Parameter 
Symbol 
Units 
Explanation of parameters 
alpha 
a 
[] 
Factor that describes the ratio of k_{L}a
in the media as compared to the k_{L}a in water/air under identical
conditions of power and gas flow rate. 
1/(w/T) 
(wBAF/T)^{1} 
[] 
Inverse of the baffling ratio. 
A 
A 

Constant in the k_{L}a equation.
A is a function of Theta,
viscosity factor, and k_{L}afactor. 
Coil surface area 
A_{COIL} 
m2 
Heat transfer surface area. 
Cross sectional area of tank 
A_{CS} 
m2 
This is the area of the circular cross section of the
cylindrical part of the reactor, tank, vessel, or fermenter. This is the
metric unit. 
Cross sectional area of tank 
A^{’}_{CS} 
ft2 
This is the area of the circular cross section of the
cylindrical part of the reactor, tank, vessel, or fermenter. American
units. 
B 
B 

Exponent on P/V. 
Baffle type(=BAF): 
BAF 

Style of baffle: Straight
standard, F, D, BeaverTail, special or none. Could also be hollow for heat transfer. 
Percent baffled 
BAF% 
% 
Percent of baffling. 100%º
NB = 0.4 
Recommended % of normal baffles

BAF%_{REC} 
% 
Based on viscosity, this factor states what the
recommended baffle width (in % or standard) should be for
Rushton Turbines. 
Henzler Baffle Factor for Mixing 
BF_{HENZLER,MIX} 
[] 
Henzler baffle factor for mixing. 
Henzler Baffle Factor for power 
BF_{HENZLER,P} 
[] 
Henzler Baffle Factor for Power 
Baffle Power Factor * Swirl Factor 
BFi·SFi 
[] 
Baffle Power Factor * Swirl Factor for the iimpeller. 
Oldshue Baffle Factor for Power 
BF_{OLDSHUE,P} 
[] 
Oldshue Baffle Factor for Power. 
Oldshue Baffle Factor for power 
BF_{OLDSHUE,P} 
[] 
Oldshue Baffle Factor for Power 
C 
C 

Exponent on F or vsg. 
c*(Head Space) with reaction 
c*_{ACTUAL,TOP} 
ppm 
Actual c* at the top of the reactor, tank, vessel, or fermenter, which is in equilibrium
with the offgas concentration of oxygen. 
c*(H_{2}O,O_{2}) at 1 bar and temp 
c*_{H2O/O2} 
ppm 
cstar of clean water/oxygen (in air) at 1 bar and process temperature 
c*(H_{2}O,O_{2})(bottom) 
c*_{H2O/O2,BOT} 
ppm 
c* of clean water/oxygen (in air) at the bottom and process temperature 
c*(H_{2}O,O_{2})(i) 
c*_{H2O/O2,i} 
ppm 
c* of clean water/oxygen (in air) at iimpeller and process temperatur 
c*(H_{2}O,O_{2})(middepth) 
c*_{H2O/O2,MD} 
ppm 
c* of clean water/oxygen (in air) at middepth and process temperature 
c*(H_{2}O,O_{2})(sparge) 
c*_{H2O/O2,SP} 
ppm 
c* of clean water/oxygen (in air) at the sparge and process temperature 
c*(H_{2}O,O_{2})(Head Pressure) 
c*_{H2O/O2,TOP} 
ppm 
c* of clean water/oxygen (in air) at head pressure and process temperature 
c*(LnMean) 
c*_{LnMean} 
ppm 
Log mean average of c* from the bottom of the reactor,
tank, vessel, or fermenter (oxygen inlet) to the top of the reactor, tank,
vessel, or fermenter (oxygen outlet) 
Coil type(=COIL): 
COIL 

