Hong Life CalculatorsUnderstanding the agitator power calculator — concept and principle
An agitator turns a motor's shaft power into fluid motion. Before choosing a motor or impeller, this calculator gives the turbulent shaft power, the impeller Reynolds number, the power per unit volume and the impeller tip speed.
How it is calculated
- Speed in revolutions per second: n = N ÷ 60, where N is in rpm.
- Shaft power: P = Np × ρ × n³ × D⁵ in watts (ρ in kg/m³, D in m), shown in kW.
- Impeller Reynolds number: Re = ρ × n × D² ÷ μ (μ in Pa·s).
- Power per volume: P ÷ V (W/m³).
- Tip speed: π × D × n (m/s).
The principle
Dimensional analysis shows that the power drawn by a geometrically fixed impeller depends on a single group, Np = P/(ρn³D⁵), which is a function of the Reynolds number. In fully turbulent flow (roughly Re above 10⁴) in a baffled tank, Np becomes almost constant: about 5 for a six-blade Rushton turbine, about 1.3 for a 45° pitched-blade turbine and about 0.3 for a hydrofoil. Viscosity then no longer matters and power rises with the cube of speed and the fifth power of diameter. That is why a small change in diameter has a large effect: a 10% larger impeller at the same speed draws about 61% more power.
Worked example
- Defaults: Np = 5, ρ = 1000 kg/m³, N = 120 rpm, D = 0.5 m, μ = 0.001 Pa·s, V = 2 m³.
- n = 120 ÷ 60 = 2 rev/s, so n³ = 8 and D⁵ = 0.03125.
- P = 5 × 1000 × 8 × 0.03125 = 1250 W = 1.25 kW.
- Re = 1000 × 2 × 0.25 ÷ 0.001 = 500,000, well into the turbulent range, so the constant-Np formula applies.
- P/V = 1250 ÷ 2 = 625 W/m³.
- Tip speed = π × 0.5 × 2 = 3.14 m/s.
| Impeller diameter (m) | Power (kW, turbulent) |
|---|---|
| 0.125 | 0.0012207031 |
| 0.25 | 0.0390625 |
| 0.375 | 0.2966308594 |
| 0.5 | 1.25 |
| 0.625 | 3.814697266 |
| 0.75 | 9.4921875 |
| 1 | 40 |
How to read the result
Check the Reynolds number first. Below about 10⁴ the flow is transitional and the real power number differs from the turbulent value; below about 10 the flow is laminar and power becomes proportional to μn²D³ instead. Power per volume is the usual measure of mixing intensity: gentle blending of thin liquids needs far less than gas dispersion or solids suspension, so compare your figure with values from similar duties.
Common mistakes
- Using the turbulent power number for viscous liquids or unbaffled tanks, where vortexing lowers the power draw.
- Sizing the motor at the shaft power alone, without gearbox losses, start-up and a service margin.
Frequently asked questions
Why does power depend on D⁵?
The flow rate pumped by the impeller scales as nD³ and the head it develops as n²D², so their product, the power, scales as n³D⁵.
Does gassing change the power?
Yes. Gas bubbles collect behind the blades and the gassed power can be well below the ungassed value calculated here.
Is the result the motor rating?
No. It is shaft power; the motor must also cover gearbox and seal losses plus a margin.
Sources: Rushton, J. H., Costich, E. W. & Everett, H. J. (1950). Power characteristics of mixing impellers. Chemical Engineering Progress, 46, 395–404 and 467–476. · Paul, E. L., Atiemo-Obeng, V. A. & Kresta, S. M. (eds.) (2004). Handbook of Industrial Mixing. Wiley.