What is the formula for calculating agitator power consumption?

The power absorbed by a mixing impeller in a fluid is calculated using the power number (Np) formula: P = Np * rho * N^3 * D^5, where P is shaft power in Watts, rho is fluid density in kg/m3, N is rotational speed in rev/sec, and D is impeller diameter in meters.

Why is an 85% motor loading factor applied in agitator motor selection?

Agitator power is proportional to the cube of rotational speed (N^3) and the fifth power of diameter (D^5). Minor process fluctuations, fluid viscosity increases, fluid level changes, or speed adjustments can lead to dramatic increases in absorbed power. Sizing the motor so the nominal demand does not exceed 80-85% of rated capacity protects against motor overload and thermal tripping.

How do tank baffles affect agitator power draw?

In unbaffled tanks operating in the turbulent regime, fluid undergoes bulk swirl and forms a central vortex, which dramatically reduces the power draw and mixing efficiency. Installing standard wall baffles (typically 4 baffles of width T/10 to T/12) converts swirl into vertical turnover and allows the impeller to reach its full turbulent Power Number (Np).

Tank agitator power calculation

Power calculation for typical blade turbine impellers

Question or remark ? Please contact us at contact@myengineeringtools.com

1. STEP 1 : Calculate the power number of the agitator
2. STEP 2 : Calculate the power number at actual process conditions
3. STEP 3 : Calculate the motor power required for the agitator
4. STEP 4 : Select the actual size of the motor
5. Interactive Online Agitator Power Calculator (SI & Imperial)
6. STEP by STEP example : agitator power requirement calculation
7. Industrial Best Practices, Baffling & Sizing Rules of Thumb
8. Free Excel calculation tool for agitator power requirement calculation

This page is explaining step by step how to calculate the power required for the motor of a turbine agitator of a tank holding liquid.

Introduction

Tanks holding liquid are often equipped with an agitator. The agitator can have many functions, like improving the heat transfer, homogenizing different liquid, preventing sedimentation...etc... One of the most common agitator design for holding tanks or for mixing liquids is a turbine impeller. The following design are standard :

Figure 1 : Values of turbulent power number Np for various impeller geometries (W/D is the actual blade-width-to-impeller-diameter-ratio)

With :

\(Np_{\text{standard}}\) = standard power number (-)
\(W\) = width of the blades of the impeller (m)
\(D\) = diameter of the impeller (m)

One of the key design parameter to calculate when implementing such an agitator is the size (power) of the motor which will drive the agitator.

WARNING : the calculation is only to define the power required to run the agitator, however it is not giving assurance that the agitation in the tank will be adequate, further calculations are required.

1. STEP 1 : Calculate the power number of the agitator

The power number in turbulent conditions is tabulated for standard design in the table above. The Engineer must select the type of agitator and then may correct the standard power number according to the actual size of the agitator in the tank.

If \((W/D)_{\text{standard}} = 1/5\) on table above :

\[Np = Np_{\text{standard}} \cdot \left[ \frac{(W/D)}{1/5} \right]^{1.25}\]

Np = Np_standard * [(W/D)/(1/5)]^1.25

If \((W/D)_{\text{standard}} = 1/6\) on table above :

\[Np = Np_{\text{standard}} \cdot \left[ \frac{(W/D)}{1/6} \right]\]

Np = Np_standard * [(W/D)/(1/6)]

With :

\(Np\) = power number in the geometry considered (-)
\(Np_{\text{standard}}\) = standard power number (-)
\(W\) = width of the blades of the impeller (m)
\(D\) = diameter of the impeller (m)

2. STEP 2 : Calculate the power number at actual process conditions

Step 2.1 : calculate the Reynolds number

The Reynolds number for an agitator can be calculated with the following formula :

\[N_{Re} = \frac{D^2 \cdot N \cdot \rho}{\mu}\]

N_Re = D².N.ρ / μ

With :

\(N_{Re}\) = impeller Reynolds number (-)
\(D\) = impeller diameter (m)
\(N\) = agitator speed (r/s)
\(\rho\) = liquid density (kg/m3)
\(\mu\) = liquid dynamic viscosity (Pa.s)

