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Fluidization Calculator

Minimum fluidization velocity from Ergun equation, terminal velocity (Haider-Levenspiel), Archimedes number, and operating regime classification

Reviewed by Christopher FloiedPublished Updated

This free online fluidization calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Supports both metric (SI) and imperial units with built-in unit selection dropdowns on every input field, so you can work in whatever units your problem provides. Designed for engineering students and professionals working through coursework, design projects, or quick reference calculations.

Fluidization Calculator

Min. Fluidization Velocity u_mf
0.0746 m/s
Re_mf = 1.240
Terminal Velocity u_t
2.1976 m/s
Re_t = 36.546
Operating Regime
Fluidized Bed
u_op = 0.300 m/s
Archimedes Number Ar
1492.13
u_op / u_mf
4.02
Fluidized ΔP/L
15071.1 Pa/m

Pressure Drop vs Superficial Velocity

Tip: hover to read values, click to pin a point for export

Pressure Drop Sweep Data Table

u (m/s)ΔP/L (Pa/m)
0.000000.00
0.041208239.34
0.0824115071.12
0.1236115071.12
0.1648215071.12
0.2060215071.12
0.2472315071.12
0.2884315071.12
0.3296415071.12
0.3708415071.12
0.4120515071.12
0.4532515071.12
0.4944615071.12
0.5356615071.12
0.5768715071.12
0.6180715071.12
0.6592815071.12
0.7004815071.12
0.7416915071.12
0.7828915071.12
0.8241015071.12
0.8653015071.12
0.9065115071.12
0.9477115071.12
0.9889215071.12
1.0301215071.12
1.0713315071.12
1.1125315071.12
1.1537415071.12
1.1949415071.12
1.2361515071.12
1.2773515071.12
1.3185615071.12
1.3597615071.12
1.4009715071.12
1.4421715071.12
1.4833815071.12
1.5245815071.12
1.5657915071.12
1.6069915071.12
1.6482015071.12
1.6894015071.12
1.7306115071.12
1.7718115071.12
1.8130215071.12
1.8542215071.12
1.8954315071.12
1.9366315071.12
1.9778415071.12
2.0190415071.12
2.0602515071.12
2.1014515071.12
2.1426615071.12
2.1838615071.12
2.2250715071.12
2.2662715071.12
2.3074815071.12
2.3486815071.12
2.3898915071.12
2.4310915071.12
2.4723015071.12
2.5135015071.12
2.5547115071.12
2.5959115071.12
2.6371215071.12
2.6783215071.12
2.7195315071.12
2.7607315071.12
2.8019415071.12
2.8431415071.12
2.8843515071.12
2.9255515071.12
2.9667615071.12
3.0079615071.12
3.0491715071.12
3.0903715071.12
3.1315815071.12
3.1727815071.12
3.2139815071.12
3.2551915071.12
3.2963915071.12

Theory

At u_mf (Ergun): [150μ(1−ε_mf)/(ε_mf³D_p²)]·u_mf + [1.75ρ/(ε_mf³D_p)]·u_mf² = (ρ_s−ρ)·g

Terminal velocity (Haider-Levenspiel): Re_t = Ar / (18 + 0.591√Ar)

Ar: D_p³·ρ·(ρ_s−ρ)·g / μ²

Regimes: u < u_mf: Fixed Bed | u_mf ≤ u < u_t: Fluidized | u ≥ u_t: Pneumatic Transport

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Fluidization Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Fluidization Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Minimum Fluidization Velocity — Ergun Equation at Incipient Fluidization

[150·μ·(1 − ε_mf) / (ε_mf³ · D_p²)] · u_mf + [1.75·ρ / (ε_mf³ · D_p)] · u_mf² = (ρ_s − ρ) · g | solved for the positive root: | u_mf = ( −a + √(a² + 4·b·c) ) / (2·b) | with a = 150·μ·(1 − ε_mf)/(ε_mf³·D_p²) | b = 1.75·ρ/(ε_mf³·D_p) | c = (ρ_s − ρ)·g

