Inputs SI Units US UnitsFluid

Mixing purposeDegree of agitation

ro Fluid density kg/m3 1000 lb/ft3 62.43mu Fluid viscosity kg/m-s 0.001 lb/ft-s 0.000672

Tank GeometryT Diameter m 3 ft 9.84252H Filled Height m 3.5 ft 11.48294

ImpellerLowest impellerType

D1 Diameter m 2 ft 6.56168W1 Projected blade height m ft 0L1 Distance to mounting flange m ft 0L' Distance to lower bearing m ft 0C Distance off bottom m ft 0

Second impellerType

D2 Diameter m 2 ft 6.56168W2 Projected blade height m ft 0L2 Distance to mounting flange m ft 0

N Speed rps 1.42 rps 1.42

BafflesNumber of baffles 4 4

B Baffle width m 0.25 ft 0.82021Space between baffle and wall m 0.041667 ft 0.136702

Data Lookup and CalculationsNre Reynolds number 12780000 12778151gc Conversion factor 1 32.17NQ Pumping number 0.8 0.8Q Pumping capacity m3/s 9.088 ft3/s 320.9397

Problem Statement:Calculate the blend time for a mixer with one or two impellers

NP Power number - lower impeller 1.3 1.3P Power W 119112.8 ft-lbf/s 87867.01

hp 159.7582

NP Power number - upper impeller 1.3 1.3P Power W 119112.8 ft-lbf/s 87867.01

P Total power (assume additive) W 238225.6 ft-lbf/s 175734hp 319.5164

Mixing zone calculation, Np^(1/3) * Nre 13948001 13945983Mixing zone Turbulent Turbulent

Theta95 Mixing time, 95% uniformity s 9 9

Desired mixing uniformity 99% 99%Adjusted mixing time s 14.2 14.2

Volume m3 24.74004 ft3 873.6863Turnovers, 95% uniformity 3.40 3.40

Inputs SI Units US UnitsFluid

Mixing purpose Blendro Fluid density kg/m3 1000 lb/ft3 62.43mu Fluid viscosity kg/m-s 100 lb/ft-s 67.20882

Tank GeometryT Diameter m 3 ft 9.84252H Filled Height m 3.5 ft 11.48294

Helical Ribbon GeometryD Diameter m 2.85 ft 9.350394h Overall height of impeller m 3.5 ft 11.48294p Pitch (height of one turn) m 0.5 ft 1.64042w Blade width m 0.285 ft 0.935039nb Number of blades 2 2

N Speed rps 0.1 rps 0.1gc Conversion factor 1 32.17

Calculationsc wall clearance m 0.075 ft 0.246063

clearance % of tank diameter 2.5%

Kp Power factor for helical ribbon 807.1066 807.1066P Power W 18683.81 ft-lb/s 13784.65

hp 25.063

Theta Blend time s 109.5456 109.5456

Problem Statement:Calculate power and blend time for a helical ribbon impeller working in the laminar flow range

Inputs SI Units US UnitsSolids

Descriptive Spheres Spheresps density kg/m3 1,100 lb/ft3 68.53 dn nominal diameter mm 1.0 in 0.039

solids concentration in slurry wt % 55% wt % 55%Liquidp density kg/m3 1,000 lb/ft3 62.30 u dynamic viscosity Pa-s 0.0010 cP 1.0 v kinematic viscosity cSt 1.0 cSt 1.0

Otherg gravitational acceleration m/s2 9.80 ft/s2 32.17

Calculations and Resultss specific gravity, solids 1.10 1.10 A formula coefficient A 0.79 0.79 B formula coefficient B 4.61 4.61 S* dimensionless particle parameter 7.83 7.83 W* dimensionless settling velocity 0.72 0.72

terminal settling velocity 2.26 4.46 correction factor 1.85 1.85

ws settling velocity cm/s 4.19 ft/min 8.25

DataCoefficients for Equation A B

Crushed 0.995 5.211Natural Sediment 0.954 5.121Well-Rounded 0.89 4.974Spheres 0.794 4.606

Correction for Solids Concentration Solids% Factor0 0.752 0.8

Result

Problem Statement:Estimate the settling velocity of solids in liquid

5 0.8410 0.9115 120 1.125 1.230 1.335 1.4240 1.5545 1.750 1.85

Result

Inputs SI Units US UnitsGeometry and ParametersT Tank diameter m 1.30 ft 4.27 D Impeller diameter m 0.52 ft 1.71