Style of coil. Examples: None, helical coils, vertical
coils, vertical plate coils or other. 
Ungassed COV/D 
COV_{i,0 /Di} 
[] 
Ratio: Distance above an impeller to the liquid surface (coverage) to impeller diameter
when the reactor, tank, vessel, or fermenter is ungassed for the iimpeller. 
Gassed COV/D 
COV_{i,G /Di} 
[] 
Ratio: Distance above an impeller to the liquid surface
(coverage) to impeller diameter when the reactor, tank, vessel, or
fermenter is gassed for the iimpeller. 
Chem Scale 
CS_{i} 
ft/min 
ChemScale: A term from Chemineer to show the intensity of agitation for the iimpeller. 
Coil swept diameter 
d_{COIL} 
mm 
For helical coils: CL of coil to shaft center times 2; For
vertical coils and vertical plate coils: inner and outer swept diameters. 
Hole diameter 
d_{HOLE} 
mm 
For pipe sparge: hole diameter = pipe diameter. For ring
sparge: diameter of the holes where the gas (air) comes out. 
Disk diameter(i) 
d_{i,DISK} 
mm 
Diameter of the idisk of a Rushtontype
impeller. Only valid for impellers with a disk. 
d(disk)/D 
d_{i,DISK/}D_{i} 
[] 
Ratio: Disk diameter to impeller diameter for the iimpeller. 
Hub diameter(i) 
d_{i,HUB} 
mm 
Diameter of the hub of the iimpeller. This is the metal
that holds the impeller onto the shaft. 
d(hub)/d(disk) 
d_{i,HUB} /d_{i,DISK} 
[] 
Ratio: Hub diameter to disk diameter for the iimpeller. 
Manway diameter 
d_{MW} 
mm 
The inner diameter of the manway. If there is no manway,
the inner diameter of the tank. This is useful when determining the
maximum size impeller that can be put into the tank. 
Pipe diameter 
d_{PIPE, SP} 
mm 
Inner diameter of the sparge pipe. 
Coil pipe diameter 
d_{PIPE,COIL} 
mm 
For helical and vertical pipes: Outer diameter of pipes;
For vertical plate coils: overall thickness of the plates. 
Shaft diameter(bottom) 
d_{SHAFT,BOT} 
mm 
If there is a step down in shaft size, this is the diameter near the lowest impeller. 
Bottom Shaft d/T 
d_{SHAFT,BOT}/T 
[] 
Ratio: Shaft diameter near the bottom of the reactor,
tank, vessel, or fermenter above the steady bearing to tank diameter. 
Shaft diameter(middle) 
d_{SHAFT,MID} 
mm 
If the shaft is stepped down in size, this is the diameter
of the shaft in the middle of the reactor, tank, vessel, or fermenter. If
there is only one step down, this in irrelevant. 
Middle Shaft d/T 
d_{SHAFT,MID}/T 
[] 
Ratio: Shaft diameter in the middle of the reactor, tank,
vessel, or fermenter to tank diameter. 
d(shaft)/d(disk) 
d_{SHAFT,T} /d_{i,DISK} 
[] 
Ratio: Shaft diameter to impeller disk diameter for the iimpeller. 
Shaft diameter(top) 
d_{SHAFT,TOP} 
mm 
Diameter of the shaft near the entry to the reactor, tank, vessel, or fermenter. 
Top Shaft d/T 
d_{SHAFT,TOP}/T 
[] 
Ratio: Shaft diameter near the top of the reactor, tank,
vessel, or fermenter (near seal) to tank diameter. 
Swept CL diameter 
d_{SP} 
mm 
CL=Center Line. For ring sparge: Center diameter of the
sparge. For pipe: distance from pipe opening to shaft center times 2. 
D(sparge)/D(bottom) 
d_{SP}/D_{B} 
[] 
Ratio: Sparge diameter to bottom impeller diameter. For a pipe it is the outlet diameter. 
Bottom head thickness 
D_{BOT} 
mm 
Thickness of the bottom dish. Often found on data
describing the ASME pressure testing of the tank. 
Impeller diameter(i) 
D_{i} 
mm 
Swept diameter of the iimpeller. 
D/T 
D_{i}/T 
[] 
Ratio: Impeller diameter to tank diameter for the iimpeller 
Mass transfer driving force 
DF_{LnMean} 
ppm 
The log mean driving force of the oxygen mass transfer 
DO [% of Saturation] 
DO 
% 
Dissolved Oxygen in percent of the saturated value. 
DO at 1 bar pressure and temp 
DO_{1,t} 
ppm 
Dissolved Oxygen in parts per million at 1 bar and process temperature. 
DO(actual) at pressure and temp 
DO_{MD,t} 
ppm 
Dissolved Oxygen in parts per million at middepth pressure and temperature. 
DO(Sat) at 1 bar and temp 
DO_{SAT} 
ppm 
Dissolved oxygen concentration at saturation at 1 bar, process temperature and process media.

dZ(i) 
dZ_{i} 
mm 
Liquid depth of an impeller zone above and below the iimpeller for the iimpeller. 
dZ(i)/T 
dZ_{i} /T 
[] 
Ratio of the impeller zone liquid depth to tank diameter for the iimpeller. 
Gas Holdup 
e_{G} 
[%] 
The amount of volume increase due to the sparging of the
media with air. This does not include a stable foam layer. 
Gas Holdup (Post) 
e_{G,POST} 
% 
Gas holdup according to Post. 
Gas Holdup Smith 
e_{G,SMITH} 
% 
Gas holdup according to Smith. 
Gas Holdup Whitton 
e_{G,Whitton} 
% 
Gas holdup according to Whitton. 
Motor efficiency 
eff_{MOTOR} 
% 
Motor efficiency. The standard value can be found on the
nameplate. Best is to acquire a motor curve for each system from the vendor. 
Superficial gas velocity (middepth) 
F^{’}_{MD} 
ft/min 
The actual superficial gas velocity at middepth at
operating conditions, assuming no consumption of oxygen, in American units. 
Superficial gas velocity (sparge) 
F^{’}_{SP} 
ft/min 
The actual superficial gas velocity at spargedepth at
operating conditions, assuming no consumption of oxygen, in American units. 
Superficial gas velocity (middepth) 
F^{'}_{MD,ft/s} 
ft/s 
The actual superficial gas velocity at middepth at
operating conditions, assuming no consumption of oxygen, in American units. 
Superficial gas velocity (sparge) 
F^{'}_{SP,ft/s} 
ft/s 
The actual superficial gas velocity at spargedepth at
operating conditions, assuming no consumption of oxygen, in American units. 
Fr(i) 
Fr_{i} 
[] 
Froude Number for the iimpeller. It is usually used to determine the affinity to vortexing.

