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):

rps

Impeller Diameter (D):

Power Number (N_p):

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1. What is the Power Number Formula?

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.

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 (rps)
\( D \) — Impeller diameter (m)

Explanation: The power number represents the ratio of power input to the inertial forces in the fluid, providing insight into the efficiency and performance of mixing equipment.

3. Importance of Power Number Calculation

Details: The power number is crucial for designing and scaling mixing systems, optimizing energy consumption, and ensuring proper agitation in various industrial processes including chemical reactors, bioreactors, and food processing.

4. Using the Calculator

Tips: Enter power in watts, density in kg/m³, rotational speed in revolutions per second (rps), and impeller diameter in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of power numbers?
A: Power numbers vary by impeller type, typically ranging from 0.2 to 5 for common impellers like turbines and propellers.

Q2: How does impeller type affect power number?
A: Different impeller designs (turbine, propeller, anchor, etc.) have characteristic power numbers that depend on their geometry and flow patterns.

Q3: What is the significance of power number in scale-up?
A: Power number remains constant during geometric scale-up, making it a key parameter for predicting power requirements in larger systems.

Q4: How does fluid viscosity affect power number?
A: Power number generally increases with Reynolds number in the laminar and transitional flow regimes, becoming constant in fully turbulent flow.

Q5: Can this formula be used for non-Newtonian fluids?
A: For non-Newtonian fluids, additional considerations are needed as viscosity varies with shear rate, affecting the power number relationship.