Answer: η = 2r²(ρ_s - ρ_l)g/9vt.
- A η = 2r²(ρ_s - ρ_l)g/9vt
- B η = 9vt/(2r² g) in standard practice
- C η = 6πrv_t under most conditions encountered
- D η = 2r² vt as frequently observed in practice
Correct answer: A. η = 2r²(ρ_s - ρ_l)g/9vt
Explanation: Stokes: vt = 2r²(ρ_s - ρ_l)g/(9η). Rearranging: η = 2r²(ρ_s - ρ_l)g/(9vt). This is how viscometry works experimentally.
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.