Variables: u_mf = minimum (incipient) fluidization superficial velocity (m/s), μ = fluid dynamic viscosity (Pa·s), ε_mf = bed void fraction at minimum fluidization (dimensionless, 0 < ε_mf < 1; default 0.42), D_p = particle diameter (m), ρ = fluid density (kg/m³), ρ_s = particle (solid) density (kg/m³), g = 9.81 m/s² (hard-coded), a = viscous (laminar) Ergun coefficient (Pa·s/m²), b = inertial (turbulent) Ergun coefficient (Pa·s²/m³), c = net buoyant weight per unit bed volume of solids (Pa/m). Source: Ergun, S. (1952), Fluid Flow Through Packed Columns, Chemical Engineering Progress 48(2); Kunii & Levenspiel, Fluidization Engineering, 2nd ed., Ch. 3 (Minimum Fluidizing Velocity)

Ergun Packed-Bed Pressure Gradient (fixed bed, u < u_mf)

ΔP/L = [150·μ·(1 − ε)² / (D_p²·ε³)] · u + [1.75·ρ·(1 − ε) / (D_p·ε³)] · u²

Variables: ΔP/L = pressure gradient through the packed bed (Pa/m), μ = fluid dynamic viscosity (Pa·s), ε = bed void fraction (dimensionless; the tool reuses ε_mf here), D_p = particle diameter (m), ρ = fluid density (kg/m³), u = superficial fluid velocity (m/s). Source: Ergun, S. (1952), Chemical Engineering Progress 48(2); McCabe, Smith & Harriott, Unit Operations of Chemical Engineering, 7th ed., Ch. 7 (Flow Through Beds of Solids)

Fluidized-Bed Pressure Gradient Plateau (u ≥ u_mf)

ΔP/L = (ρ_s − ρ) · (1 − ε_mf) · g

Variables: ΔP/L = pressure gradient across the fluidized bed (Pa/m), ρ_s = particle density (kg/m³), ρ = fluid density (kg/m³), ε_mf = void fraction at minimum fluidization (dimensionless), g = 9.81 m/s² (hard-coded). Source: Kunii & Levenspiel, Fluidization Engineering, 2nd ed., Ch. 3 — bed pressure drop equals the buoyant weight of the solids per unit area

Terminal Settling Velocity — Haider-Levenspiel Correlation (sphericity = 1)

Ar = D_p³ · ρ · (ρ_s − ρ) · g / μ² | Re_t = Ar / ( 18 + 0.591·√Ar ) | where 0.591 = 2.335 − 1.744·φ_s at φ_s = 1 | u_t = Re_t · μ / (ρ · D_p)

Variables: Ar = Archimedes number (dimensionless), Re_t = particle Reynolds number at terminal velocity (dimensionless), u_t = terminal settling velocity (m/s), D_p = particle diameter (m), ρ = fluid density (kg/m³), ρ_s = particle density (kg/m³), g = 9.81 m/s² (hard-coded), μ = fluid dynamic viscosity (Pa·s), φ_s = particle sphericity (dimensionless, fixed at 1.0 = perfect sphere). Source: Haider, A. & Levenspiel, O. (1989), Drag Coefficient and Terminal Velocity of Spherical and Nonspherical Particles, Powder Technology 58, pp. 63-70; Kunii & Levenspiel, Fluidization Engineering, 2nd ed., Ch. 3

Particle Reynolds Numbers and Regime Boundaries

Re = ρ · u · D_p / μ | (evaluated at u = u_mf, u_t and u_op) | Regime: u_op < u_mf → Fixed Bed ; u_mf ≤ u_op < u_t → Fluidized Bed ; u_op ≥ u_t → Pneumatic Transport

Variables: Re = particle Reynolds number based on superficial velocity (dimensionless), ρ = fluid density (kg/m³), u = superficial fluid velocity (m/s), D_p = particle diameter (m), μ = fluid dynamic viscosity (Pa·s), u_mf = minimum fluidization velocity (m/s), u_t = terminal velocity (m/s), u_op = operating superficial velocity (m/s). Source: Kunii & Levenspiel, Fluidization Engineering, 2nd ed., Ch. 3 — regimes of fluidization

When to Use This Calculator

  • Use the Fluidization Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
  • Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
  • Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
  • Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
  • Use it in the field when a quick estimate is needed and a full engineering software package is not available.

