Agitator Design Calc

 AGITA  AGITATOR DESIGN DESIGN Method to arrive at motor rating: Impeller power for slurry mixing agitator is calculated using following mathematical relations. Impeller Power, P = Np * ρ *N3 * Di5 / (16*104) h.p. Where Di = Diameter of impeller in meters, N = Revolution per minute for impeller Np = Power number for impeller ρ = Specific gravity of slurry

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 Diameter of tank,

Dt  = 14 m

Slurry volume in tank  = π *Dt 2*H/4 = π * (14)2*16 /4 = 2463 m3 Solid consistency in Slurry = 50 % (w/w), Specific gravity of slurry, ρ = 1.602,

Viscosity of slurry, μ = 550 cp Agitator Impeller Diameter, Di = 33 % of tank diameter = 14 * 33% m = 4.62 m Tip 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 Nq = 0.56 and Power Number, Np = 0.51 (assumed figures)

Pumping Capacity

= Nq * N * Di3 m3/minute = 0.56 * 20 * 4.62 3 = 1104.44 m 3/min = 18.41 m3/sec

Area of Tank

= π * Dt 2 = π *142 / 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*(Dt 2- Di2 ) /4 = 3.14 * (14 2 – (4.622) / 4 = 137.18 m 2 Where, Dt  = Diameter of tank  Di = Diameter of impeller in meters. 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 Np = 0.51 Shaft Power, P = N p* ρ *(Di)5 * N3 /(16 *104)

Where, Np = Impeller power no., Di = Diameter of impeller in meters, Shaft RPM, N = revolutions per minute

∴

Shaft Power, P = 0.51 * 1.602 * (4.402)5 * 203 / (16 *104) = 85.98 h.p.

Taking Gear Box Efficiency = 80% 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 m3 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.