Henry (Water/O2)=f(temperature) 
H_{H2O/O2} 
bar/ppm 
Henry coefficient for water/oxygen in air. 
Blade height(i) 
h_{i} 
mm 
Height of each blade of the iimpeller. For Smith
Turbines, hydrofoils, and pitched bladed turbines use
projected height of the blade (zdimension). 
Hub height(i) 
h_{i,HUB} 
mm 
Height of the hub of the iimpeller. 
h/D 
h_{i}/D_{i} 
[] 
Ratio: Blade height to impeller diameter for the iimpeller. 
standard h/D 
h_{i}/D_{i,STD} 
[] 
h/D of a standard impeller of this type for the iimpeller. 
Amperes 
I_{MOTOR} 
Amps 
Motor amperes can be found on the nameplate. 
Overall Interstage mixing efficiency factor 
IEF_{AVG} 
(x) 
This is a factor that describes the rate of mixing
exchange between impellers. This number represents an overall average of
all impellers in the reactor, tank, vessel, or fermenter. A more precise
model contains individual factors for each pair of impellers. Whereas
Rushton Turbines (RT) will have a high number, axial foil hydrofoils will
have a very low number. The lower the number the faster the mixing. 
Impeller Type(=i): 
IMP_{i} 

Type of impeller. 
Design kfactor 
KF_{i} 
% 
Ratio of the power under gassed conditions as compared to
ungassed conditions at the same impeller speed for the iimpeller. There
is no overall kfactor as there is for SF, because each impeller has
different characteristics. 
Literature kfactor 
KF_{LIT,i} 
% 
Literature kFactor for Rushton Turbines for the iimpeller.

Impeller design k_{L}a 
k_{L}a_{IMP} 
hr^{1} 
Mass transfer coefficient k_{L}a (of the impeller design) 
Required process k_{L}a 
k_{L}a_{PROC} 
hr^{1} 
Mass transfer coefficient k_{L}a (of the process) 
Baffle length

L_{BAF} 
mm 
Vertical distance from the bottom of the
baffle to the top of the baffle. 
L(baffle)/T 
L_{BAF}/T 
[] 
Ratio: Length of a baffle to tank diameter. 
Coil length 
L_{COIL} 
mm 
Total length of coil pipe. 
Shaft length 
L_{SHAFT} 
mm 
For top entry, inside length of shaft from head to the
bottom of the shaft. For bottom entry, from bottom to top of shaft. This
is the total length of the shaft within the reactor, tank, vessel, or
fermenter. 
Ungassed torque 
Md^{’}_{i,0} 
in lbs 
Ungassed torque of the impeller for the iimpeller. 
Gassed torque 
Md^{’}_{i,G} 
in lbs 
Gassed torque of the impeller for the iimpeller. 
Ungassed Total Torque 
Md_{TOT,0} 
Nm 
The sum of all individual impeller torques. 
Ungassed Total Torque 
Md^{’}_{TOT,0} 
in lbs 
The sum of all individual impeller torques. 
Torque Md_{G} 
Md_{TOT,G} 
Nm 
This is the sum of the individual impeller torques. 
Torque Md_{G} 
Md^{’}_{TOT,G} 
in lbs 
This is the sum of the individual impeller torques. 
Torque nameplate 
Md_{MOTOR} 
Nm 
Motor torque. 
Number of baffles

n_{BAF} 
[] 
Number of baffles in the reactor,
tank, vessel or fermenter. 
Number of coil bundles 
n_{COIL} 
[] 
Bundles are groups of similar coil structures. 
Number of holes 
n_{HOLE} 
[] 
For pipe sparge: number = 1; for ring sparge: number of holes for the gas (air) to come out.

