**Hi Friends,**

Today I am presenting the gist of my technical paper on "Motor rating calculations for slurry mixing agitators in Alumina refinery" which has been published recently in aluminium issue of the magazine

# Sample calculations:

# Conclusions

Thanks and regards.

**"Minerals & Metals Review" (page 30 and 31 in MMR, August 2011 issue).**In various technical forums, process experts as well as equipment manufacturers have opined that the design of agitators for mixing bauxite, residue and hydrate in Alumina refinery is complicated and tricky issue. In this paper, we will discuss the subject with brief description of involved terminology, associated design parameters and methodology with sample motor rating calculations for the slurry mixing agitator of a Pre-desilication tank of Alumina refinery.

# Method to arrive at motor rating:

Impeller power for slurry mixing agitator is calculated using following mathematical relations-

Impeller Power, P = N

_{p}* ρ *N^{3}* D_{i}^{5}/(16*10^{4}) h.p.Where D

_{i}= Diameter of impeller in meters,N = Revolution per minute for impeller,

N

_{p}= Power number for impeller andρ = Specific gravity of slurry.

# Sample calculations:

Simplified calculations to arrive at the motor rating for the agitator of Pre-desilication tank of around 3000 m

^{3}gross capacity with realistic assumptions have been presented below-Fluid Height in Tank , H = 16 m and Diameter of tank, D

_{t}= 14 mSlurry volume in tank = π *D

_{t}^{2}*H/4 = π * (14)^{2}*16 /4 = 2463 m^{3}Solid consistency in Slurry = 50 % (w/w), Specific gravity of slurry, ρ = 1.602,

Viscosity of slurry, μ = 550 cp

Agitator Impeller Diameter, D

_{i}= 33 % of tank diameter = 14 * 33% m = 4.62 mTip speed of Impeller = 290 m/minute, Drive motor RPM = 1500 rpm.

Gear Box Reduction Ratio = 75

∴ Agitator RPM, N = Drive Motor RPM/Gear Box Reduction Ratio = 1500/75 = 20 rpm

Flow Number N

_{q}= 0.56 and Power Number, N_{p}= 0.51 (assumed figures)∴ Pumping Capacity = N

_{q}* N * D_{i}^{3}m^{3}/minute= 0.56 * 20 * (4.62)

^{3}= 1104.44 m^{3}/min. = 18.41 m^{3}/sec.Area of Tank = π * D

_{t}^{2 }= π *(14)^{2}/ 4 = 153.94 m^{2}Bulk fluid Velocity = pumping capacity/area of tank

= 1104.44 / 153.94= 7.18 m/min.= 23.55 ft./min.

Degree of Agitation = bulk fluid velocity / 6

(For 6 ft/min., degree of agitation =1 and Degree of agitation varies from 0 to 10)

= 23.55 / 6 = 3.93 ~ 4

Annular Area = π * (D

_{t}^{2}- D_{i}^{2}) /4Where D

_{t}= Diameter of tank and D_{i }= Diameter of impeller in meters.= 3.14 * (14

^{2}– (4.62^{2}) / 4 = 137.18 m^{2}Rising velocity of particles = pumping capacity / annular area

= 1104.44 / 137.18 = 8.051 m/min. = 0.1342 m/sec.

Tank Turnover rate = Pumping capacity / tank capacity

= 1104.44 / 2463 = 0.45 times / min.

Power Number N

_{p}= 0.51Shaft Power, P = N

_{p}* ρ *(D_{i})^{5}* N^{3}/(16 *10^{4})Where N

_{p}= Impeller power no., D_{i}= Diameter of impeller in meters,Shaft RPM, N = revolutions per minute

∴ Shaft Power, P = 0.51 * 1.602 * (4.402)

^{5}* 20^{3}/ (16 *10^{4}) = 85.98 h.p.Taking Gear Box Efficiency = 80% and Drive Motor Efficiency = 95%,

Design margin = 1.15

∴ Drive Motor Rating = 1.15 * 85.98/(0.80 * 0.95) =130 h.p. = 97.0 kW.

**Thus the drive motor of about 100 kW shall be adequate for successful operation of agitator of 3000 m**

^{3}Pre-desilication tank in Alumina refinery.# Conclusions

The developed methodology clearly reveals that motor rating calculations for any slurry mixing agitator can be carried out easily by simply replacing the associated input process conditions, operating parameters, dimensions of tanks / vessel and appropriate power number for impeller in above simplified derivation.

Please put your views / suggestion / remarks / comments, if any.

**If you like this article, then please press your rating as +1 .**

Thanks and regards.

**Kunwar Rajendra**

Hi, I would like ask is it the method you proposed above can be use for design the precipitation tank as well?

ReplyDeleteDear Mr. Roger Soon,

ReplyDeleteYes, you are absolutely correct. This is the method to carry out the basic design depending on the characteristics of material to be handled and operating conditions suiting the process requirement more particularly the RPM of agitator blades. Based on the basic design, Mechanical design of agitator is done.

Regards.

Kunwar Rajendra

Dear Mr. Rajendra ,

ReplyDeleteI have a open top slurry tank which holds 5 m3 of Ca(OH)2 ,in other words it is called milk of lime .

The tank height & internal diameter both are about 2.0 m and i intend to design and install a top mounted agitator on top of the tank.

Much appreciated if you could post a typical calculation methodology for sizing agitator based on the below data.

Slurry density =1080 kg/m3

Viscocity = 10 cP

% Solids (w/w)=12.5

Fluid temp = 50 deg max

Dear Mr. Kiran Kumar,

ReplyDeleteIt appears from your e.mail that you do not want to learn new things. May be that you are either very old or lethargic in nature.Do you want that some body else should develop calculations for you? It is just too much.Request you to take a piece of paper and a simple calculator to carry out calculations systematically as explained above. It will not take more than 10 minutes for you. Take this small challenge and let me know the outcome of your design calculations.

Hope, you will follow my advice and keep me posted.

Regards.

Kunwar Rajendra

Hi,

ReplyDeleteCan you suggest me how would we assume the impeller power number and flow number?

Hi Manas,

DeleteThanks for the very interesting question. Flow number and Power number are purely based on the design of impeller carried out by manufacturers. Thus, based on the experience of Designer with various types of impellers used in operating plants, these numbers are assumed and taken into consideration while designing such complicated system.

Hope, the above clarifies your doubts.

Regards.

Kunwar Rajendra

Hi,

DeleteKindly clarify me whether the slurry viscosity plays any role for selection of agitator or not?

Dear Manas,

ReplyDeleteViscosity, Specific gravity and Particle size in slurry play vital role in selection of agitator including its drive components.

Thanks and regards.

Kunwar Rajendra

Dear Mr. Rajendra, thanks for this important contribution. I have two questions.

ReplyDelete1. How can we integrate the fact if having 2 impellers on the same shaft.

2. What are the main differences with calculating a thickener

Dear Roger,

ReplyDeleteThank you very much for appreciating the articles published on my blog. The number of stages of impellers are decided on the basis of degree of agitation required for particular service conditions to prevent settling of solids. However, agitator (rake) for settling tanks are designed on the basis of torque developed for movement of settled mud.

Trust, the above clarifies your doubts.

Regards.

Kunwar Rajendra