Settling Velocity

Calculate signed ideal spherical-particle Stokes settling and check Re≤1; upward buoyancy is retained, and nonspherical, flocculated and hindered settling are not modeled.

Description

Stokes settling balances buoyant weight with viscous drag for small spherical particles.

Stokes settling balances buoyant weight with viscous drag for small spherical particles. A signed velocity distinguishes sinking dense particles from rising particles lighter than the water.^[1]

Calculate signed ideal spherical-particle Stokes settling and check Re≤1; upward buoyancy is retained, and nonspherical, flocculated and hindered settling are not modeled.

When to use Settling Velocity

Use this tool to calculate signed ideal spherical-particle Stokes settling and check Re≤1; upward buoyancy is retained, and nonspherical, flocculated and hindered settling are not modeled.

Prepare the cohort, water, feed or equipment measurements for one consistent operating period. Confirm nitrogen reporting bases, dry/wet masses, flow units and supplied design assumptions.

How to use Settling Velocity and understand its results

Prepare the cohort, water, feed or equipment measurements for one consistent operating period. Confirm nitrogen reporting bases, dry/wet masses, flow units and supplied design assumptions.
Enter particleDiameterM, particleDensityKgPerM3, waterDensityKgPerM3, dynamicViscosityPaSeconds, gravityMPerSecondSquared using the field table and calculation rules, then run the tool.
Read signedStokesVelocityMPerSecond, particleReynoldsNumber, withinCreepingFlowScreen. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
particleDiameterM	Particle diameter m	number	Required
particleDensityKgPerM3	Particle density kg per m3	number	Required
waterDensityKgPerM3	Water density kg per m3	number	Required
dynamicViscosityPaSeconds	Dynamic viscosity Pa seconds	number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required

Enter positive densities, diameter meters, dynamic viscosity Pa·s and acceleration m/s². The tool calculates signed Stokes velocity, Reynolds number and a flag for Re≤1. Equal densities give zero speed; lower particle density gives negative speed.

v=(particleDensity−waterDensity)g diameter²/(18 viscosity); Re=waterDensity |v| diameter/viscosity

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
signedStokesVelocityMPerSecond	Signed stokes velocity m per second	number
particleReynoldsNumber	Particle reynolds number	number
withinCreepingFlowScreen	Within creeping flow screen	boolean

json

{
  "input": {
    "particleDiameterM": 0.0001,
    "particleDensityKgPerM3": 1100,
    "waterDensityKgPerM3": 1000,
    "dynamicViscosityPaSeconds": 0.001,
    "gravityMPerSecondSquared": 9
  },
  "output": {
    "signedStokesVelocityMPerSecond": 0.0004999999999999999,
    "particleReynoldsNumber": 0.04999999999999999,
    "withinCreepingFlowScreen": true
  }
}

Limitations and assumptions

The flag screens a low-Reynolds regime rather than proving validity. Shape, turbulence, aggregation and concentration effects are excluded; settling velocity alone does not size a separator.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use Clarifier Sizing: Size an ideal circular clarifier against caller hydraulic and solids loadings and report detention; settling performance, inlet hydraulics and short circuiting are external. For a complementary task, use Solids Production Rate: Partition supplied dry feed into uneaten and fecal solids then apply mechanical capture; dry-mass basis excludes dissolved organics and biological sludge.

References

Settling Velocity — tool.io

Similar or alternative tools

Clarifier Sizing
Size an ideal circular clarifier against caller hydraulic and solids loadings and report detention; settling performance, inlet hydraulics and short circuiting are external.
Solids Production Rate
Partition supplied dry feed into uneaten and fecal solids then apply mechanical capture; dry-mass basis excludes dissolved organics and biological sludge.