Power Calculation Formula for Agitator

Power Calculation Formula:

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

Power Number (N_p):

unitless

Density (ρ):

kg/m³

Rotational Speed (N):

rev/s

Diameter (D):

Power (P):

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1. What is the Power Calculation Formula for Agitator?

The Power Calculation Formula for Agitator is used to determine the power required to operate an agitator or mixer in fluid systems. This formula considers the power number, fluid density, rotational speed, and impeller diameter to calculate the mechanical power consumption.

2. How Does the Calculator Work?

The calculator uses the power calculation formula:

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

Where:

\( P \) — Power (W)
\( N_p \) — Power number (unitless)
\( \rho \) — Density (kg/m³)
\( N \) — Rotational speed (rev/s)
\( D \) — Diameter (m)

Explanation: The formula demonstrates that power consumption is highly dependent on rotational speed (cubed relationship) and impeller diameter (fifth power relationship), making these the most critical factors in agitator design.

3. Importance of Power Calculation

Details: Accurate power calculation is essential for proper motor selection, energy efficiency optimization, and ensuring adequate mixing performance in industrial processes involving liquids, suspensions, and emulsions.

4. Using the Calculator

Tips: Enter power number (typically 0.5-5 for different impeller types), fluid density in kg/m³, rotational speed in revolutions per second, and impeller diameter in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for power number (N_p)?
A: Power number varies with impeller type: 0.2-0.5 for propellers, 1-5 for turbines, and can be higher for specialized impellers depending on geometry and flow conditions.

Q2: Why is rotational speed raised to the third power?
A: The cubic relationship reflects that power consumption increases dramatically with speed due to increased fluid resistance and energy dissipation.

Q3: How does impeller diameter affect power consumption?
A: Diameter has the strongest influence (fifth power) because larger impellers move more fluid and create greater resistance, significantly increasing power requirements.

Q4: When is this formula most accurate?
A: The formula works best for Newtonian fluids in turbulent flow conditions. For non-Newtonian fluids or transitional/laminar flow, additional corrections may be needed.

Q5: Can this be used for scale-up calculations?
A: Yes, this formula is fundamental for scaling agitator systems from laboratory to industrial scale while maintaining similar power per unit volume or other scaling criteria.