Notation
SI units are given first (followed by English and/or cgs units).
| a | shape factor, dimensionless |
| a | particle radius, m (ft) |
| a | area, m2 (ft2); also m2 area/m3 volume bed or packing (ft2/ft3) |
| ae | acceleration from centrifugal force, m/s2 (ft/s2) |
| aν | specific surface area of particle, m−1 (ft−1) |
| A | cross-sectional area, m2 (ft2, cm2); also area, m2 (ft2) |
| A | absorption factor = L/mV, dimensionless; also filter area, m2 (ft2) |
| Am | membrane area, cm2, m2 (ft2) |
| Aw | solvent permeability constant, kg/s · m2 · atm |
| As | solute permeability constant, m/s (ft/h) |
| b | length, m (ft, cm) |
| B | length of side in structured packing, cm (in.) |
| B | flow rate of dry solid, kg/h (lbm/h); also filtration constant, s/m3 (s/ft3) |
| B | physical property of membrane, atm−1 |
| Bo | nucleation rate, number of nuclei/h · L |
| c | concentration, kg/m3, kg mol/m3 (lbm/ft3, g mol/cm3) |
| c | concentration of absorbate in fluid, kg/m3 (lbm/ft3) |
| cA | concentration of A, kg mol/m3 (lb mol/ft3, g mol/cm3) |
| cb | break-point concentration, kg/m3 (lbm/ft3) |
| cg | concentration of solute in gel, kg solute/m3 (lbm/ft3, g/cm3) |
| cs | concentration of solute at surface of membrane, kg solute/m3 (lbm/ft3, g/cm3) |
| cS | concentration of A in solid, kg mol A/m3 (lbm/ft3, g mol/cm3) |
| cS | concentration of solids in slurry, kg/m3 (lbm/ft3) |
| cS | humid heat, kJ/kg dry air · K (btu/lbm dry air · °F) |
| cx | concentration of solids in slurry, mass frac |
| cp | heat capacity at constant pressure, J/kgK, · kJ/kgK, · kJ/kg mol · K (btu/lbm · °F, cal/g · °C) |
| cw2 | concentration of solvent in permeate, kg solvent/m3 |
 | deviation of concentration from mean concentration  , kg mol/m3 |
| cp | concentration of P, kg P/m3 |
| cν | heat capacity at constant volume, J/kg · K |
| C | filtration constant, N/m2 (lbf/ft2); also, number of components |
| C | fluid heat capacity, W/K (btu/h · °F) |
| C | height of bottom of agitator above tank bottom, m (ft) |
| C | total concentration in liquid solution, equiv/L |
| Cp | pitot tube coefficient, dimensionless |
| CD | drag coefficient, dimensionless |
| Cν, Co, Cn | Venturi coefficient, orifice coefficient, flow nozzle coefficient, dimensionless |
| dp | packing diameter, mm (in.) |
| do | hole diameter, ft |
| D | molecular diffusivity, m2/s (ft2/h, cm2/s); also diameter, m (ft) |
| D | decimal reduction time, min; also distillate flow rate, kg/h, kg mol/h (lbm/h) |
| DAB | molecular diffusivity, m2/s (ft2/h, cm2/s) |
 | molecular diffusivity in dilute solution, cm2/s (ft2/h) |
| Dp | particle diameter, m (ft) |
| DKA | Knudsen diffusivity m2/s (ft2/h, cm2/s) |
| DNA | transition-region diffusivity, m2/s (ft2/h, cm2/s) |
| DA eff | effective diffusivity, m2/s (ft2/h, cm2/s) |
| Dp,m | effective mean diameter for mixture, m (ft) |
| Da | diameter of agitator, m (ft) |
| Dt | diameter of tank, m (ft) |
| Dpc | critical diameter, m (ft) |
| DAP | diffusivity of A in protein solution, m2/s |
| D+ | molecular diffusivity of cation, cm2/s |
| D− | molecular diffusivity of anion, cm2/s |
| E | height of element in structured packing, cm (in.) |
