How to Calculate Power Number of Agitator

Power Number Equation:

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

Power (P):

Density (ρ):

kg/m³

Speed (N):

rps

Diameter (D):

Power Number (N_p):

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1. What is the Power Number of Agitator?

The Power Number (N_p) is a dimensionless number used in mixing and agitation to characterize the power consumption of an impeller. It relates the power input to the fluid properties and impeller geometry, providing crucial information for mixer design and scale-up.

2. How Does the Calculator Work?

The calculator uses the Power Number equation:

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

Where:

\( N_p \) — Power Number (dimensionless)
\( P \) — Power input (Watts)
\( \rho \) — Fluid density (kg/m³)
\( N \) — Impeller rotational speed (revolutions per second)
\( D \) — Impeller diameter (meters)

Explanation: The Power Number represents the ratio of power input to the inertial forces in the fluid. It varies with impeller type, geometry, and flow regime.

3. Importance of Power Number Calculation

Details: The Power Number is essential for designing mixing systems, selecting appropriate impellers, scaling up mixing processes, and optimizing energy consumption in industrial applications.

4. Using the Calculator

Tips: Enter power in watts, density in kg/m³, speed in revolutions per second (rps), and diameter in meters. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of Power Numbers?
A: Power Numbers typically range from 0.3 to 6.0 depending on impeller type, with high-efficiency impellers having lower values and high-shear impellers having higher values.

Q2: How does impeller type affect Power Number?
A: Different impeller types (marine propeller, turbine, anchor, etc.) have characteristic Power Numbers that remain relatively constant in the turbulent regime.

Q3: What flow regime is this equation valid for?
A: The equation is primarily valid for turbulent flow conditions (Re > 10,000), where Power Number becomes relatively constant.

Q4: Can Power Number be used for scale-up?
A: Yes, Power Number is a key parameter for geometric scale-up of mixing systems while maintaining similar power per unit volume.

Q5: How does viscosity affect Power Number?
A: In laminar flow (Re < 10), Power Number becomes inversely proportional to Reynolds number, while in transitional flow it varies significantly.