Number of blades(i) 
n_{i,BLADES} 
[] 
Number of blades of the iimpeller. 
Number of impellers 
n_{IMP} 
[] 
Number of impellers on the shaft. 
Number of pipes 
n_{PIPE} 
[] 
Number of pipes in each bundle. 
Impeller Speed 
N 
RPM 
Rotational speed of the impellers. 
Maximum impeller speed 
N_{MAX} 
RPM 
Maximum impeller speed. Often this is at 60 Hz on the
frequency drive for variable speed drives. Some drives may run at higher frequencies. For a
twospeed motor, this is the higher speed. This is the
same as the typical speed for fixed speed drives. 
Minimum impeller speed 
N_{MIN} 
RPM 
Minimum speed that the agitator can be run at. It is not 1
for variable speed drives. For a twospeed motor, this is the lower speed.
This is the same as the typical speed for fixed speed drives. 
Maximum Motor Speed 
N_{MOTOR} 
RPM 
Output motor speed. 
Typical impeller speed 
N_{TYP} 
RPM 
Typical impeller speed, which is process specific for
variable speed drives or the speed of a fixed speed drive. 
World Nae for current dispersion for the bottom impeller 
Nae_{B,W} 
% 
World definition of Aeration Number for the current
dispersion of the bottom impeller. 
World Nae for a flooded dispersion for the bottom impeller 
Nae_{B,W, FLOODED} 
% 
World definition of Aeration Number for the transition of
flooded to intermediate dispersion for the bottom impeller. 
World Nae for a great dispersion for the bottom impeller 
Nae_{B,W, GREAT} 
% 
World definition of Aeration Number for the transition of
intermediate to well dispersed (great) dispersion for the bottom impeller. 
LIGHTNIN Nae for a flooded dispersion 
Nae_{L,FP,i} 
% 
Same as world Nae but with the inclusion of Nq (Lightnin
method) for the iimpeller. 
LIGHTNIN Nae for current dispersion 
Nae_{L,i} 
% 
Same as world Nae but with the inclusion of Nq (Lightnin
method) for the iimpeller. 
LIGHTNIN Nae for a great dispersion 
Nae_{L,WD,i} 
% 
Same as world Nae but with the inclusion of Nq (Lightnin
method) for the iimpeller. 
World Nae for a flooded dispersion 
Nae_{W,FP,i} 
% 
World definition Aeration number for the transition
between intermediate and flooded gas dispersion at impeller i conditions
for the iimpeller. 
World Nae for current dispersion 
Nae_{W,i} 
% 
World definition Aeration number at impeller i conditions
for the iimpeller. 
World Nae for a great dispersion 
Nae_{W,WD,i} 
% 
World definition Aeration number for the transition
between intermediate and well dispersed (Great) gas dispersion at impeller
i conditions for the iimpeller. 
NB (Baffle Number) 
NB 
[] 
Baffle number. Describes the relative area of resistance to flow. 
Np0 
Np_{i,0} 
[] 
Ungassed power number for the iimpeller. 
Np(g) 
Np_{i,G} 
[] 
Gassed power number (operating conditions) for the iimpeller. 
Nq 
Nq_{i} 
[] 
Flow Number. Dimensionless fluid flow rate for the iimpeller. 
Offbottom impeller ratio 
OB_{B} /D_{B} 
[] 
Ratio: Bottom impeller offbottom to bottom impeller diameter 
Baffle
offbottom 
OB_{BAF} 
mm 
OB= Off Bottom. Vertical distance from the lowest point of
the baffle to the inner bottom of the reactor, tank, vessel, or fermenter. 
Steady bearing offbottom 
OB_{BOT,SB} 
mm 
Height of the center of the bottom steady bearing or limit
ring from the tank bottom. 
Coil offbottom 
OB_{COIL} 
mm 
Off Bottom distance to bottom of coils. 
OffBottom of dip tube 
OB_{DIP} 
mm 
Distance of the outlet of a dip tube to the bottom of the
tank. 
Offbottom(i) 
OB_{i} 
mm 
Off bottom distance from the inner center bottom of the
tank to the vertical midpoint of the iimpeller. For Rushton
Turbines it is to the disk centerline. 
Int. steady bearing offbottom 
OB_{INT,SB} 
mm 
Height of the center of the intermediate steady bearing or
limit ring from the tank bottom. 
Sparger CL offbottom 
OB_{SP} 
mm 
For pipe sparge: Off bottom distance to center of opening;
For ring sparge: Off bottom to center of pipe. 
OB(sparge)/D 
OB_{SP/}D_{B} 
[] 
Ratio: Off bottom distance of the sparge to bottom
impeller diameter 
OB(sparge)/D(sparge) 
OB_{SP/}D_{SP} 
[] 
Ratio: Off bottom distance of the sparge to sparge
diameter 
Measured OTR 
OTR 
mmol O2/L hr 
Oxygen Transfer Rate is the rate of transfer of oxygen as a
result of the dispersion of gas from the impellers. 
Design OTR 
OTR _{ IMP} 
gr/L/hr 
Oxygen Transfer Rate based on impeller characteristics 
OTR (based on N and Q_{G}) 
OTR _{ N,QG} 
mmol/L/hr 
Oxygen Transfer Rate based on given N and
Q_{G} 
Process OTR 
OTR _{ PROC} 
gr/L/hr 
Oxygen Transfer Rate based on process characteristics 
Baffle offwall

