Terminal Velocity (vt = 2a²(ρ − σ)g/(9η))
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vt = 2a²(ρ − σ)g/(9η)
What each symbol means
| Symbol | What it stands for |
|---|---|
| a | Radius of the sphere (m) |
| g | Acceleration due to gravity (m/s²) |
| vt | Terminal velocity (m/s) |
| η | Coefficient of viscosity of the fluid (Pa·s) |
| ρ | Density of the sphere (kg/m³) |
| σ | Density of the fluid (kg/m³) |
When to use this
Reached when net force is zero: weight = buoyant force + Stokes drag. Derived from 6πηavt = (4/3)πa³(ρ−σ)g. Terminal velocity ∝ a² (proportional to square of radius) and ∝ 1/η (inversely proportional to viscosity). If ρ < σ, the sphere rises (e.g., air bubble in water).