Answer: vt = 2r²(ρ-σ)g/9η.
- A vt = 2r²(ρ-σ)g/9η
- B vt = 6πηrv
- C vt = r(ρ-σ)/η
- D vt = 4πr³ρg/3
Correct answer: A. vt = 2r²(ρ-σ)g/9η
Explanation: At terminal velocity, weight - buoyancy = Stokes drag: (4/3)πr³(ρ-σ)g = 6πηr vt. Solving: vt = 2r²(ρ-σ)g/9η.
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.