Stokes' Law Calculator
Calculate terminal velocity, drag force, and viscosity for spherical particles in viscous fluids
Calculate Terminal Velocity
Standard Earth gravity is 9.80665 m/s²
Diameter of the spherical particle
Density of the falling particle
Density of the viscous fluid
Dynamic (absolute) viscosity of the fluid
Stokes' Law Results
Formula: v = g × d² × (ρp - ρm) / (18 × μ)
Density difference: 0.0 kg/m³
Converted diameter: 0.000e+0 m
Validity Check
Example Calculation
Aluminum Sphere in Oil
Particle: Aluminum sphere (d = 1 cm = 0.01 m)
Particle density (ρp): 2710 kg/m³
Medium: Oil (ρm = 850 kg/m³, μ = 0.38 Pa·s)
Gravity (g): 9.81 m/s²
Calculation Steps
1. Density difference: ρp - ρm = 2710 - 850 = 1860 kg/m³
2. g × d²: 9.81 × (0.01)² = 0.000981 m³/s²
3. 18 × μ: 18 × 0.38 = 6.84 Pa·s
4. v = (0.000981 × 1860) / 6.84 = 0.27 m/s
Common Fluid Properties
Water (20°C)
Density: 998 kg/m³
Viscosity: 0.001 Pa·s
Oil (typical)
Density: 850 kg/m³
Viscosity: 0.38 Pa·s
Honey
Density: 1420 kg/m³
Viscosity: 10 Pa·s
Air (20°C)
Density: 1.2 kg/m³
Viscosity: 1.8×10⁻⁵ Pa·s
Common Material Densities
Physics Tips
Stokes' law applies to spherical particles in creeping flow (Re < 0.1)
Particle must be denser than the medium to fall
Used in falling ball viscometers
Valid for laminar flow conditions
Understanding Stokes' Law
What is Stokes' Law?
Stokes' law describes the motion of spherical particles falling through a viscous fluid at terminal velocity. It relates the drag force on a sphere to the fluid's viscosity, the particle's size, and its velocity. This fundamental principle is crucial in fluid mechanics and particle physics.
Applications
- •Falling ball viscometers for measuring fluid viscosity
- •Particle settling in sedimentation processes
- •Centrifugation and separation techniques
- •Quality control in oil and lubricant industries
Terminal Velocity Formula
v = g × d² × (ρₚ - ρₘ) / (18 × μ)
- v: Terminal velocity (m/s)
- g: Gravitational acceleration (9.81 m/s²)
- d: Particle diameter (m)
- ρₚ: Particle density (kg/m³)
- ρₘ: Medium density (kg/m³)
- μ: Dynamic viscosity (Pa·s)
Validity: Stokes' law is accurate for Reynolds numbers Re < 0.1 (creeping flow)
Physical Interpretation
Drag Force
The viscous drag force opposes the particle's motion and is proportional to velocity, viscosity, and particle size: Fₐ = 6πμrv
Terminal Velocity
When drag force equals gravitational force, the particle reaches constant velocity. Larger, denser particles fall faster in less viscous fluids.
Reynolds Number
Re = ρvd/μ determines flow regime. For Stokes' law validity, Re must be much less than 1, indicating laminar, creeping flow conditions.