Calculator Live
Enter reactor geometry, agitator type and process conditions. Results and the reactor drawing update instantly.
Mixing Scale · Scale-Up Comparison
| Parameter | Current scale | Target scale |
| Batch volume | — | — |
| Vessel diameter (T) | — | — |
| Impeller diameter (D) | — | — |
| Impeller speed (N) | — | — |
| Reynolds number | — | — |
| Tip speed | — | — |
| Shaft power | — | — |
| Power per unit volume | — | — |
| Mixing time estimate | — | — |
About This Calculator
Understanding the mechanics behind the numbers.
Mechanical agitation is used throughout the process industries to blend miscible liquids, suspend solids, disperse gases, promote heat transfer and control reaction rate. The agitator converts shaft work into fluid motion; the fraction of that work that goes into bulk flow versus turbulent dissipation depends on impeller geometry, rotational speed, fluid rheology and vessel internals such as baffles.
Agitator power calculations are central to process design because they set the motor and gearbox rating, the mechanical seal and shaft design loads, and — through power per unit volume — the mixing intensity delivered to the batch. Under-sizing starves the process of turbulence or suspension capability; over-sizing wastes capital and energy and can shear-damage sensitive products such as crystals, cells or emulsions.
This tool applies the classical dimensionless-group approach (Reynolds number, Power number, Froude number, Pumping number) that underlies impeller correlations published by Rushton, Oldshue, Nagata and the Handbook of Industrial Mixing. Because published power and pumping numbers vary by manufacturer and exact blade geometry, the constants used here are representative literature values, not a substitute for vendor-certified performance curves.
Scale-up considerations
- Geometric similarity (constant T/D, C/T, blade proportions) must be preserved between lab, pilot and plant scale for correlations to remain valid.
- Common scale-up rules — equal tip speed, equal power/volume, equal Reynolds number, or equal blend time — give different impeller speeds at large scale; the correct rule depends on the controlling mechanism (shear, suspension, mass transfer).
- Power per unit volume typically falls with scale-up at constant tip speed, and rises at constant power/volume if blend time is the constraint — always check more than one criterion.
- Reynolds number normally increases with scale at fixed tip speed, so a laminar lab trial can become transitional or turbulent at plant scale.
Industrial applications
- Solid suspension: crystallizers, catalyst slurries, leaching tanks.
- Gas dispersion: fermenters, oxidation reactors, hydrogenation.
- Blending and homogenization: batch reactors, storage/day tanks.
- Heat transfer enhancement: jacketed and coil-cooled reactors.
- High-viscosity processing: polymer finishing, adhesives, food pastes (anchor, helical ribbon, sigma).
How to Use
Five steps from geometry to a sized motor.
- Enter reactor and liquid data. Diameter, liquid height, working volume, density and viscosity drive every downstream calculation — get these right first.
- Define the geometry. Choose top and bottom head types; this shapes the visualization and total vessel height check.
- Select the agitator. Pick from radial, axial, high-viscosity or specialized impeller families, then fill in impeller diameter, speed, blade count and elevation.
- Set baffles and process duty. Baffled vessels suppress the central vortex and are assumed for the turbulent power number; unbaffled vessels get a vortex-correction warning. Select the process objective for the intensity guideline.
- Calculate. Read power, torque, Reynolds number, mixing time and the recommended motor in the results table, and inspect the live reactor drawing.
Mathematical Formulas Used in This Calculator
Every equation below is implemented exactly as shown in the JavaScript that drives the results table.
Reynolds Number (impeller)
Re = ρ · N · D² / μ
Meaning: ratio of inertial to viscous forces at the impeller tip; sets the flow regime. Assumption: Newtonian fluid. Limitation: non-Newtonian (shear-thinning/thickening) fluids need an apparent-viscosity correction (e.g. Metzner–Otto) not applied here.
Flow Regime Classification
Re < 10 → Laminar | 10 ≤ Re ≤ 10,000 → Transitional | Re > 10,000 → Turbulent
Thresholds are the conventional mixing-literature bands (distinct from pipe-flow Re = 2,300/4,000) and are approximate; the transition is gradual, not a hard cut.
Power Number
Turbulent (Re > 10,000): Np = Np,turb (impeller constant)
Laminar (Re < 10): Np = Kp / Re
Transitional: log-linear interpolation between the two limits
Limitation: constants are representative literature values (Rushton, Oldshue, Handbook of Industrial Mixing); actual Np varies with exact blade geometry and vendor.
Froude Number & Unbaffled Vortex Correction
Fr = N²·D / g
If unbaffled: Np,corrected = Np · Fr^[(a − log₁₀Re)/b], a = 1, b = 40 (approximate)
Meaning: Fr compares centrifugal to gravitational force and governs central vortex depth in unbaffled/partially baffled vessels. Assumption: correction applied only when baffles = "None" or "Partial".
