Agitator Scale Up Calculation

Power Scale Equation:

\[ Power\ Scale = \left(\frac{N_2}{N_1}\right)^3 \times \left(\frac{D_2}{D_1}\right)^5 \]

Initial Speed (N₁):

rpm

Final Speed (N₂):

rpm

Initial Diameter (D₁):

Final Diameter (D₂):

Power Scale:

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1. What is Agitator Scale Up Calculation?

The Agitator Scale Up Calculation determines the power requirements when scaling agitator systems from laboratory to industrial scale. It helps engineers properly size motors and predict power consumption for mixing operations.

2. How Does the Calculator Work?

The calculator uses the Power Scale equation:

\[ Power\ Scale = \left(\frac{N_2}{N_1}\right)^3 \times \left(\frac{D_2}{D_1}\right)^5 \]

Where:

\( N_1 \) — Initial agitator speed (rpm)
\( N_2 \) — Final agitator speed (rpm)
\( D_1 \) — Initial agitator diameter (m)
\( D_2 \) — Final agitator diameter (m)

Explanation: The equation shows that power scales with the cube of speed and the fifth power of diameter, making diameter changes particularly significant in scale-up operations.

3. Importance of Power Scale Calculation

Details: Accurate power scale calculation is crucial for designing efficient mixing systems, selecting appropriate motors, and ensuring process consistency when scaling up from laboratory to production scale.

4. Using the Calculator

Tips: Enter initial and final agitator speeds in rpm, and initial and final diameters in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why does diameter have a fifth power relationship?
A: The fifth power relationship comes from the combination of area (D²) and torque (D³) dependencies, resulting in power ∝ D⁵ for geometrically similar systems.

Q2: What are typical power scale values?
A: Power scale values can range from less than 1 (scale-down) to thousands (large scale-up), depending on the size difference between systems.

Q3: When is this calculation most applicable?
A: This calculation is most accurate for geometrically similar systems operating in the turbulent flow regime with Newtonian fluids.

Q4: Are there limitations to this equation?
A: The equation assumes geometric similarity and may not account for changes in fluid properties, non-Newtonian behavior, or different impeller types.

Q5: How does viscosity affect the calculation?
A: For highly viscous fluids or laminar flow conditions, the power relationship may differ from the standard turbulent flow equation.