Engineering calculator reviewed for preliminary design use · Last updated: March 2026
Calculate agitator power P = Np × ρ × n³ × D⁵ from power number Np, fluid density, rotational speed, and impeller diameter. Apply to mixer and agitator selection for reactors and blending tanks.
What this calculator is used for
Correctly estimating agitator power is essential for motor selection and process vessel design. Power is calculated using the dimensionless Power Number (Np), which depends on impeller geometry and the mixing Reynolds number.
Typical engineering use cases
Sizing motors and gearboxes for stirred tanks and reactors
Setting power per unit volume (P/V) for blending, suspension, or heat transfer
Maintaining consistent P/V or tip speed during scale-up
Selecting impeller type and judging laminar vs turbulent regime for viscous fluids
Governing equation and methodology
In the turbulent regime the required agitation power is:
P = Np × ρ × n³ × d⁵
where Np is the Power Number, ρ the liquid density [kg/m³], n the rotational speed [rev/s], and d the impeller diameter [m]. Np depends on impeller type and flow regime (turbulent values ≈ 5 for a Rushton turbine, ≈ 2 for a paddle, ≈ 0.35 for a propeller). The regime is set by the mixing Reynolds number Re = ρ·n·d²/μ: Re > 10,000 is turbulent (constant Np) and Re < 10 is laminar.
Engineering assumptions and limitations
Assumes a standard baffled tank with standard geometric ratios
Np is constant only in the turbulent regime; it is Re-dependent in transition/laminar flow
Gas–liquid and solid–liquid systems need gassing/loading corrections
Non-Newtonian fluids require an apparent-viscosity assessment
Practical design notes
Because power scales with the cube of speed and the fifth power of impeller diameter, small geometry or speed changes have a large effect. For scale-up, choose a basis suited to the duty (constant P/V or constant tip speed). Allow generous motor margin for start-up against high viscosity or a full vessel.
Worked Example
Given:
Rushton turbine, Power number Np = 5.0 (turbulent)
Liquid ρ = 1000 kg/m³, μ = 0.001 Pa·s
Impeller D = 0.5 m, speed N = 2 rev/s (120 rpm)
Method: Check regime: Re = ρ·N·D²/μ = 1000·2·0.25/0.001 = 5×10⁵ (turbulent, Np constant). Power P = Np·ρ·N³·D⁵ = 5·1000·2³·0.5⁵.
Result: P ≈ 1.25 kW (impeller draw).
Interpretation: Power scales with N³ and D⁵, so a 20 % speed increase pushes draw up ~70 % — sizing the motor and gearbox is acutely sensitive to final rpm. Add transmission losses and a margin for start-up of a settled/viscous batch, where the instantaneous torque can far exceed this steady value.
Common Mistakes & Misuse
Reading a turbulent Power number Np off the chart when Re is in the laminar/transitional range, where Np = constant no longer holds and Np ∝ 1/Re.
Using the baffled-tank Np for an unbaffled vessel, which vortexes and draws markedly different (usually lower) power.
Ignoring the gassed-power reduction — sparging gas can cut impeller power draw by 30–50% versus the ungassed value.
Treating a shear-thinning (non-Newtonian) fluid with a single viscosity, when the apparent viscosity depends on the impeller shear rate.
Frequently Asked Questions
How do I determine the Power number Np?
Np depends on impeller type and Reynolds number. For turbulent flow: Rushton turbine ~5, pitched blade ~1.3, marine propeller ~0.35. Np is approximately constant in the turbulent regime (Re > 10,000).
Does this account for baffles?
The Power number values assume standard baffled tank geometry (4 baffles, width = T/10). Unbaffled tanks produce vortexing and require different correlations. Baffle configuration affects both Np and mixing performance.
For preliminary estimation and educational use only. Results may depend strongly on assumptions, input data, fluid or material properties, and the range of validity of the underlying equation. Verify critical calculations independently and follow the applicable code, specification, and formal engineering review process before using any result for design, procurement, fabrication, operation, or safety decisions.