Step 2.2 : calculate the turbulent power number considering the actual viscosity

The Reynolds number allows to calculate a viscosity power factor by using the graph below :

Graph 1 : fμ as a function of N_Re = D².N.ρ/μ

The actual turbulent power number can then be calculated with :

\[Np_{\text{actual}} = f_\mu \cdot Np\]

Np_actual = fμ * Np

With :

\(Np_{\text{actual}}\) = actual turbulent power number (-)
\(f_\mu\) = viscosity power factor (-) - see graph above
\(Np\) = power number in the geometry considered (-) - see step 1

3. STEP 3 : Calculate the motor power required for the agitator

Now that the value of the power number is known, it is possible to go back to the definition of the power number to calculate the required power :

\[Np_{\text{actual}} = \frac{P}{\rho \cdot N^3 \cdot D^5}\]

Np_actual = P / (ρ.N³.D⁵)

\[P = Np_{\text{actual}} \cdot (\rho \cdot N^3 \cdot D^5)\]

P = Np_actual*(ρ.N³.D⁵)

With :

\(P\) = motor power required (W)
\(Np_{\text{actual}}\) = actual turbulent power number (-)
\(D\) = impeller diameter (m)
\(N\) = agitator speed (r/s)
\(\rho\) = liquid density (kg/m3)

4. STEP 4 : Select the actual size of the motor

Selecting a motor with the exact power as calculated on step 3 is not advisable as a small variation of speed could lead to an important variation in power. In practice, the actual load should not be over 85% of the calculated power requirement. Thus :

\[P_{\text{actual}} = \frac{P}{0.85}\]

P_actual = P/0.85

With :

\(P_{\text{actual}}\) = actual power requirement / recommended motor rating (kW)
\(P\) = calculated motor power requirement (kW)

⚡ Interactive Agitator Power Calculator

Units: Metric (SI) US / Imperial

Impeller Geometry Preset:

Standard Power Number \(Np_{\text{std}}\):

[-]

Standard \((W/D)_{\text{std}}\) Ratio:

Impeller Diameter (\(D\)):

Please enter a valid diameter > 0

Blade Width (\(W\)):

Please enter a valid width > 0

Agitator Speed (\(N\)):

rpm

Please enter a valid speed > 0

Liquid Density (\(\rho\)):

kg/m³

Please enter density > 0

Dynamic Viscosity (\(\mu\)):

cP (mPa·s)

Please enter viscosity > 0

Max Motor Load Fraction:

[-] (85%)

Impeller Width/Diameter Ratio (\(W/D\)): 0.200 [-]

Corrected Turbulent Power Number (\(Np\)): 1.27 [-]

Impeller Reynolds Number (\(N_{Re}\)): 89,600 [-] (Turbulent)

Viscosity Power Factor (\(f_\mu\)): 1.00 [-]

Actual Operating Power Number (\(Np_{\text{actual}}\)): 1.27 [-]

Tip Speed (\(v_{\text{tip}} = \pi \cdot D \cdot N\)): 5.03 m/s (16.49 ft/s)

Hydraulic Shaft Power (\(P\)): 3.50 kW (4.69 HP)

Recommended Motor Rating (\(P_{\text{actual}} = P / 0.85\)): 4.12 kW (5.52 HP) → Standard 5.5 kW (7.5 HP)

5. STEP by STEP example : agitator power requirement calculation

A chemical mixing vessel holds a fluid with density \(\rho = 1050 \text{ kg/m}^3\) and viscosity \(\mu = 15 \text{ cP} = 0.015 \text{ Pa}\cdot\text{s}\). The vessel is equipped with a 4-blade pitched blade turbine (45°) of diameter \(D = 0.80\text{ m}\) and blade width \(W = 0.16\text{ m}\), operating at a speed of \(N = 120\text{ rpm} = 2.0\text{ rev/s}\).

