Power Number Calculation

Power Number Equation:

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

Power (P):

Density (ρ):

kg/m³

Speed (N):

rev/s

Diameter (D):

Power Number (N_p):

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1. What is Power Number?

The Power Number (N_p) is a dimensionless number used in fluid mixing to characterize the power consumption of agitators and impellers. It relates the power required for mixing to the fluid properties and agitator geometry.

2. How Does the Calculator Work?

The calculator uses the Power Number equation:

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

Where:

\( N_p \) — Power Number (dimensionless)
\( P \) — Power input (Watts)
\( \rho \) — Fluid density (kg/m³)
\( N \) — Impeller rotational speed (revolutions per second)
\( D \) — Impeller diameter (meters)

Explanation: The Power Number represents the ratio of power consumed to the power required to accelerate the fluid. It varies with impeller type and flow regime.

3. Importance of Power Number Calculation

Details: Power Number is essential for designing mixing systems, selecting appropriate agitators, estimating power requirements, and optimizing energy consumption in industrial mixing processes.

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), and anchors (0.2-1.0).

Q2: How does Reynolds number affect Power Number?
A: In laminar flow (Re < 10), Power Number decreases with increasing Reynolds number. In turbulent flow (Re > 10,000), Power Number becomes constant.

Q3: Why is Power Number dimensionless?
A: Power Number is dimensionless because it represents a ratio of forces (inertial to viscous forces) and is derived through dimensional analysis.

Q4: Can Power Number be used for non-Newtonian fluids?
A: Yes, but modified approaches using apparent viscosity or Metzner-Otto correlation are needed for accurate calculations with non-Newtonian fluids.

Q5: How does impeller geometry affect Power Number?
A: Different impeller designs (turbines, propellers, anchors) have characteristic Power Numbers due to variations in flow patterns and energy dissipation.