Particle Reynolds Number Calculator

Calculator Inputs

Computation method

Use density and dynamic viscosity

Use kinematic viscosity directly

Both options compute the same dimensionless number with consistent SI conversions.

Relative velocity

Use slip speed between particle and fluid.

Particle diameter

For non-spherical shapes, use an equivalent diameter.

Fluid density

Required for the dynamic-viscosity method.

Dynamic viscosity

Water near 20°C is about 1 mPa·s.

Kinematic viscosity

Good when ν is known from datasheets.

Formula Used

The particle Reynolds number measures the ratio of inertial to viscous forces around a moving particle. It is defined as:

Dynamic-viscosity form: Re_p = (ρ · v · d) / μ

Kinematic-viscosity form: Re_p = (v · d) / ν, where ν = μ/ρ.

Here ρ is fluid density, v is relative velocity, d is particle diameter, μ is dynamic viscosity, and ν is kinematic viscosity.

How to Use This Calculator

Choose a method based on available fluid properties.
Enter the particle diameter and relative velocity.
Provide density and viscosity, or provide kinematic viscosity.
Press Calculate to see results above the form.
Use CSV or PDF buttons to save the computed summary.

Tip: For settling particles, use the slip velocity relative to the fluid.

Example Data Table

Fluid ρ (kg/m³)	μ (Pa·s)	v (m/s)	d (m)	Re_p	Typical note
1000	0.001	0.20	0.0010	200	Transitional; use empirical drag.
1.20	1.8e-5	2.00	0.0002	26.7	Laminar wake; correlations help.
850	0.05	0.05	0.0020	1.70	Near Stokes limit; check assumptions.

Professional Guide to Particle Reynolds Number

1) Why this dimensionless number matters

Particle Reynolds number (Re_p) compares inertial forces to viscous forces near a particle. It guides whether simple viscous models are acceptable or whether wake effects and stronger drag models are needed.

2) Interpreting typical ranges

Below about 0.1, creeping flow is common and viscosity dominates. From ~0.1 to 1, Stokes-type behavior often holds. Between 1 and ~1000, inertia grows and correlation-based drag becomes important. Beyond ~1000, strong separation and unsteadiness are likely. Many practical liquid–solid systems fall in the 10–500 range in practice.

3) Fluid property data to use

Use density and viscosity at the operating temperature. Water near room temperature is roughly ρ ≈ 1000 kg/m³ and μ ≈ 0.001 Pa·s. Light oils can be 0.01–0.2 Pa·s, while glycerol mixtures can be much higher. Viscosity is usually the most sensitive input.

4) Diameter and particle shape

The diameter in the formula should represent the particle interacting with the flow. For spheres, use the true diameter. For irregular particles, choose an equivalent diameter (volume- or area-based) and pair it with a suitable drag correlation that accounts for shape. Consistency matters more than perfection when comparing cases.

5) Choosing the right relative velocity

Enter the slip velocity between particle and fluid. In settling, this is the particle’s speed relative to the surrounding fluid. In transport flows, bulk velocity may differ from local slip, so interpret the regime with that limitation in mind.

6) Linking Re_p to drag decisions

Drag coefficient varies strongly with Re_p. At low values, drag scales nearly linearly with velocity. As Re_p increases, nonlinearity and wake formation appear, so empirical correlations are preferred for credible terminal-velocity or pressure-drop estimates. For Re_p above 1, published correlations usually outperform constant drag assumptions.

7) Worked example using realistic numbers

For d = 1 mm and v = 0.2 m/s in water (ρ = 1000 kg/m³, μ = 0.001 Pa·s), Re_p ≈ 200. That lies in the transitional range, so a correlation-based drag model is typically recommended over a pure Stokes approximation.

8) Practical engineering tips

Confirm whether your viscosity is dynamic (Pa·s) or kinematic (m²/s). If ν is given, use the kinematic method directly. For design work, recompute at temperature extremes to quantify viscosity-driven variation and keep safety margins realistic. Record assumptions (diameter definition, slip velocity, temperature) so results remain auditable.

FAQs

1) What is the particle Reynolds number used for?

It indicates whether flow around a particle is viscous- or inertia-dominated. It helps choose drag correlations, interpret settling behavior, and anticipate wake formation in dispersed or multiphase flows.

2) Should I use diameter or radius in the formula?

Use particle diameter. If you have radius, convert using d = 2r. For irregular particles, use an equivalent diameter and apply drag correlations that match particle shape.

3) What velocity should I enter for settling particles?

Use the slip (relative) velocity between the particle and the surrounding fluid. Using only the bulk flow speed can misrepresent the local regime around the particle.

4) How do dynamic and kinematic viscosity methods differ?

They are equivalent. One uses Re = ρvd/μ, and the other uses Re = vd/ν. Kinematic viscosity satisfies ν = μ/ρ.

5) What does a very low Re_p imply?

Very low values suggest creeping flow where viscous forces dominate. In many cases, Stokes-type assumptions become reasonable and drag varies nearly linearly with velocity.

6) What does a very high Re_p imply?

High values indicate strong inertial effects with separation and a wake. Flow can be unsteady, so robust empirical drag models are usually required for accurate predictions.

7) Why can temperature change my result so much?

Viscosity is temperature-sensitive for most fluids. Because Re_p is inversely proportional to viscosity, warming a fluid often increases Re_p noticeably even if density changes little.