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Tank agitator power calculation

Power calculation for typical blade turbine impellers

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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. STEP by STEP example : agitator power requirement calculation
6. 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 :

Values of turbulent power number Np for various impeller geometries

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

With :

Npstandard = 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)standard = 1/5 on table above :

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

If (W/D)standard = 1/6 on table above :

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

With :

Np = power number in the geometry considered (-)
Npstandard = 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 :

NRe = D2.N.ρ / μ

With :

NRe = impeller Reynolds number (-)
D = impeller diameter (m)
N = agitator speed (r/s)
ρ = liquid density (kg/m3)
μ = liquid 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 NRe = D2.N.ρ/μ

The actual turbulent power number can then be calculated with :

Npactual = fμ * Np

With :

Npactual = actual turbulent power number (-)
fμ = 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 :

Npactual = P / (ρ.N3.D5)

P = Npactual*(ρ.N3.D5)

With :

P = motor power required ()
Npactual = actual turbulent power number (-)
D = impeller diameter (m)
N = agitator speed (r/s)
ρ = 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 varation in power. In practice, the actual load should not be over 85% of the calculated power requirement. Thus :

Pactual = P/0.85

With :

Pactual = actual power requirement (kW)
P = calculated motor power requirement (kW)

5. STEP by STEP example : agitator power requirement calculation

Will be updated soon.

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.

Screenshot Agitator Power calculator


Sources

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