Chapter 16: Blending and Agitation Rules of Thumb for Chemical Engineers, 5th Edition by Stephen Hall
This Excel workbook includes Visual Basic for Application function subroutines. Macros must be enabled for them to work.
ChemEng Software sells an Excel template called PIPESIZE. www.chemengsoftware.com PIPESIZE sizes pipes for gases and liquids. It includes a database of properties for piping materials, fluids, roughness values, and recommended velocities. Order on-line or by telephone, 24-h/d; credit cards accepted.
Problem Statement: Calculate the blend time for a mixer with one or two impellers
Inputs Fluid Mixing purpose Degree of agitation Fluid density Fluid viscosity
SI Units
US Units
ro mu
kg/m3 kg/m-s
1000 0.001
lb/ft3 lb/ft-s
62.43 0.000672
Tank Geometry T Diameter H Filled Height Impeller Lowest impeller Type Diameter Projected blade height Distance to mounting flange Distance to lower bearing Distance off bottom Second impeller Type Diameter Projected blade height Distance to mounting flange Speed
m m
3 3.5
ft ft
9.84252 11.48294
D1 W1 L1 L' C
m m m m m
ft ft ft ft ft
6.56168 0 0 0 0
D2 W2 L2 N Baffles B
m m m rps
ft ft ft rps
6.56168 0 0 1.42
1.42
Number of baffles Baffle width Space between baffle and wall
m m
4 0.25 0.041667
ft ft
4 0.82021 0.136702
Data Lookup and Calculations Nre Reynolds number gc Conversion factor NQ Pumping number Q Pumping capacity NP Power number - lower impeller
m3/s
12780000 1 0.8 9.088 1.3
ft3/s
12778151 32.17 0.8 320.9397 1.3
Power
119112.8
ft-lbf/s hp
87867.01 159.7582 1.3 87867.01 175734 319.5164
NP P P
Power number - upper impeller Power Total power (assume additive)
W W
1.3 119112.8 238225.6
ft-lbf/s ft-lbf/s hp
Mixing zone calculation, Np^(1/3) * Nre Mixing zone Theta95 Mixing time, 95% uniformity Desired mixing uniformity Adjusted mixing time Volume Turnovers, 95% uniformity s
13948001 Turbulent 9 99% 14.2 24.74004 3.40 ft3
13945983 Turbulent 9 99% 14.2 873.6863 3.40
s m3
Problem Statement: Calculate power and blend time for a helical ribbon impeller working in the laminar flow range
Inputs Fluid ro mu Mixing purpose Fluid density Fluid viscosity kg/m3 kg/m-s
SI Units Blend 1000 100
US Units
lb/ft3 lb/ft-s
62.43 67.20882
Tank Geometry T Diameter H Filled Height Helical Ribbon Geometry D Diameter h Overall height of impeller p Pitch (height of one turn) w Blade width nb Number of blades N gc Speed Conversion factor
m m
3 3.5
ft ft
9.84252 11.48294
m m m m
2.85 3.5 0.5 0.285 2 0.1 1
ft ft ft ft
9.350394 11.48294 1.64042 0.935039 2 0.1 32.17
rps
rps
Calculations c wall clearance clearance % of tank diameter Kp P Power factor for helical ribbon Power
0.075 2.5% 807.1066 18683.81
ft
0.246063
ft-lb/s hp
807.1066 13784.65 25.063 109.5456
Theta
Blend time
109.5456
Problem Statement: Estimate the settling velocity of solids in liquid
Inputs Solids ps dn Liquid p u v Descriptive density nominal diameter solids concentration in slurry density dynamic viscosity kinematic viscosity kg/m3 mm wt % kg/m3 Pa-s cSt
SI Units Spheres 1,100 1.0 55% 1,000 0.0010 1.0
US Units Spheres 68.53 0.039 55% 62.30 1.0 1.0
lb/ft3 in wt % lb/ft3 cP cSt
Other g
gravitational acceleration
m/s2
9.80
ft/s2
32.17
Calculations and Results s specific gravity, solids A formula coefficient A B formula coefficient B S* dimensionless particle parameter W* dimensionless settling velocity terminal settling velocity correction factor ws settling velocity
cm/s
1.10 0.79 4.61 7.83 0.72 2.26 1.85 4.19
ft/min
1.10 0.79 4.61 7.83 0.72 4.46 1.85 8.25
Data Coefficients for Equation Crushed Natural Sediment Well-Rounded Spheres Correction for Solids Concentration
A 0.995 0.954 0.89 0.794 Solids% 0
B 5.211 5.121 4.974 4.606 Factor 0.75
2 5 10 15 20 25 30 35 40 45 50
