Power Number Formula For Agitator

Power Number Formula:

\[ N_p = \frac{P}{\rho N^3 D^5} \]

Power (P):

Density (ρ):

kg/m³

Rotational Speed (N):

rev/s

Diameter (D):

Power Number (N_p):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Power Number Formula?

The Power Number (N_p) is a dimensionless number used in agitation and mixing processes to characterize the power consumption of an impeller or agitator. It relates the power input to the fluid properties and operating conditions.

2. How Does the Calculator Work?

The calculator uses the Power Number formula:

\[ N_p = \frac{P}{\rho N^3 D^5} \]

Where:

\( N_p \) — Power Number (dimensionless)
\( P \) — Power input (W)
\( \rho \) — Fluid density (kg/m³)
\( N \) — Rotational speed (rev/s)
\( D \) — Impeller diameter (m)

Explanation: The Power Number represents the ratio of power input to the inertial forces in the fluid. Lower values indicate more efficient mixing.

3. Importance of Power Number Calculation

Details: The Power Number is crucial for agitator design, scale-up studies, and optimizing mixing efficiency in chemical processes, bioreactors, and industrial mixing applications.

4. Using the Calculator

Tips: Enter power in watts, density in kg/m³, rotational speed in revolutions per second, and diameter in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of Power Numbers?
A: Power Numbers typically range from 0.2 to 5 for most impeller types, with specific values depending on impeller geometry and flow regime.

Q2: How does impeller type affect Power Number?
A: Different impeller designs (turbine, propeller, anchor) have characteristic Power Numbers that vary with Reynolds number and geometric parameters.

Q3: What is the relationship between Power Number and Reynolds number?
A: In laminar flow, Power Number is inversely proportional to Reynolds number, while in turbulent flow, it becomes relatively constant.

Q4: Can this formula be used for non-Newtonian fluids?
A: For non-Newtonian fluids, modified approaches using apparent viscosity may be required, and Power Number relationships can be more complex.

Q5: How is Power Number used in scale-up?
A: Power Number similarity is maintained during geometric scale-up to ensure similar power consumption per unit volume and mixing characteristics.