OW_{BAF} 
mm 
OW= Off Wall. Horizontal space between the tank sidewall
and the side of the baffle closest to the wall. 
P(bottom) 
>p_{BOT} 
bar 
Total pressure at the bottom 
BackPressure 
p_{BP} 
bar 
This is the additional pressure above the station pressure
that is put into the reactor, tank, vessel, or reactor. 
P(i) 
p_{i} 
bar 
Total pressure at the iimpeller 
P(middepth) 
p_{MD} 
bar 
Total pressure at middepth 
P(sparge) 
p_{SP} 
bar 
Total pressure at the sparge 
Station Pressure 
p_{STAT} 
bar 
This is the true atmospheric pressure on the outside of
the reactor, tank, vessel or fermenter during a recorded run. This is
different from the reported barometric pressure. The barometric pressure
is corrected down to sea level from the actually measured station
pressure. It is important to know the distance above sea level to achieve
the station pressure if only the barometric pressure is known. 
P(Head Pressure) 
p_{TOP} 
bar 
Total pressure at the top of the tank 
Measured Power 
P 
kW 
The measured power draw at the motor. 
Ratio of measured/calc Power 
P/ P_{TOT,G} 
[] 
How does the measured power compare to the calculated
operating power? 
Ungassed Power 
P_{i,0} 
kW 
Ungassed power consumption of the impeller, metric units
for the iimpeller. 
Ungassed Power 
P’_{i,0} 
Hp 
Ungassed power consumption of the impeller, American units
for the iimpeller. 
Gassed Power 
P_{i,G} 
kW 
Gassed power consumption of the impellers, metric units for the iimpeller. 
Gassed Power 
P’_{i,G} 
Hp 
Gassed power consumption of the impeller, American units
for the iimpeller. 
Isothermal expansion Power/Volume(middepth) 
P_{IEG,MD}/ V_{LIQ} 
kW/m3 
Based on the power per volume given off to the fluid of
the rising gas bubbles at middepth. 
Isothermal expansion Power/Volume(middepth) 
P’_{IEG,MD} /V’_{LIQ} 
Hp/kgal 
Based on the power per volume given off to the fluid of
the rising gas bubbles at middepth. (kgal = 1000 US gallons) 
Isothermal expansion Power/Volume(sparge) 
P_{IEG,SP}/ V_{LIQ} 
kW/m3 
Based on the power per volume given off to the fluid of
the rising gas bubbles at spagedepth. 
Isothermal expansion Power/Volume(sparge) 
P’_{IEG,SP} /V’_{LIQ} 
Hp/kgal 
Based on the power per volume given off to the fluid of
the rising gas bubbles at spargedepth. (kgal = 1000 US gallons) 
Motor Power 
P’_{MOTOR} 
Hp 
American units of the motor power. 
Maximum Impeller Power 
P_{MAX} 
kW 
Maximum power drawn. Often this is at 60 Hz on the
frequency drive. Some drives may run at higher frequencies. This is at
N_{MAX}. 
Minimum impeller power 
P_{MIN} 
kW 
Minimum power that the agitator can be run at. This is at N_{MIN}. 
Motor HP nameplate 
P_{MOTOR} 
kW 
Motor power can be found on the nameplate. 
Motor Power 
P_{MOTOR} 
kW 
Metric units of the motor power. 
Motor P / V total 
P_{MOTOR}/V_{TOT} 
kW/m3 
Theoretical P/V when the motor is running full out and the
reactor, tank, vessel, or fermenter is completely full. 
Ungassed total shaft power 
P_{TOT,0} 
kW 
Total power imparted from the impellers to the fluid with
no aeration. 
Ungassed total shaft power 
P’_{TOT,0} 
Hp 
Same as P_{TOT,0}, but in American units. 
Ungassed power per unit ungassed volume 
P_{TOT,0}/V_{LIQ} 
kW/m3 
Selfexplanatory. 
Ungassed power per unit ungassed volume 
P’_{TOT,0}/ V_{LIQ} 
Hp/kgal 
Selfexplanatory. This is 1/5 of the metric unit. (kgal = 1000 US gallons) 
Total operating shaft power 
P_{TOT,G} 
kW 
Total power imparted from the impellers to the fluid under actual operating conditions.
If there is no aeration this is the same as the ungassed total shaft power. 
Gassed total shaft power 
P’_{TOT,G} 
Hp 
Same as P_{TOT,G}, but in American units. 
Ratio of calc/measured powers 
P_{TOT,G}/P 
[] 
How does the calculated operating power compare to the measured power? 
Power Ratio Imp/Gas at middepth 
P_{TOT,G}/P_{IEHP,MD} 
[] 
Ratio total impeller power to gas expansion power based on
conditions at reactor, tank, vessel, or fermenter middepth. 
Power Ratio Imp/Gas at the sparge 
P_{TOT,G}/P_{IEHP,SP} 
[] 
Ratio total impeller power to gas isothermal expansion power based on conditions at the
sparge pipe or ring. 
Gassed power per unit ungassed volume 
P_{TOT,G}/V_{LIQ} 
kW/m^{3} 
Selfexplanatory. 
Gassed power per unit ungassed volume 
P’_{TOT,G}/ V_{LIQ} 
Hp/kgal 
Selfexplanatory. This is 1/5 of the metric unit. (kgal = 1000 US gallons) 
Typical impeller power 
P_{TYP} 
kW 
This is often process specific. This is a typical power
draw at N_{TYP}. 
Typical maximum head pressure 
P_{TYP,BP} 
bar 
Typical head pressure put on the reactor, tank, vessel, or fermenter. 
PF(D2) 
PF(D2)_{i} 
[] 
Proximity Factor for D2 flow patterns
for the iimpeller. 
PF(D3) 
PF(D3)_{i} 
[] 
Proximity Factor for D3 flow patterns
for the iimpeller. 
PF(R1 and R2) 
PF(R1,R2)_{i} 
[] 
Proximity Factor for R1 and R2
flow patterns for the iimpeller. 
PF(U3and U2) 
PF(U2,U3)_{i} 
[] 
Proximity Factor for U2 and U3
flow patterns for the iimpeller. 
Proximity Factor 
PF_{i} 
[] 
Proximity Factor. A relative value of ungassed power based
on geometrical location of an impeller in a tank compared to a standard
location for the iimpeller. 
Ungassed Power Split 
PS_{i,0} 
% 
Ungassed Power Split. % of total power for this impeller for the iimpeller. 
Gassed Power Split 
PS_{i,G} 
% 
Gassed Power Split. % of total power for this impeller for the iimpeller. 
