This post is a little different from usual. Honestly, I seldom dealing with agitation process. As you may know from my posts, my projects are mostly in oil and gas field. So, agitation process is very rare in oil and gas processing. However, I think I need to learn something beyond what I already learned until now to improve myself.

In this post, I want to share simple calculation methods to estimate power required to rotate agitator impeller. In the future, maybe I will deal with project involving agitation process.

**Difference Between Agitation and Mixing**

I thought agitation and mixing are the same terms. However, there is difference between those two.

Agitation refers to the induced motion of “homogenous” material in specified way. While, mixing is the random distribution, into and through one another, of two or more initially separate phases.

An impeller causes the liquid to circulate through the vessel and eventually return to the impeller.

The three main types of impellers for low- to moderate-viscosity liquids are:

- Propellers
- Turbines
- High-efficiency impellers

For very viscous liquids, the most widely used impellers are helical impellers and anchor agitators.

**Agitator Impeller Power Calculation**

Procedures involve in agitator impeller power calculation are:

- Determine the turbulent power number for impeller geometry
- Determine the power number at process and operating conditions
- Calculate shaft horsepower required to rotate the impeller
- Select a standard motor horsepower

**Please be noted, **that these calculations do not give any indication of whether or not the agitation produced is adequate for process requirements. The calculation only for determine the horsepower and speed required to achieve a given process result.

**[1] Determine the turbulent power number (N _{P}) for impeller geometry**

Power number (NP) is a dimensionless variable which relates impeller power (P) to operating variables, such as liquid density, agitator rotational speed (N), and impeller diameter (D).

The correlation is as follow:

Where:

N_{P} = power number

P = horsepower (hp)

ρ = liquid density (expressed as specific gravity)

N = agitator rotational speed (rpm)

D = impeller diameter (in)

For a given impeller geometry, the power number is constant for conditions of turbulent agitation.

Values for turbulent power numbers of some agitator impellers are shown in figure below. It is function of impeller width to diameter ratio (W/D), impeller type, and number of blades.

Power numbers shown in figure above assume fully baffled conditions, which for cylindrical tank would require four equally spaced vertical plate-type baffles. The baffles should extend the full height of the vertical wall of tank and should be 1/12 to 1/10 the tank diameter in width.

When an agitator has nonstandard W/D, a factor must be applied.

For a four-blade impeller, a factor of actual W/D to standard W/D raised to 1.25 power must be applied. For example, let say we have a pitched-blade turbine impeller that is 58 in diameter and has four 12-in-wide blades. The power number (N_{P}) would be:

N_{P} = [(12/58)/(1/5)]^{1.25} x 1.37 = __1.43__

On the other hand, for a six-blade impeller, power number is the ratio of actual W/D to standard W/D. Given the same impeller width and impeller diameter as previous example, however the impeller type is pitched-blade type with six blades. The power number would be:

N_{P} = [(12/58)/(1/5)] x 1.70 = __1.75__

**[2] Determine the power number (N _{P}) at process and operating conditions**

Power number is a function of Reynolds number and impeller geometry. A correction factor based on Reynolds number accounts primarily for the effects of viscosity on power.

Reynolds number is expressed by the following equation:

Where:

N_{Re} = Reynolds Number

D = impeller diameter (in)

N = agitator rotational speed (rpm)

ρ = liquid density (expressed as specific gravity)

μ = viscosity (cP)

After Reynolds number is computed, we need to find viscosity power factor. It can be found by graph below. Viscosity power factor is a function of Reynolds number and type of impeller.

Power number calculated in Step 1 is then corrected with viscosity power factor.

**[3] Calculate shaft horsepower (P) required to rotate the impeller**

Shaft horsepower requirement can be determined by rearranging the power number in Step 1. Therefore, the equation will be:

**[4] Select a standard motor horsepower**

A typical turbine impeller-type agitator consists of motor, gear reducer, shaft, and one or more impellers. Losses through gear reducer are typically only 3 to 8 percent. However, slight deviation in actual speed and fluctuations in process conditions make motor loadings in excess of 85% of calculated impeller power unadvisable. Therefore, minimum motor power would be:

Minimum motor power = Calculated shaft horsepower/85%

Selected motor power should consider commercially available motor.

**Free Spreadsheet of Agitator Impeller Power Calculation**

**This spreadsheet **show you how to compute agitator impeller power calculation based on steps above. Please feel free to download and I hope you find this useful.

**Reference**

Chopey, Nicholas P, “Handbook of Chemical Engineering Calculations – Fourth Edition”, The McGraw-Hill Companis, 2012.