Impeller speed rpm 42 rpm 42 NP Power number 5.0 5.0

LiquidH Liquid height m 3.77 ft 12.37 pL Density, liquid kg/m3 1,000 lb/ft3 62.3 uL Viscosity, liquid Pa-s 0.0010 lb/ft-s 0.00067

GasGas flow rate, actual am3/h 14 acfm 8

Otherg Gravitational acceleration m/s2 9.81 ft/s2 32.17 gc Conversion factor m/s2 1.00 ft/s2 32.17

CalculationsA Tank cross-section m2 1.33 ft2 14.29 V Volume m3 5.00 ft3 176.7 v Superficial gas velocity m/s 0.003 ft/s 0.010

QG Gas flow rate, actual m3/s 0.004 ft3/s 0.14 N Impeller speed rps 0.70 rps 0.70

NFl Gas Flow Number 0.040 0.040 NFr Impeller Froude Number 0.03 0.03

D/T Impeller ratio 0.40 0.40

No discernable action No discernable actionGas Dispersion Regime Flooding Flooding

Gas Flow number at transition 0.04 0.04 RPD at transition 0.86 0.86

Problem Statement:Calculate the ungassed and gassed power required in an agitated vessel designed for gas dispersion

RPD Relative Power Demand 0.85 0.85 Nre Reynolds NumberP Power, ungassed W 65 hp 0.09 pG Power, gassed W 56 hp 0.07

Data

N P Regime40 49 No discernable actionFlooding60 152 80 360

100 713 120 1,255 140 2,025 160 3,067 Recirculating180 4,421 Recirculating200 6,131 Recirculating220 8,237 Recirculating240 10,782 Recirculating260 13,808 Recirculating280 17,358 Recirculating300 21,472 Recirculating320 26,194 Recirculating340 31,565 Recirculating360 37,628 Recirculating380 44,425 Recirculating400 51,998 Recirculating420 60,388 Recirculating440 69,639 Recirculating460 79,792 Recirculating

Results

Regenerate Power Curve

No discernable action

10 100 1000 10

100

1,000

10,000

100,000

Impeller Speed, rpm

Unga

ssed

Pow

er, W

10 100 1000 10

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Impeller Speed, rpm

Unga

ssed

Pow

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Inputs SI Units US UnitsImpellersD Diameter m 0.660 in 26.0

Number of impellers 2 2 Np Power Number 5.0 5.0 fH Hydraulic service factor 1.0 1.0 ShaftNp Speed rps 2.08 rpm 125.0 L Shaft length from bottom bearing m 4.22 in 166.0 Sb Bearing span, Sb m 0.30 in 12.0

Distance between impellers m 2.01 in 79.0 Modulus of elasticity N/m2 1.97E+11 psi 2.86E+07Shaft density kg/m3 8,027 lb/in3 0.29 Allowable shear stress N/m2 4.10E+07 psi 6,000 Allowable tensile stress N/m2 6.90E+07 psi 10,000

Mixturero Density of mixed liquid kg/m3 1,000 lb/in3 0.036 P Power, total W 5,588 hp 7.50

Intermediate CalculationsGeometry and Power - impeller-specific

Shaft length, top impeller m NA in NA Shaft length, middle impeller m 2.21 in 87.0 Shaft length, bottom impeller m 4.22 in 166.0 Power per impeller W 2,794 hp 3.75

Weight of blades, per impellerhydrofoil kg 7.35 lb 16.2 4-blade PBT kg 5.70 lb 12.6

CalculationsTorque N-m 434 in-lbf 3,782 Bending moment (maximum) N-m 626 in-lbf 5,547

Shaft diameterBased on shear m 0.05 in 1.79

mm 45.57 mm 45.37 Based on tensile m 0.05 in 1.84

mm 46.79 mm 46.77 Selected shaft diameter mm 50 in 2.0

Problem Statement:Calculate shaft diameter, torque, and first critical speed, for up to 3 identical impellers on one shaft. Assume that power is equally distributed among the impellers.

Weight of hubRead from chart kg 9.0 lb 20.0

Total weight for each impeller with hubhydrofoil kg 16.35 lb 36.24

W 4-blade PBT kg 14.70 lb 32.58

Equivalent weight, not including shaftWe hydrofoil kg 18.71 lb 41.45

4-blade PBT kg 16.81 lb 37.27

Natural frequency - First Critical Speedhydrofoil rps 1.24 rpm 76.15 4-blade PBT rps 1.27 rpm 78.25

DataConversion factors for blade weight formula

hydrofoil 0.14 0.54-blade PBT 0.084 0.3

0

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4-Blade PBT

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4-Blade PBT

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4-Blade PBT

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Results

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