Design of Agitator

Example Data Batch Volume Vessel Diameter

8840 9.5

gal ft

Specific Gravity difference Viscosity Ratio Density Viscosity

0.4 1200 1100 15000

kg/m3 cp

33.46294 m3 2.8956 m

Enter value in colored cell

15 kg/m s

1180.83 ft3

Step-1 Defining the intensity of mixing

Mixing Scale

0.4

Bulk Velocity (ft/sec) Application

ft/sec Specific Gravity Difference

1

0.1

Miniumum Liquid Motion

Less than 0.1

2

0.2

Miniumum Liquid Motion

Less than 0.1

3 4 5

0.3 0.4 0.5

6

0.6

7 8 9

0.7 0.8 0.9

10

1

Characteristic of most agitation used in chemical industry Less than 0.6

Requires high degree of agitation Less than 1.0

Viscosity Ratio

Others

Less than 100 Less than 100

Less than 10000

Suspend trace solids less than 2% with settling rate of 2 to 4 ft/min

Less than 100000

Suspend trace solids less than 2% with settling rate of 4 to 6 ft/min

Step-2 Calculating Teq assuming square batch tank Volume of the contents

V

=

1180.825 ft3

Equivalent Diameter

Teq

=

11.45791 ft

Volumetric flow rate

Q

=

41.22306 ft3/sec

=

2473.384 ft3/min

Don’t alter any value

3.49237 m

Step-3 Selecting Agitator Dia Agitator Type D/T ratio W/D

Pitched Blade Impeller with 4 blades 0.2 to 0.6 1/5

Select Ratio of D/T

0.4

Impeller Dia Impeller Width

1.4 m 0.28 m

55.0 in 11.0 in

Step-4 Calculation of Required rpm Iteration Assume initial rpm Impeller reynolds Number From graph, impeller pumping number Recalculating the rpm required Difference

1 100 238.5

2 90 214.7

3 70 167.0

4 65 155.0

0.44

0.43

0.4

0.395

58.4 41.6

59.7 30.3

64.2 5.8

65.0 0.0

Step-5 Closest standard rpm Reynolds number

68 rpm 162.2

Viscosity correction factor

1.35

Power Number

1.85

Power Requirement

Assume loading % HP Required

15755.1 kg m2 / s3 15755.1 Watts 21.1 hp 85 24.9 hp 25 hp

1.133 rpm

4.58 ft

Step-6 Deciding number of impellers Calculated rpm Power required

N P

68 rpm 25 hp

1.133333

Calculating Height of the tank Vessel Dia

T

2.8956 m

For 1 in height, Volume occupied

V

For occupying Height will be Height to Diameter ratio No of Impeller required

Load shared by each impeller

0.16717853 m3 33.462936 m3

Z Z/T

200.162876 in

5.084137

1.75581471 2

10.563798 hp

7877.553

Initial estimate of diameter Power Number

1.8495

Diameter

1.21611392 m

Impeller Reynolds number

122.915771

47.87841

For the above reynolds number, Viscosity correction factor Power Number Recalculating Diameter

1.47 2.0139 1.19557699 m

47.06987

Lower Impeller Location from bottom

0.9652 m

37.99992

Upper Impeller Location from bottom

3.38942471 m

133.4417

Instead of I no of

55.00 in Impeller, two nos with

rps

Viscosity,cp 25001

m

kg m2 / s3

in

in in in

Maximum Level,Z/T 1.4 2.1 0.8 1.6

No of Impeller 1 2 1 2

, two nos with

47.06987 in diameter is required to provide the same agitation degree

Impeller clearance Lower Upper Z/3 T/3 (2/3) Z Z/3 T/3 (2/3) Z

Pumping Number curve for 4 blade pitched blade turbine impeller (Np = 1.37)

Viscosity correction factor as a function of reynolds number

Values of turbulent power number NP for various impeller geometries. Note: W/D is actual blade-width-to-impeller-diameter ratio.

Vessel Dia ft m 3 0.91 3.5 1.07 4 1.22 4.5 1.37 5 1.52 5.5 1.68 6 1.83 6.5 1.98 7 2.13 7.5 2.29 8 2.44 8.5 2.59 9 2.74 9.5 2.90 10 3.05 11 3.35 11.5 3.51 12 3.66

Volume m3/in gal/in 0.02 4.40 0.02 5.99 0.03 7.83 0.04 9.91 0.05 12.23 0.06 14.80 0.07 17.62 0.08 20.68 0.09 23.98 0.10 27.53 0.12 31.32 0.13 35.36 0.15 39.64 0.17 44.16 0.19 48.94 0.22 59.21 0.24 64.72 0.27 70.47

m3 0.60 0.95 1.42 2.03 2.78 3.70 4.80 6.10 7.62 9.38 11.38 13.65 16.20 19.06 22.23 29.59 33.81 38.41

Square batch gal 158.55 251.77 375.82 535.10 734.03 976.99 1268.40 1612.65 2014.17 2477.34 3006.57 3606.27 4280.84 5034.68 5872.21 7815.91 8930.89 10147.17

L 600 953 1423 2026 2779 3698 4801 6105 7624 9378 11381 13651 16205 19058 22229 29586 33807 38411

Scale up ratio

Assume

DT1

=

H1

(original vessel is standard cylindrical )

Volume

V1

= =

0.785* DT1² * H1 0.785* DT1³

V2

=

DT2³

Ratio of volume

V1 Scale up ratio, R

DT1³ =

V2 V1

⅓

=

Using this ratio for all factors, ex Da2

=

R Da1

J2

=

R J1

Agitator Speed,

n=1 for equal liquid motion, 3/4 for equal suspension of solid, 2/3 for equal mass transfer

n=2/3, power per unit volume is constant n=1, tip speed is constant

For Mild agitation and blending

0.1 to 0.2

KW/m3 of fluid

For vigarous agitation

0.4 to 0.6

KW/m3 of fluid

For intense agitation

(Mass transfer is importanr0

0.8 to 2

KW/m3 of fluid

Example

Agitator Type Dia of Tank Dia of agitator Height of the Tank Width No of Baffles Baffle width Speed Viscosity Density

Flat blade turbine agitator Dt1 1.83 m Da1 0.61 m H1 1.83 m W1 0.122 m 4 J1 0.15 m N1 90 rpm µ 10 CP ℓ 929 kg/m3

1.5 rps 0.01 Kg / m s

Scale up for 3 times larger for 1)Equal rates of mass transfer is required 2) Equal liquid motion is required

Solution -1

Original Volume Scale up volume

V1 V2

4.810862 m3 14.43259 m3

Ratio Da2 For equal mass transfer

1.442 0.879772 n

m =

N2

1.175072

rps

Nre

84492.96

Reynolds Number

Np

Power required

3

0.667 70.504 rpm

5

3972.189

J/sec

3.97 KW

5.33

Solution -2

Original Volume Scale up volume Ratio Da2 For equal liquid motion N2

Reynolds Number

Np

Power required

V1 V2

4.810862 m3 14.43259 m3

3

1.442 0.880 n

m =

1

1.040042

rps

62.403

Nre

74783.72

5

2754.162

J/sec

2.75 KW

3.70

ssel is standard cylindrical )

DT2

DT1

hp

hp