Agitator (Shaft) Power
P = Np · ρ · N³ · D⁵
Assumption: single impeller power; for multiple impellers on one shaft, total P is multiplied by an interaction factor (0.9–1.0 per additional impeller, spacing-dependent, simplified here as N_impellers × 0.92 per extra stage).
Shaft Torque & Tip Speed
τ = P / (2π·N) | vᵍ = π · D · N
Pumping Number & Circulation Rate
Q = Nq · N · D³
Nq is an impeller-specific constant (see table). Q is the primary (impeller-discharge) circulation flow, not total bulk turnover.
Motor Power & Sizing
Pᵍ₀ᵩ₀ᵣ = (P / η⃦ᵣᵫᵦᵩᵝᴸᵢᴸᵌ) · SF, η ≈ 0.92, SF = 1.15
The next standard motor size at or above Pᵍ₀ᵩ₀ᵣ is selected from the IEC list 0.25–110 kW.
Mixing (Blend) Time
N · θᵤ = 5.4 · (T/D)² · Np⁻¹⁵³ → θᵤ = 5.4·(T/D)² / (N · Np⁻¹⁵³)
Grenville-type turbulent blend-time correlation. Limitation: strictly valid for turbulent, low-viscosity, single-phase blending; not applicable to laminar high-viscosity mixing, where blend time is orders of magnitude longer and geometry-specific.
Power Density & Specific Mixing Energy
P/V (W/m³) = P / V⃗ᴸᵣᵍᵢᵝ
SME (kJ/m³) = (P · θᵤ) / V⃗ᴸᵣᵍᵢᵝ
Heat Generated by Agitation
Qᴸᴸ ≈ P (mechanical shaft energy dissipates almost entirely as heat in the batch)
Assumption: negligible energy leaves as noise/vibration; for gassed systems some energy transfers to bubble compression and is excluded here.
Mixing Scale of Agitation (Oldshue 1–10)
Scale = interpolate(vᵍ [ft/min] against reference table: 50→1, 90→2, 130→3, 170→4, 210→5, 250→6, 290→7, 330→8, 370→9, 410→10)
Meaning: a classical Oldshue/Chemineer industrial heuristic (originally tabulated as turbine HP per 1,000 gallons versus tip speed) used for quick, qualitative agitator selection — 1–2 is mild blending, 5–6 is typical solids-suspension/blending duty, 9–10 is vigorous dispersion. Limitation: it is a rule-of-thumb selection guide, not a rigorous design correlation, and was developed for turbine impellers in water-like fluids; treat it as a sanity check alongside the Np/Re-based power calculation, not a replacement for it.
Frequently Asked Questions
Common questions on agitator sizing, impeller selection and mixing calculations.
Engineering Assumptions
- Fluid is Newtonian and single-phase unless gas sparging is enabled.
- Power and pumping numbers are constant literature values per impeller family, not vendor-specific curves.
- Fully turbulent behaviour is assumed above Re = 10,000; below Re = 10 the laminar Kp/Re relation is used; the band between is log-linearly interpolated.
- Standard baffles (4, at 90°, width ≈ T/12) are assumed to fully suppress vortexing; "Partial" and "None" trigger a Froude-number power correction.
- Multiple impellers on a common shaft are summed with a simplified 0.92 interaction factor per additional stage rather than a full spacing-dependent model.
- Motor sizing uses a flat 92% drive-train efficiency and 1.15 service factor, then rounds up to the nearest standard IEC frame in the list provided.
- Vessel head volumes are not integrated from head type; working volume is taken from the user-entered value for power and mixing-time calculations.
- Gas sparging power correction (gassed vs ungassed) uses a simplified empirical de-rating factor based on aeration number, not a full Nienow/Roushton hold-up model.
- The 1–10 mixing scale of agitation is a qualitative heuristic derived from tip speed alone; it does not account for viscosity, impeller type or vessel geometry the way the Np/Re-based power calculation does.
Limitations
- Not a substitute for vendor-certified performance curves or a mechanical/seal/shaft design calculation.
- Non-Newtonian rheology is not modelled; high-viscosity, shear-thinning or thixotropic fluids will show inaccurate Reynolds numbers and power without an apparent-viscosity correction.
- Mixing time correlation applies to turbulent, low-viscosity blending only — do not use it for laminar or high-viscosity duties (anchor, ribbon, screw, sigma).
- Solid suspension (just-suspended speed, N₌₊) and gas hold-up/mass-transfer (k⃩a) are not independently verified against Zwietering- or Van't Riet-type correlations.
- Visualization groups the 20+ named agitators into representative geometric families for rendering; exact vendor blade profiles are not reproduced to scale.
- Applicable range: laboratory to typical production scale (roughly 1 L–500 m³); extreme scales should be verified against full-scale trial data.