Hi Friends,
Capacity of the tank = p*r2*h
You will appreciate the efforts made in elaborating such a complicated design calculations in simpler form for easy understanding. With presented basic calculations, design for mixing agitator for any duty can be carried out very easily just by replacing the applicable parameters and variables. I am sure, you will not find such systematic calculations in any published document as I have developed the same in the interest of community around.
Please put your views / suggestions / remarks / comments, if any, on the matter.
Kunwar Rajendra
In earlier posts, we have studied various terminology as well as basic guidelines for design of mixing agitators used in Alumina refinery. In present post, all out efforts have been made for carrying out the step-by-step calculations in working out drive motor rating calculations for slurry mixing agitators used in Alumina refineries.
Following is the sample process design calculation for Agitator for Pre-desilication tanks of a typical Alumina Refinery having production capacity of 1.5 Mtpa calcined alumina. A few engineering data like power number for impellers of agitator have been taken from the published literature of reputed manufacturers for agitators in the World.
The sample calculations have been developed for a typical size of slurry tank with the dimensions as detailed below-
Fluid Height in Tank = 16 m = 16000 mm
This is the height of the fluid in the tank
Diameter of the tank = 14 m = 14000 mm
Normally the fluid height and the tank diameter are the same but the tank height is little more to keep some space for overflow of the material to the next tank.
= 3.14 * 7*7*16
= 2463 m3
Solids in Slurry = 50 % (w/w)
For typical plant capacity of 1.5 Mtpa Alumina refinery,
Slurry Flow Rate = 260 m3/ hr.
Specific gravity of solids and liquid in slurry-
- Solids = 2.57
- Liquid = 1.28
- Slurry = 1.60
Density of slurry = 1660 kg/m3
Temperature-
- Inlet = 100*C
- Outlet = 100*C
Viscosity of slurry = 550 cp
= 5.5 poise (1 cp = 0.01 poise)
= 0.55 Pa.s
Hardness index of solids = 3-4 Moh’s scale
pH of slurry =14 (highly alkaline)
Max. Particle size = 0.21 mm
= 210 microns (1mm = 1000 microns)
Settling velocity of solids = 0.25
Specific gravity of slurry = 290 / 240 – 1.22* %solids)
= 290 / 240 – 1.22* 50)
= 1.62 (% solids = 50)
Agitator Impeller Diameter= (30-35 % of tank diameter)
= 14 * 33%
= 4.62 m
Tip speed of Agitator Impeller = 290 m / min (assumed)
Drive motor RPM = 1500 rpm (from standard data)
Gear Box Reduction Ratio = 75
Estimated Agitator RPM = Drive Motor RPM/Gear Box Reduction Ratio
= 1500 / 75
= 20 rpm
Flow Number Nq = 0.56 (assumed)
Power Number Np = 0.51 (assumed)
Pumping Capacity = Nq * rpm * D3 *60 (m3/hr)
= 0.56 * 20 * 4.62* 4.62*4.62*60
= 66266.68 m3/hr.
= 1104.44 m3/min.
= 18.41 m3/sec.
Area of Tank = p * D2/4
= 3.14 * 14 * 14 / 4
= 153.86 m2
Bulk fluid Velocity = pumping capacity / area of tank
= 1104.44 / 153.86
= 7.18 m / min.
= 23.55 ft./min ( 1 m = 3.281 ft.)
Degree of Agitation = bulk fluid velocity / 6
(For 6 ft/min., degree of agitation =1)
Degree of agitation varies from 0 to 10)
= 23.55 / 6
= 3.93
Annular Area = p * (Dt)2 - (Di)2 /4
Where Dt = Diameter of tank & Di = Diameter of impeller
= 3.14 * (14)2 – (4.62)2 / 4
= 137.10 m2
Rising velocity of particles= pumping capacity / annular area
= 1104.44 / 137.10
= 8.055 m/min.
= 0.13 m/sec. ( 1 min. = 60 sec.)
Tank Capacity = p * r2 * h
= 3.14 * 7 * 7 * 14
= 2463 m3
Tank Turnover rate = Pumping capacity / tank capacity
= 1104.44 / 2463
= 0.45 times / min.
Ratio of fluid height/tank dia.= 16/14
= 1.14 times
No. of impellers = 1 (assumed for calculation)
D2*N*r
Reynolds Number, NRe = --------------
µ
Where D = Impeller diameter in m
N = Revolutions per second
r = density in kg/m3
µ = viscosity in kg / m.sec
= (4.62)2 * 20 * 1.620 *103 / 0.550 *60
(r = density = specific gravity *103 )
(µ = 550 cp, 1 cp = 0.01 poise, 1 poise – 1 g/cm.sec)
= 20957.77
Process Torque = N2 * D5
= 202 * 4.625
= 841918.14
Power Number Np = 0.51
Shaft Power = Np*(Di)5 * N3 * sp. Gravity / 1.525 *1013
Where Np = impeller power no., Di = dia. of impeller in inches
N = revolutions per minute
= 0.51 * 1825 * 203 * 1.6 / 1.525 *1013
= 85.5 hp
Gear Box Efficiency = 80% = 0.80
Drive Motor Efficiency = 95% = 0.95
Design margin = 1.15
Shaft power * Design margin
Drive Motor Rating = --------------------------------------------------------
Gear box efficiency * Drive motor efficiency
= 85.5 * 1.15 / (0.80 * 0.95)
= 129 hp
= 96.0 kW.
Thus drive motor having rating close to 96 kW may be installed for satisfactory operation of the agitation system for required duty. Please prefer to have the service factor of the gear box more than 2.1. Please also note that helical gears are always the preferred choice over others.
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Thanks and regards.
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