Top Impeller power split 
PS_{i,G} 
% 
Percentage of the total power being consumed by the iimpeller. 
O_{2} vol. feed rate/volume 
q_{O2,IN} 
nm^{3}/L/hr 
Volume specific volumetric flow rate of pure oxygen in the
feed at normal conditions 
Coolant rate 
Q_{COIL} 
kg/hr 
Flow rate through the heat exchanger coils. 
Gas Flow Rate 
Q_{G} 
nm^{3}/hr 
The flow rate of the gas (for example air) into the
reactor, tank, vessel or fermenter under normal conditions (1 bar and
20oC). 
Gas Rate Maximum 
Q_{G,MAX} 
nm^{3}/hr 
The maximum normal gas rate you can put through the sparge pipe or ring. 
gas flow rate(normal) 
Q_{G,nLPM} 
nLPM 
Gas flow rate under standard conditions converted to Liters per Minute. 
gas flow rate(standard) 
Q’_{G,SCFH} 
SCFH 
Gas flow rate under standard conditions converted to cubic feet per hour. 
gas flow rate(standard) 
Q’_{G,SCFM} 
SCFM 
Gas flow rate under standard conditions converted to cubic feet per minute. 
Q_{G}(middepth) 
Q_{G,MD,aLPM} 
aLPM 
Actual gas flow rate at middepth under operating conditions, assuming no consumption of
oxygen. 
Q_{G}(middepth) 
Q_{G,MD,m3/hr} 
m^{3}/hr 
Actual gas flow rate at middepth under operating conditions, assuming no consumption of
oxygen. 
Q_{G}(middepth) 
Q_{G,MD,m3/min} 
m^{3}/min 
Actual gas flow rate at middepth under operating conditions, assuming no consumption of
oxygen. 
Q_{G}(middepth) 
Q’_{G,MD} 
ACFM 
Actual gas flow rate at middepth under operating
conditions, assuming no consumption of oxygen. 
Q_{G}(sparge) 
Q_{G,SP,aLPM} 
aLPM 
Actual gas flow rate at spargedepth under operating
conditions, assuming no consumption of oxygen. 
Q_{G}(sparge) 
Q_{G,SP,m3/hr} 
m^{3}/hr 
Actual gas flow rate at spargedepth under operating
conditions, assuming no consumption of oxygen. 
Q_{G}(sparge) 
Q_{G,SP,m3/min} 
m^{3}/min 
Actual gas flow rate at spargedepth under operating
conditions, assuming no consumption of oxygen. 
Q_{G}(sparge) 
Q’_{G,SP} 
ACFM 
Actual gas flow rate at spargedepth under operating
conditions, assuming no consumption of oxygen. 
Gas flow rate at the impeller 
Q_{i,G} 
ALPM 
Actual gas flow rate at the impeller assuming no
consumption of oxygen for the iimpeller. 
Gas flow rate at the impeller 
Q’_{i,G} 
ACFM 
Actual gas flow rate at the impeller assuming no
consumption of oxygen for the iimpeller. 
Flooded Minimum Gas Flow Rate 
Q_{i,FLOODED} 
ALPM 
Minimum gas flow rate that begins flooding for the iimpeller. 
Well Dispersed Maximum Gas Flow Rate 
Q_{i,GREAT} 
ALPM 
Maximum gas flow rate that is still considerd well dispersed for the iimpeller. 
Q(LIQ): Liquid flow rate 
Q_{LIQ,i} 
m^{3}/hr 
Liquid flow rate generated directly from the impeller for the iimpeller. 
Q’(LIQ): Liquid flow rate 
Q’_{LIQ,i} 
GPM 
Liquid flow rate generated directly from the impeller for the iimpeller. 
O_{2} vol. feed rate 
Q_{O2,IN} 
nm^{3}/hr 
Volumetric flow rate of pure oxygen in the feed at normal conditions 
Bottom dish/knuckle radius 
r_{BOT} 
mm 
The radius of the bottom dish and the radius of the bottom
dish segment (knuckle) closest to the straight side. This info is found on
tank drawings. 
Top Dish/Knuckle radius 
r_{TOP} 
mm 
The radius of the top dish and the radius of the top dish
segment (knuckle) closest to the straight side. This info is found on tank drawings. 
Gear Ratio 
R_{GEAR} 
[] 
Ratio of the motor speed to output impeller speed. This is often found
on the nameplate or drawings from the vendor. 
Ratio kW/(Volts*Amps/1000) 
R_{P/VI} 
[] 
This is a calculated value of the Motor HP nameplate, Volts and Amps of
the motor. This ratio is fairly constant among brands and can be used to determine a value
if one of the three other parameters are missing. 
Re 
Re_{i} 
[] 
Reynold’s Number. A dimensionless number that discribes
the turbulence for the iimpeller. 
Coil spacing 
s_{COIL} 
mm 
For helical and vertical pipes: Space between pipes; For
plate coils, space between plates if in bundles. 
Impeller spacing 
S_{i} 
mm 
Spacing (distance) between the iimpeller and the one
below it. The "spacing" of the bottom impeller is the OB. 
S/D 
S_{i} /D_{i} 
[] 
Ratio: Impeller spacing to impeller diameter for the iimpeller. 
S(sparge)/D 
S_{SP}/D_{B} 
[] 
Ratio: Space (distance) between the sparge and the bottom
impeller to the impeller diameter. 
SEff (automatic input) initial assumption to calc c*(top) 
SEff 
% 
Stripping Efficiency: The amount of oxygen stripped from
the oxygen feed. 
SEff calculated 
SEff_{CALC} 
% 
Calculated SEff derived from a mass balance. 
Overall Avg. Swirl&Viscosity Factor 
SF_{AVG} 
[] 
This factor is needed when the unaerated measured power
and the calculated power do not match. In order to keep it simple, I have
combine the two factors into one. Viscosity factors are generally >1
(except for Rushton Turbines) when Re (Reynold’s Number) < 2000.
Swirl factors are generally < 1, because coils and real baffles may not
achieve the desired fully baffled
condition. In the case of reactors,
tanks, vessels or fermenters with more than 4 standard
baffles, SF > 1. 
Swirl&Viscosity Factor 
SF_{i} 
[] 
SF for the iimpeller. Under normal circumstances SFi =
SFAVG unless there are geometrical differences to the rest of the reactor,
tank, vessel, or fermenter. 
Motor Service Factor 
SF_{MOTOR} 
% 
Service factor of the motor. This value can be found on the nameplate. 
Sparger type(=SP): 
SP 

