<sup>1/3</sup> ≈ 1.26r
- B r<sub>new</sub> = 2r, as if the radii generally added together
- C r<sub>new</sub> = r√2, as if the surface areas generally added
- D r<sub>new</sub> = r/√2, shrinking instead of growing on merging
Correct answer: A. r<sub>new</sub> = r × 2<sup>1/3</sup> ≈ 1.26r
Explanation: Volume is conserved: (4/3)π r<sub>new</sub>³ = 2 × (4/3)π r³. r<sub>new</sub> = r × 2<sup>1/3</sup> ≈ 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.