Free · Physics models
Stokes Settling Velocity of a Sphere
Estimate signed terminal settling velocity for an isolated sphere in a Newtonian fluid under creeping flow.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
terminal velocity = 0.0000081722083 ms.
vt = g d²(ρp − ρf)/(18μ).
Worked example
Enter these known values and leave the other values blank.
- Acceleration of gravity (g)
- 9.80665 m/s²
- Particle diameter (d)
- 0.1 mm
- Particle density (ρ_p)
- 2500 kg/m³
- Medium density (ρ_m)
- 1000 kg/m³
- Medium viscosity (μ)
- 1 Pa⋅s
- Terminal velocity (v)
- 0.00000817221 m/s
Assumptions and limitations
- Estimate signed terminal settling velocity for an isolated sphere in a Newtonian fluid under creeping flow.
- Use dynamic viscosity, spherical diameter and uniform densities. Stokes drag assumes particle Reynolds number much less than one, no significant wall effects and negligible particle interactions.
- Positive velocity denotes settling when the particle is denser than the fluid; a negative value denotes buoyant rise in the signed model.
- Inputs and inverse outputs share the displayed unit selectors. Clear a known field to solve for it, and lock quantities that must remain fixed. Singular inverses may have no finite result.
Common questions
Is this valid for any particle size?
Only when creeping flow is a reasonable approximation. Check Reynolds number using the calculated speed.
What if densities are equal?
The buoyancy-corrected driving force and terminal speed are zero.
References
Enforce the explicitly stated physical domain: Gravitational acceleration magnitude must be positive.