Description of the device that injects air or gas into the
reactor, tank, vessel, or fermenter, such as pipe or ring, or rotating pipes. 
Temperature 
t 
C 
Temperature at operating conditions inside the reactor,
tank, vessel, or fermenter. 
Outlet temperature 
t_{COIL, OUT} 
C 
Temperature exiting the coils. 
Inlet temperature 
t_{COIL,IN} 
C 
Temperature entering the coils. 
Stage MixTime(95%) 
t_{i,MIX} 
s 
Stage mixing time for a 95% Degree of Mixing for the iimpeller. 
Desired blending time 
t_{MIXDES} 
s 
Desired overall mixing time in the tank. 
Tank diameter 
T 
mm 
Inner diameter of the reactor, tank, vessel, or fermenter. 
Tip Speed 
TS_{i} 
m/s 
Tip Speed. Peripheral speed of the impeller blade tips for the iimpeller. 
v(sparge exit velocity) 
v_{SP,EXIT} 
m/s 
Actual exit gas velocity from the sparge pipe or sparge holes. 
v(sparge exit velocity) 
v’_{SP,EXIT} 
ft/s 
Actual exit gas velocity from the sparge pipe or sparge holes, American units. 
v(sparge pipe velocity) 
v_{SP,PIPE} 
m/s 
Actual gas velocity through the pipe feeding the sparger. 
v(sparge exit velocity) 
v’_{SP,EXIT} 
ft/s 
Actual exit gas velocity from the sparge pipe or sparge holes. 
70% of the total fermenter volume. 
V_{70} 
Liters 
Volume when the reactor, tank, vessel, or fermenter is 70% full. 
Volume of the baffles 
V_{BAF} 
Liters 
Displacement volume of the baffles. 
Bottom head volume 
V_{BOT} 
Liters 
Volume of the bottom head. 
ASME dish volume 
V_{BOT,a} 
Liters 
Volume of an ASME bottom dish. 
Other dish volume 
V_{BOT,o} 
Liters 
Volume of a dish not matching any of the standards. 
SemiElliptical dish volume 
V_{BOT,s} 
Liters 
Volume of a semielliptical bottom dish. 
Flat head volume 
V_{BOT.f} 
Liters 
Volume of a flat bottom head. 
Coil Volume 
V_{COIL} 
Liters 
Displacement volume of the coils. 
Displacement Volume of Internals 
V_{DISP} 
Liters 
Displacement volume of all internals in the reactor, tank, vessel, or fermenter. 
Gassed liquid volume 
V_{G} 
Liters 
Volume of gassed liquid in the reactor, tank, vessel, or fermenter. 
Ratio: Gassed liquid volume to total tank volume. 
V_{G}/ V_{TOT} 
[%] 
Percent of total gassed volume. 
Ungassed liquid volume 
V_{LIQ} 
Liters 
Volume of ungassed liquid in the reactor, tank, vessel, or
fermenter. 
Ratio: Ungassed liquid volume to total tank volume. 
V_{LIQ}/ V_{TOT} 
[%] 
Percent of total ungassed volume. 
Listed volume 
V_{LIST} 
Liters 
Volume according to the tank vendor or listed on the tank drawings. 
Volts 
V_{MOTOR} 
Volts 
Motor volts can be found on the nameplate. 
Dish volume for other dishes 
V_{o} 
Liters 
For dish shapes labeled as o (other), the actual volume of the
dish or head. 
Shaft Volume 
V_{SHAFT} 
Liters 
Volume of the shaft within the reactor, tank, vessel, or fermenter. 
Straight side volume 
V_{SS} 
Liters 
Volume of the cylindrical portion of the reactor, tank, vessel, or fermenter. 
Top head volume 
V_{TOP} 
Liters 
Volume of the top head. 
ASME dish volume 
V_{TOP,a} 
Liters 
Volume of an ASME top dish. 
Other dish volume 
V_{TOP,o} 
Liters 
Volume of a dish not matching any of the standards. 
SemiElliptical dish volume 
V_{TOP,s} 
Liters 
Volume of a semielliptical top dish. 
Flat head volume 
V_{TOP.f} 
Liters 
Volume of a flat top head. 
Total fermenter volume 
V_{TOT} 
Liters 
Volume when the reactor, tank, vessel, or fermenter is
completely full. 
Typical volume at end 
V_{TYP,}_{
¥} 
Liters 
Typical volume of the reactor, tank, vessel, or fermenter
at the end of a run. 
Typical volume at beginning 
V_{TYP,0} 
Liters 
Typical volume of the reactor, tank, vessel, or fermenter
at the beginning of a run. 
Typical gassed volume 
V_{TYP,G} 
Liters 
This is process specific and will vary from process to
process. This does not include foam height. This reflects “typical” values. 
Superficial gas velocity (middepth) 
vsg_{MD} 
m/min 
The actual superficial gas velocity at middepth at
operating conditions, assuming no consumption of oxygen, in metric units. 
Superficial gas velocity (middepth) 
vsg_{MD,m/s} 
m/s 
The actual superficial gas velocity at middepth at
operating conditions, assuming no consumption of oxygen, in metric units. 
Superficial gas velocity (middepth) 
vsg_{MD,m/s} 
m/s 
The actual superficial gas velocity at middepth at
operating conditions, assuming no consumption of oxygen, in metric units. 
Superficial gas velocity (sparge) 
