How To Calculate Power Number Of Agitator

Power Number Equation:

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

Power (P):

Density (ρ):

kg/m³

Speed (N):

s⁻¹

Diameter (D):

Power Number (N_p):

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1. What Is The Power Number Of Agitator?

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

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 (dimensionless)
\( P \) — Power input (W)
\( \rho \) — Fluid density (kg/m³)
\( N \) — Impeller rotational speed (s⁻¹)
\( D \) — Impeller diameter (m)

Explanation: The Power Number represents the ratio of power consumed by the impeller to the power required to accelerate the fluid. It depends on impeller type, geometry, and flow regime.

3. Importance Of Power Number Calculation

Details: Power Number is crucial for agitator design, motor sizing, energy consumption estimation, and scaling up mixing processes from laboratory to industrial scale.

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: radial flow impellers (4-6), axial flow impellers (0.3-1.5), and anchor impellers (0.2-1.0).

Q2: How does Reynolds number affect Power Number?
A: In laminar flow (Re < 10), N_p is inversely proportional to Re. In turbulent flow (Re > 10⁴), N_p becomes constant.

Q3: Why is Power Number dimensionless?
A: It's derived from dimensional analysis and represents the ratio of drag force to inertial force, making it independent of scale.

Q4: How does impeller geometry affect Power Number?
A: Blade shape, number of blades, diameter-to-tank ratio, and off-bottom clearance significantly influence the Power Number value.

Q5: Can Power Number predict mixing efficiency?
A: While Power Number indicates power consumption, mixing efficiency depends on other factors like flow patterns, blend time, and shear rates.