How to Calculate Power Required for Agitator

Agitator Power Equation:

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

Power Number (N_p):

unitless

Density (ρ):

kg/m³

Rotational Speed (N):

rev/s

Impeller Diameter (D):

Power Required (P):

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1. What is the Agitator Power Equation?

The agitator power equation calculates the power required to operate a mixing impeller in a fluid. It is based on the relationship between power number, fluid density, rotational speed, and impeller diameter, providing essential data for mixer design and selection.

2. How Does the Calculator Work?

The calculator uses the agitator power equation:

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

Where:

\( P \) — Power required (W)
\( N_p \) — Power number (unitless, 0.3-5 for impellers)
\( \rho \) — Fluid density (kg/m³)
\( N \) — Rotational speed (rev/s)
\( D \) — Impeller diameter (m)

Explanation: The equation demonstrates that power consumption increases dramatically with both rotational speed (cubed) and impeller diameter (to the fifth power), highlighting the importance of proper impeller selection.

3. Importance of Power Calculation

Details: Accurate power calculation is crucial for selecting appropriate motors, ensuring efficient mixing, preventing equipment overload, and optimizing energy consumption in industrial mixing processes.

4. Using the Calculator

Tips: Enter power number (typically 0.3-5 for most impellers), fluid density in kg/m³, rotational speed in revolutions per second, and impeller diameter in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the power number (N_p)?
A: The power number is a dimensionless parameter that characterizes the resistance of an impeller to rotation in a fluid. It depends on impeller type, geometry, and flow regime.

Q2: How do I determine the power number for my impeller?
A: Power numbers are typically obtained from manufacturer specifications, technical literature, or experimental data. Common values range from 0.3 for high-efficiency impellers to 5 for high-shear impellers.

Q3: Why is power proportional to D⁵?
A: The fifth power relationship comes from the combination of increased swept area (D²) and increased tip speed (N×D), resulting in power ∝ N³D⁵ due to fluid dynamic principles.

Q4: What factors affect power requirements?
A: Fluid viscosity, impeller type, baffle configuration, tank geometry, and operating conditions all influence power requirements beyond the basic equation parameters.

Q5: Should I include a safety factor?
A: Yes, it's recommended to include a safety factor (typically 10-25%) to account for startup torque, fluid property variations, and potential process changes.