| E | activation energy, J/kg mol (cal/g mol) |
| E | energy for size reduction, kW · h/ton; also tray efficiency, dimensionless |
| E | total energy, J/kg (ft · lbf/lbm) |
| E | fraction unaccomplished change, dimensionless |
| E | emitted radiation energy, W/m2 (btu/h · ft2) |
| E | axial dispersion coefficient, m2/s (ft2/h) |
| EBλ | monochromatic emissive power, W/m3 (btu/h · ft3) |
| Eo | fraction or % tray efficiency |
| ƒ | fraction of feed vaporized; also cycle fraction, dimensionless |
| ƒ | fanning friction factor, dimensionless |
| ƒp | relative mass-transfer coefficient, dimensionless |
| ƒt | mixing factor, dimensionless |
| F | number of degrees of freedom |
| F | frictional loss, J/kg (ft · lbf/lbm) |
| F | flow rate, kg/h, kg mol/h (lbm/h) |
| F | force, N (lbf, dyn) |
| FT | correction factor for temperature difference, dimensionless |
| F0 | process time at 121.1°C(250°F), min |
| Fp | packing factor, m−1(ft−1) |
 | geometric view factor for gray surfaces, dimensionless |
| F12 | geometric view factor, dimensionless |
| g | standard acceleration of gravity (see Appendix A.1) |
| gc | gravitional conversion factor (see Appendix A.1) |
| G | mass velocity = νρ, kg/s · m2, kg/h · m2 (lbm/h · ft2) |
| G | growth constant, mm/h |
| G' | mass velocity = ν'ρ, kg/s · m2, kg/h · m2 (lbm/h · ft2) |
| G | irradiation on a body, W/m2 (btu/h · ft2) |
| h | constant spacing in x for Simpson's rule |
| h | head, J/kg (ft · lbf/lbm); also height of fluid, m (ft) |
| h | heat-transfer coefficient, W/m2 · K (btu/h · ft2 · °F) |
| h | enthalpy of liquid, J/kg, kJ/kg, kJ/kg mol (btu/lbm) |
| h | height of triangle in structured packing, cm (in.) |
| hƒg | latent heat of vaporization, J/kg, kJ/kg (btu/lbm) |
| hc | contact resistance coefficient, W/m2 · K (btu/h · ft2 · °F) |
| H | distance, m (ft) |
| H | Henry's law constant, atm/mol frac |
| H | head, J/kg (ft · lbf/lbm); also height of fluid, m (ft) |
| H | enthalpy, J/kg, kJ/kg, kJ/kg mol (btu/lbm); also enthalpy kJ/kg dry air (btu/lbm dry air) |
| H | humidity, kg water vapor/kg dry air (lb water vapor/lb dry air) |
| H | enthalpy of vapor, J/kg, kJ/kg, kJ/kg mol (btu/lbm) |
| H | equilibrium relation, kg mol/m3 · atm |
| H | bed length, m (ft); also effective length of spindle, m (ft) |
| H | height of packing, m (ft) |
| H' | enthalpy, kJ/kg dry solid (btu/lbm); also enthalpy, kJ/kg dry air (btu/lbm dry air) |
| HB | length of bed used up to break point, m (ft) |
| HG, HL, Hy, Hoy HOG, HOL, Hx, Hox | height of transfer unit, m (ft) |
| HP, HR | percentage humidity, percentage relative humidity, respectively |
| HT | total bed length, m (ft) |
| HUNB | length of unused bed, m (ft) |
| HETS | height of equilibrium stage, m (ft) |
| HETP | height equivalent of packed tower equal to one theoretical plate, m (ft) |
| i | unit vector along x axis |
| I | intensity of turbulence, dimensionless; also current, amp |
| IB | radiation intensity of black body, W/m2 · sr (btu/h · ft2 · sr) |
| Iλ | intensity of radiation, W/m2 (btu/h · ft2) |
| j | unit vector along y axis |
| J | width of baffle, m (ft) |
| jA | mass flux of A relative to mass average velocity, kg/s · m2 |
 | mass flux of A relative to molar average velocity, kg/s · m2 |
