Power Number Calculator

Case	Power	Density	Speed	Diameter	Viscosity	Power Number
Water Test	2.5 kW	998 kg/m³	120 rpm	0.35 m	0.001 Pa·s	5.17
Light Slurry	4.2 kW	1120 kg/m³	95 rpm	0.42 m	0.008 Pa·s	6.47
Viscous Blend	1.8 kW	1045 kg/m³	60 rpm	0.50 m	0.120 Pa·s	4.43

Formula Used

Primary equation: Np = P / (ρ × N³ × D⁵)

Here, Np is the power number, P is shaft power in watts, ρ is fluid density in kg/m³, N is rotational speed in revolutions per second, and D is impeller diameter in meters.

Reynolds number: Re = (ρ × N × D²) / μ

This supporting value helps classify laminar, transitional, or turbulent mixing behavior. Power number trends often depend on flow regime and impeller geometry.

How to Use This Calculator

Select what you want to solve for.
Enter mixer power, density, speed, and diameter with matching units.
Add viscosity to estimate Reynolds number and flow regime.
Set drive efficiency if motor power differs from shaft power.
Press the calculate button to show results above the form.
Use the CSV or PDF buttons to export the summary.

FAQs

1. What does power number represent?

Power number is a dimensionless value that compares agitator power demand across different sizes, fluids, and speeds. It supports mixer design, scale-up, and equipment comparison.

2. Why is shaft power used instead of motor rating?

Shaft power reflects the actual mechanical energy delivered to the impeller. Motor nameplate power can overstate mixing energy if transmission losses are present.

3. Why does viscosity matter here?

Viscosity changes Reynolds number, which influences flow regime. In laminar systems, power number behavior can differ greatly from turbulent systems.

4. Can I use rpm directly in the formula?

No. The main equation requires rotational speed in revolutions per second. This calculator converts rpm automatically before solving.

5. Does impeller type change the answer?

Yes. Different impellers produce different characteristic power numbers. The selected impeller note is informational, but final design should use tested geometry data.

6. Is this useful for scale-up studies?

Yes. Engineers often compare power number, tip speed, and Reynolds number when scaling mixers from pilot equipment to production vessels.

7. What if my process is non-Newtonian?

This tool assumes a single apparent viscosity input. Strongly non-Newtonian fluids may require rheology-based correlations and more specialized agitation models.