Answer: vc = 2000η/(ρd).
- A vc = 2000η/(ρd)
- B vc = 2000ρd
- C vc = η/(ρd)
- D vc = ρd/η
Correct answer: A. vc = 2000η/(ρd)
Explanation: Re = ρvd/η. For Re = 2000 (laminar-turbulent transition): vc = 2000η/(ρd). For water in a 1 cm pipe: vc ≈ 0.2 m/s.
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.