| JA | molar flux of A relative to mass average velocity, kg mol/s · m2 |
 | molar flux vector of A relative to molar average velocity, kg mol/s · m2 (lb mol/h · ft2, g mol/s · cm2) |
| JD' JH | mass-transfer and heat-transfer factors, dimensionless |
| k | unit vector along z axis |
| k, k' | reaction velocity constant, h−1, min−1, or s−1 |
| k | thermal conductivity, W/m · K (btu/h · ft · °F) |
| k | reaction velocity constant, h−1, min−1, or s−1 |
 | first-order heterogeneous reaction velocity constant, m/s (cm/s) |
 , kc, kG, kx, . . . | mass-transfer coefficient, kg mol/s · m2 · conc diff (lb mol/h · ft2 · conc diff, g mol/s · cm2 · conc diff); kg mol/s · m2 · Pa, kg mol/s · m2 · atm (lb mol/h · ft2 · atm). (See Table 7.2-1.) |
| kc | mass-transfer coefficient, m/s (ft/ h, cm/s) |
 | mass transfer coefficient defined by Eq. (7.2-23), m/s (ft/h, cm/s) |
| kGa, kxa, kya, . . . | volumetric mass-transfer coefficient, kg mol/s · m3 · conc diff (lb mol/h · ft3 · conc diff, g mol/s · cm3 · conc diff); kg mol/s · m3 · Pa |
| ks | surface reaction coefficient, kg mol/s · m2 · mol frac |
kw,  | wall constants, dimensionless |
 ,  | overall mass-transfer coefficient, kg mol/s · m2 · mol frac (lb mol/h · ft2 · mol frac, g mol/s · cm2 · mol frac) |
| K | consistency index, N · sn/m2 (lbf · sn/ft2) |
| K | overall mass transfer coefficient in crystallization, kg mol/s · m2 · mol frac |
| Kν | constant in allowable vapor velocity equation, ft/s |
| K | relative molar selectivity coefficient, dimensionless |
| KAB | equilibrium constant for exchange of ions A and B |
| K1 | constant in Eq. (3.1-39), m/s (ft/s) |
| K', Ks | equilibrium distribution coefficient, dimensionless |
| K″ | consistency index, N · sn'/m2 (lbf · sn'/ft2) |
| K | equilibrium distribution coefficient, dimensionless |
| Kp | filtration constant, s/m6 (s/ft6) |
| KV | filtration constant, N/m5 (lbf/ft5) |
| Kc, Kex, Kƒ | contraction, expansion, fitting loss coefficient, dimensionless |
| L | length, m (ft); also amount, kg, kg mol (lbm); also kg/h · m2 |
| L | liquid flow rate, kg/h, kg mol/h (lbm/h) |
| L | crystal size, mm |
| L | residue or reject flow rate, cm3 (STP)/s, m3/s (ft3/h) |
| L | Prandtl mixing length, m (ft) |
| L | mean beam length, m (ft) |
| La | average crystal size, mm |
| Ld | predominant crystal size, mm |
| Lƒ | feed flow rate, cm3 (STP)/s, m3/s (ft3/h) |
| LS | dry solid weight, kg dry solid (lbm dry solid) |
| L' | flow rate, kg inert/h, kg mol inert/h (lbm inert/h) |
| m, m', m'' | slope of equilibrium line, dimensionless |
| m | flow rate, kg/s, kg/h (lbm/s) |
| m | dimensionless ratio = k/hx1; also, position m |
| m | parameter in Table 7.1-1, dimensionless; also position parameter |
| m | ratio, kg wet cake/kg dry cake (lb wet cake/lb dry cake) |
| M | molecular weight, kg/kg mol (lbm/lb mol) |
| M | total mass, kg (lbm); also parameter = (Δx)2/αΔt, dimensionless |
| M | modulus = (Δx)2/DABΔt, dimensionless |
| M | flow rate, kg/h, kg mol/h (lbm/h) |
| M | amount of adsorbent, kg(lbm) |
| ML | average molecular weight of liquid |
| n | number of theoretical stages |
| n | number of crystals/(L · mm) |