Step 1: Calculate the geometric power number \(Np\)

From standard reference data, for a 4-blade pitched turbine, \(Np_{\text{standard}} = 1.27\) with \((W/D)_{\text{standard}} = 1/5 = 0.20\).
Actual \(W/D = 0.16 / 0.80 = 0.20\). Since the ratio matches standard geometry: \[Np = 1.27 \cdot \left[\frac{0.20}{0.20}\right]^{1.25} = 1.27\]

Step 2: Calculate the Reynolds number and Viscosity Factor

The impeller Reynolds number is: \[N_{Re} = \frac{D^2 \cdot N \cdot \rho}{\mu} = \frac{(0.80\text{ m})^2 \cdot 2.0\text{ s}^{-1} \cdot 1050\text{ kg/m}^3}{0.015\text{ Pa}\cdot\text{s}} = 89,600\] Since \(N_{Re} > 10,000\), the mixing flow is fully turbulent, giving a viscosity power factor \(f_\mu = 1.00\).
Hence, \(Np_{\text{actual}} = f_\mu \cdot Np = 1.00 \cdot 1.27 = 1.27\).

Step 3: Calculate required shaft power \(P\)

Applying the turbulent power equation: \[P = Np_{\text{actual}} \cdot \rho \cdot N^3 \cdot D^5\] \[P = 1.27 \cdot (1050) \cdot (2.0)^3 \cdot (0.80)^5 = 1.27 \cdot 1050 \cdot 8 \cdot 0.32768 = 3,496.6\text{ W} \approx 3.50\text{ kW}\]

Step 4: Determine actual electric motor rating

Applying the standard 85% design load limit to prevent motor overloading under density surges or speed variations: \[P_{\text{actual}} = \frac{P}{0.85} = \frac{3.50\text{ kW}}{0.85} = 4.12\text{ kW} \quad (5.52\text{ HP})\] The plant engineer should select the next standard motor frame size: 5.5 kW (7.5 HP).

Industrial Agitation Best Practices & Rules of Thumb

Power Density Guidelines (\(P/V\)):
- Mild Blending & Storage: \(0.1 - 0.3\text{ kW/m}^3\) (\(0.5 - 1.5\text{ HP/1,000 gal}\)).
- Liquid-Liquid Dispersion & Solid Suspension: \(0.5 - 1.5\text{ kW/m}^3\) (\(2.5 - 7.5\text{ HP/1,000 gal}\)).
- Gas Dispersion & High-Mass Transfer Reactions: \(2.0 - 5.0+\text{ kW/m}^3\) (\(10 - 25+\text{ HP/1,000 gal}\)).
Impeller-to-Tank Diameter Ratio (\(D/T\)): Standard turbine impellers typically operate with \(D/T = 0.30 \text{ to } 0.45\). High-viscosity anchor and helical ribbons require \(D/T = 0.90 \text{ to } 0.98\).
Tank Baffling Rules: For turbulent flow (\(N_{Re} > 10,000\)), full baffling is essential to prevent deep vortexing and surface gas ingestion. Use 4 vertical wall baffles with width \(W_b = T / 12 \text{ to } T / 10\), offset from the wall by \(T / 50\) to eliminate stagnant solids accumulation.
Impeller Tip Speed Limits (\(v_{\text{tip}} = \pi D N\)):
- Shear-sensitive fluids (polymers, biological slurries, crystals): \(v_{\text{tip}} \le 2.0 - 3.5\text{ m/s}\).
- Standard blending and chemical mixing: \(v_{\text{tip}} = 3.5 - 7.5\text{ m/s}\).
- High-shear emulsification / dispersing: \(v_{\text{tip}} > 10 - 15\text{ m/s}\).
Mechanical Drive Losses: Remember to account for gearbox efficiency (\(\eta_{\text{gear}} \approx 95 - 97\%\)) and mechanical shaft seal drag (especially pressurized double mechanical seals with barrier fluid).

6. Free Excel calculation tool for agitator power requirement calculation

The power required to agitate a tank can be calculated thanks to this free Excel calculator : Calculation Tool - tank agitator power requirement calculation (click here)

Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.

Sources

[Chopey] Handbook of Chemical Engineering calculations, Chopey et al, McGraw Hill, 2004

[Perry] Perry's Chemical Engineers' Handbook, 8th Edition, Section 18: Liquid-Solid Operations and Agitation.