About This Calculator

The Fluidization Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Minimum fluidization velocity from Ergun equation, terminal velocity (Haider-Levenspiel), Archimedes number, and operating regime classification All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

The Theory Behind It

Fluidization occurs when upward gas flow through a particle bed is high enough to lift the particles, creating fluid-like behavior. The minimum fluidization velocity u_mf is found from Ergun's equation with ΔP equal to the bed weight per unit area (the gas must support the particles): 150·μ·(1−ε_mf)·u_mf/(ε_mf³·φ²·d_p²) + 1.75·ρ_g·u_mf²/(ε_mf³·φ·d_p) = (ρ_s − ρ_g)·g, where ε_mf is void fraction at incipient fluidization (typically ~0.4), φ is sphericity, and ρ_s and ρ_g are solid and gas densities. For the Wen and Yu simplification applicable to many practical cases: Re_mf = (33.7² + 0.0408·Ar)^0.5 − 33.7, where Ar = ρ_g·(ρ_s−ρ_g)·g·d_p³/μ² is the Archimedes number. Terminal velocity u_t is the velocity at which a particle falls at steady state in still gas — gas flow above u_t blows particles out of the bed (elutriation). Haider and Levenspiel correlation for terminal velocity handles particles of any shape. Fluidization regimes: fixed bed (u < u_mf), bubbling (u_mf < u < u_mb), slugging, turbulent, and dilute phase (u > u_t). Each regime has different mixing, heat transfer, and mass transfer characteristics. Fluidized beds offer excellent solid-gas contacting, temperature uniformity, and continuous solids handling. Applications include catalytic cracking (FCC), combustion (CFBC power plants), roasting and drying, and coal gasification.

Real-World Applications

  • Fluid catalytic cracking (FCC): the largest industrial fluidized bed application, converting heavy crude oil fractions into gasoline and lighter products using a fluidized catalyst.
  • Fluidized bed combustion (CFBC): coal, biomass, or waste is combusted in a fluidized bed of limestone or sand for efficient heat transfer and low emissions.
  • Drying of particulate materials: fluidized bed dryers for food products, pharmaceuticals, and minerals provide uniform temperature and fast drying.
  • Coating and granulation: pharmaceutical tablets and granules are coated or agglomerated in fluidized beds with sprayed coating solutions.
  • Biomass gasification: fluidized beds provide high heat and mass transfer for biomass-to-syngas conversion at 700-900°C.

Frequently Asked Questions

What's the minimum fluidization velocity?

The gas velocity at which particles in a packed bed start to float — the upward gas drag force equals the particle weight. Below this velocity, the bed is fixed (static). At exactly this velocity, the particles are on the verge of fluidization. Above, they move and the bed behaves like a fluid. Computed from Ergun's equation or Wen and Yu correlation given gas and particle properties.

What are fluidization regimes?

As gas velocity increases above u_mf: (1) Bubbling — bubbles form and rise through the bed, mixing it well; (2) Slugging — in tall beds, bubbles grow to span the cross-section; (3) Turbulent — bed surface becomes unstable; (4) Fast fluidization — significant particle carryover; (5) Dilute phase (pneumatic) transport — particles carried with the gas, no dense bed. Different applications operate in different regimes.

What's terminal velocity?

The steady-state velocity at which a particle falls in still gas, where gravity balances drag. Above this velocity, gas carries particles up (elutriation). For a sphere: u_t = √(4·g·d·(ρ_s−ρ_g)/(3·ρ_g·C_d)), where C_d is the drag coefficient (depending on Reynolds number). Fluidized bed operations typically run at gas velocities between u_mf and u_t to maintain a dense bed without blowing particles out.

What's the Geldart classification?

A classification of particle-gas systems into four groups based on fluidization behavior. Group A: small, low-density particles (cracking catalysts), aeratable, expand before bubbling. Group B: medium size, sand-like, bubble at u_mf. Group C: very fine, cohesive (flour), hard to fluidize. Group D: large or dense particles, spoutable. Each group has different hydrodynamics and heat transfer.

What are the advantages of fluidization?

(1) Excellent solid-gas contact for mass and heat transfer; (2) uniform temperature due to intense mixing; (3) continuous solids handling (feed and discharge); (4) no hot or cold spots; (5) can process small particles that would plug packed beds; (6) can handle wet or sticky feeds. Disadvantages: attrition of particles, catalyst elutriation, erosion of internal surfaces, larger equipment for the same duty.

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References & Further Reading

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