0.8 0.84 0.91 1 1.1 1.2 1.3 1.42 1.55 1.7 1.85
Result
Problem Statement: Calculate the ungassed and gassed power required in an agitated vessel designed for gas dispersion
Inputs Geometry and Parameters T Tank diameter D Impeller diameter Impeller speed NP Power number Liquid H pL uL Gas Gas flow rate, actual Other g gc
SI Units m m rpm 1.30 0.52 42 5.0 ft ft rpm
US Units 4.27 1.71 42 5.0
Liquid height Density, liquid Viscosity, liquid
m kg/m3 Pa-s
3.77 1,000 0.0010
ft lb/ft3 lb/ft-s
12.37 62.3 0.00067
am3/h
14
acfm
Gravitational acceleration Conversion factor
m/s2 m/s2
9.81 1.00
ft/s2 ft/s2
32.17 32.17
Calculations A Tank cross-section V Volume v Superficial gas velocity QG N NFl NFr D/T Gas flow rate, actual Impeller speed Gas Flow Number Impeller Froude Number Impeller ratio
m2 m3 m/s m3/s rps
1.33 5.00 0.003 0.004 0.70 0.040 0.03 0.40
ft2 ft3 ft/s ft3/s rps
14.29 176.7 0.010 0.14 0.70 0.040 0.03 0.40
Gas Dispersion Regime
No discernable action Flooding
No discernable action Flooding
RPD Nre
Gas Flow number at transition RPD at transition Relative Power Demand Reynolds Number
0.04 0.86 0.85
0.04 0.86 0.85
P pG
Power, ungassed Power, gassed
W W
65 56
hp hp
0.09 0.07
Data
Results
N Regenerate Power 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460
Regime 49 No discernable actionFlooding 152 360 713 1,255 2,025 3,067 Recirculating 4,421 Recirculating 6,131 Recirculating 8,237 Recirculating 10,782 Recirculating 13,808 Recirculating 17,358 Recirculating 21,472 Recirculating 26,194 Recirculating 31,565 Recirculating 37,628 Recirculating 44,425 Recirculating 51,998 Recirculating 60,388 Recirculating 69,639 Recirculating 79,792 Recirculating
No discernable action
100,000
10,000 Ungassed Power, W
1,000
100
10 10 100 Impeller Speed, rpm
1000
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.
Inputs Impellers D Diameter Number of impellers Np Power Number fH Hydraulic service factor Shaft Np Speed L Shaft length from bottom bearing Sb Bearing span, Sb Distance between impellers Modulus of elasticity Shaft density Allowable shear stress Allowable tensile stress Mixture ro Density of mixed liquid P Power, total Intermediate Calculations Geometry and Power - impeller-specific Shaft length, top impeller Shaft length, middle impeller Shaft length, bottom impeller Power per impeller Weight of blades, per impeller hydrofoil 4-blade PBT
SI Units m 0.660 2 5.0 1.0 2.08 4.22 0.30 2.01 1.97E+11 8,027 4.10E+07 6.90E+07 1,000 5,588 in
US Units
rps m m m N/m2 kg/m3 N/m2 N/m2 kg/m3 W
rpm in in in psi lb/in3 psi psi lb/in3 hp
m m m W kg kg
NA 2.21 4.22 2,794 7.35 5.70
in in in hp lb lb
Calculations Torque Bending moment (maximum) Shaft diameter Based on shear Based on tensile Selected shaft diameter Weight of hub
N-m N-m
434 626
in-lbf in-lbf
m mm m mm mm
0.05 45.57 0.05 46.79 50
in mm in mm in
Read from chart Total weight for each impeller with hub hydrofoil W 4-blade PBT Equivalent weight, not including shaft We hydrofoil 4-blade PBT Natural frequency - First Critical Speed hydrofoil 4-blade PBT
kg
9.0
lb
kg kg
16.35 14.70
lb lb
kg kg
18.71 16.81
lb lb
rps rps
1.24 1.27
rpm rpm
Data Conversion factors for blade weight formula hydrofoil 4-blade PBT
0.14 0.084
350
140
300
120
250
100
Mass of Hub, lbm
Mass of Hub, kg
200
80
Hydrofoil 150
4-Blade PBT
60
100
40
50
20
0 0 2 4 6 8
0 0
50
20
0 0 2 4 6 8
0 0
Shaft Diameter, in
Sh
llers on one
US Units 26.0 2 5.0 1.0 125.0 166.0 12.0 79.0 2.86E+07 0.29 6,000 10,000 0.036 7.50
NA 87.0 166.0 3.75 16.2 12.6
3,782 5,547
1.79 45.37 1.84 46.77 2.0
20.0
36.24 32.58
41.45 37.27
76.15 78.25
Results
0.5 0.3
140
120
100
Mass of Hub, kg
80
Hydrofoil 60
4-Blade PBT
40
20
0 0 50 100 150 200
20
0 0 50 100 150 200
Shaft Diameter, mm