vsg_{SP} 
m/min 
The actual superficial gas velocity at spargedepth at
operating conditions, assuming no consumption of oxygen, in metric units. 
Superficial gas velocity (sparge) 
vsg_{SP,m/s} 
m/s 
The actual superficial gas velocity at spargedepth at
operating conditions, assuming no consumption of oxygen, in metric units. 
Superficial gas velocity (sparge) 
vsg_{SP,m/s} 
m/s 
The actual superficial gas velocity at spargedepth at
operating conditions, assuming no consumption of oxygen, in metric units. 
vvm (normalized) 
vvm 
min^{1} 
Volume of gas per minute per volume of liquid in the reactor, tank, vessel, or
fermenter under standard conditions 
vvm(i) 
vvm_{i} 
min^{1} 
Actual average gas rate for the iimpeller 
vvm(middepth) 
vvm_{MD} 
min^{1} 
The actual vvm at middepth at operating conditions, assuming no consumption of oxygen. 
vvm(sparge) 
vvm_{SP} 
min^{1} 
The actual vvm at spargedepth at operating conditions,
assuming no consumption of oxygen. 
Width of baffles 
w_{BAF} 
mm 
Distance from the side closest to the shaft to the side
closest to the tank’s wall. 
Recommended w_{B} 
w_{BAF,REC} 
mm 
Selfexplanatory. Assumes standard w_{BAF}/T is 0.1 for water
and determines w_{BAF}. 
w(baffle)/T 
w_{BAF}/T 
[] 
Baffling ratio: Width of the
baffles to tank diameter. 
Recommended wB/T 
w_{BAF}/T_{REC} 
[] 
Selfexplanatory. Assumes standard is 0.1 for water. 
Blade width(i) 
w_{i,BLADES} 
mm 
Width of the blade of the iimpeller = distance of blade
closest to the shaft to the blade farthest out from shaft. 
w/D 
w_{i}/D_{i} 
[] 
Ratio: Blade width to impeller diameter for the iimpeller. 
Media Weight 
W_{LIQ} 
kg 
Weight of the fluid media inside the reactor, tank,
vessel, or fermenter. 
O_{2} mass feed rate 
W_{O2,IN} 
grO_{2}/hr 
Mass flow rate of pure oxygen in the feed 
O_{2} mass feed rate/volume 
w_{O2,IN} 
grO_{2}/L/hr 
Volume specific mass flow rate of pure oxygen in the feed
at normal conditions 
O_{2} Inlet Concentration 
y_{O2,IN} 
Vol% 
Concentration of the oxygen in the gas feeding the
reactor, tank, vessel, or fermenter through the gassparging device. 
Oxygen Outlet Concentration 
y_{O2,OUT} 
Vol% 
Concentration of the oxygen in the gas exiting the
reactor, tank, vessel, or fermenter through the exhaust or condensor. 
Bottom head height 
z_{BOT} 
mm 
Height from bottom of the bottom dish to the flange. If
welded, till the straight side starts. 
ASME dish height 
z_{BOT,a} 
mm 
Height of an ASME bottom dish. 
Flat head height 
z_{BOT,f} 
mm 
Height of a flat bottom head. 
Other dish height 
z_{BOT,o} 
mm 
Height of a dish not matching any of the standards. 
SemiElliptical dish height 
z_{BOT,s} 
mm 
Height of a semielliptical bottom dish. 
Coil height 
z_{COIL} 
mm 
Height of coil from lowest point of the coils to the
highest point of the coils. 
Straight side height 
z_{SS} 
mm 
Height of the straight side of the reactor, tank, vessel, or fermenter. 
Overall tank height 
z_{TOT} 
mm 
The total height of the reactor, tank, vessel, or
fermenter consisting of the straight side and the height of the bottom and upper heads 
Aspect ratio of the tank 
z_{TOT}/T 
[] 
Aspect ratio: Height to width ratio. 
Top head height 
z_{TOP} 
mm 
Height from top of the top dish to the flange. If welded,
till the straight side starts. 
ASME dish height 
z_{TOP,a} 
mm 
Height of an ASME top dish. 
Flat head height 
z_{TOP,f} 
mm 
Height of a flat top head. 
Other dish height 
z_{TOP,o} 
mm 
Height of a dish not matching any of the standards. 
SemiElliptical dish height 
z_{TOP,s} 
mm 
Height of a semielliptical top dish. 
Gassed liquid height 
Z_{G} 
mm 
Height of gassed liquid in the reactor, tank, vessel, or fermenter. 
Ratio: Gassed liquid level to tank diameter. 
Z_{G}/T 
[] 
Aspect ratio of the gassed liquid. 
Ungassed liquid height 
Z_{LIQ} 
mm 
Height of ungassed liquid in the reactor, tank, vessel, or fermenter. 
Ratio: Ungassed liquid level to total tank height. 
Z_{LIQ}/ Z_{TOT} 
[%] 
Percent of total ungassed liquid height. 
Ratio: Ungassed liquid level to tank diameter. 
Z_{LIQ}/T 
[] 
Aspect ratio of the ungassed liquid. 
Typical liquid level at end 
Z_{TYP,}_{¥} 
mm 
Typical liquid level of the media in the reactor, tank,
vessel, or fermenter at the end of a run. 
Typical liquid level at beginning 
Z_{TYP,0} 
mm 
Typical liquid level of the media in the reactor, tank,
vessel, or fermenter at the beginning of a run. 