Power Number Calculation For Agitator

Power Number Equation:

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

Power (P):

Density (ρ):

kg/m³

Speed (N):

s⁻¹

Diameter (D):

Power Number (N_p):

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1. What is the Power Number?

The Power Number (N_p) is a dimensionless number used in mixing and agitation processes to characterize the power consumption of impellers. It represents the relationship between power input and the fluid's resistance to mixing.

2. How Does the Calculator Work?

The calculator uses the Power Number equation:

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

Where:

\( N_p \) — Power Number (dimensionless)
\( P \) — Power input (W)
\( \rho \) — Fluid density (kg/m³)
\( N \) — Impeller rotational speed (s⁻¹)
\( D \) — Impeller diameter (m)

Explanation: The Power Number relates the power consumed by an agitator to the fluid properties and impeller geometry, allowing for scale-up and design of mixing systems.

3. Importance of Power Number Calculation

Details: The Power Number is crucial for designing and scaling mixing systems, selecting appropriate impellers, and optimizing energy consumption in industrial mixing processes across chemical, pharmaceutical, and food industries.

4. Using the Calculator

Tips: Enter power in watts, density in kg/m³, rotational speed in revolutions per second, and impeller 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 vary by impeller type: Rushton turbines (4-6), pitched blade turbines (1-2), propellers (0.3-1.0), anchors (0.2-1.0).

Q2: How does Power Number relate to Reynolds Number?
A: In laminar flow, Power Number is inversely proportional to Reynolds Number, while in turbulent flow, Power Number becomes constant.

Q3: Why is Power Number dimensionless?
A: The units cancel out in the equation, making it a pure number that can be used for scale-up regardless of system size.

Q4: What factors affect Power Number?
A: Impeller geometry, baffle configuration, tank geometry, and fluid rheology all influence the Power Number value.

Q5: How is Power Number used in scale-up?
A: By maintaining constant Power Number between laboratory and industrial scales, similar mixing characteristics can be achieved.