Power Number Calculation For Agitator

Power Number Equation:

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

Power (P):

Density (ρ):

kg/m³

Impeller Speed (N):

s⁻¹

Impeller Diameter (D):

Power Number (N_p):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Power Number?

The Power Number (N_p) is a dimensionless number used in agitation and mixing engineering to characterize the power requirements of an impeller in a fluid. It represents the ratio of power consumed to the power available from the fluid's inertia.

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 (unitless)
\( P \) — 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 consumption of an agitator to the fluid properties and impeller geometry, providing a standardized way to compare different mixing systems.

3. Importance of Power Number Calculation

Details: Power Number is essential for designing and scaling up mixing systems, selecting appropriate motors, optimizing energy consumption, and ensuring efficient mixing operations in chemical, pharmaceutical, and food industries.

4. Using the Calculator

Tips: Enter power in watts, density in kg/m³, impeller 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: axial flow impellers (0.3-1.0), radial flow impellers (4.0-6.0), and specialized designs may have different ranges.

Q2: How does Power Number relate to Reynolds number?
A: Power Number is relatively constant in turbulent flow (Re > 10,000) but varies significantly in transitional and laminar flow regimes.

Q3: Why is Power Number considered Reynolds number-independent?
A: In fully turbulent flow conditions, the Power Number becomes essentially constant and independent of Reynolds number, making it a reliable design parameter.

Q4: What factors affect Power Number?
A: Impeller geometry, baffle configuration, tank geometry, and fluid properties in non-turbulent regimes affect the Power Number.

Q5: How is Power Number used in scale-up?
A: Power Number remains constant during geometric scale-up in turbulent flow, allowing prediction of power requirements for larger systems.