| n | exponent, dimensionless; also flow behavior index, dimensionless |
| n' | slope of line for power-law fluid, dimensionless |
| n | position parameter; also dimensionless ratio = ×/×1 |
| n | total amount, kg mol (lb mol, g mol) |
| no | zero-size population density, number/(L · mm) |
| nA | flux of A relative to stationary coordinates, kg/s · m2 |
| n+ | valence of cation |
| n− | valence of anion |
| N | rpm or rps; also number of radiation shields |
| N | parameter = h Δx/k, dimensionless; also number of viable organisms, dimensionless |
| N | total flux relative to stationary coordinates, kg mol/s · m2 (lb mol/h · ft2, g mol/s · cm2) |
| N | modulus = kcΔx/DAB, dimensionless; also number of stages |
| N | number of crystals/L |
| N | concentration of solid B, kg solid B/kg solution (lb solid B/lb solution) |
| N | number of equal temperature subdivisions, dimensionless |
| NT | number of tubes in parallel |
| Ns | solute flux, kg/s · m2 (lbm/h · ft2) |
| Nw | solvent flux, kg solvent/s · m2 (lbm/h · ft2) |
 | residual defined by Eq. (6.6-3), kg mol/m3 (lb mol/ft3) |
| NA | molar flux vector of A relative to stationary coordinates, kg mol/s · m2 (lb mol/h · ft2, g mol/s · cm2) |
 | mass transfer of A relative to stationary coordinates, kg mol/s (lb mol/h, g mol/s) |
| (NPSH) | net positive suction head, m (ft) |
| NG, NL, NOG, NOL | number of transfer units, dimensionless |
| NGr | Grashof number defined in Eq. (4.7-4), dimensionless |
| NBi | Biot number = h×1/k, dimensionless |
| NGz | Graetz number defined in Eq. (4.12-3), dimensionless |
| NGr,δ | Grashof number defined in Eq. (4.7-5), dimensionless |
| NMa | Mach number defined by Eq. (2.11-15), dimensionless |
| NPe | Peclet number = NReNPr, dimensionless |
| NNu,δ | Nusselt number = hδ/k, dimensionless |
| NFr | Froude number = ν2/gL, dimensionless |
| NKn | Knudsen number =  dimensionless |
| NNu | Nusselt number = hL/k, dimensionless |
| NNu,x | Nusselt number = hxx/k, dimensionless |
| NPr | Prandtl number = cpμ/k, dimensionless |
| NRe | Reynolds number = Dνρ/μ, dimensionless |
 | Reynolds number =  , dimensionless |
| NRe,gen | Reynolds number defined by Eq. (3.5-11), dimensionless |
| NRe,L | Reynolds number = Lν ∞ρ/μ, dimensionless |
| NRe,x | Reynolds number = xν ∞ρ/μ, dimensionless |
 | Reynolds number defined by Eq. (3.5-39) dimensionless |
| NRe,p | Reynolds number defined by Eq. (3.1-15), dimensionless |
| NRe,mf | Reynolds number at minimum fluidization defined by Eq. (3.1-35), dimensionless |
| NEu | Euler number = ρ/ρν2, dimensionless |
| NSc | Schmidt number = μ/ρDAB, dimensionless |
| NSh | Sherwood number =  D/DAB, dimensionless |
| NP | power number defined by Eq. (3.4-2), dimensionless |
| NQ | Flow number, dimensionless |
| NSt | Stanton number =  /ν, dimensionless |
| NTU | number of transfer units, dimensionless |
| O | flow rate, kg/h, kg mol/h (lbm/h) |
| P | pressure, N/m2, Pa (lbf/ft2, atm, psia, mm Hg) |
| pνp | vapor pressure of fluid, N/m2 (lbf/ft2) |
| pA | partial pressure of A, N/m2, Pa (lbf/ft2, atm, psia, mm Hg) |
| ps | pressure at STP, Pa |
| pBM | log mean inert partial pressure of B in Eq. (6.2-21), N/m2, Pa (lbf/ft2, atm, psia, mm Hg) |
| ph | total pressure in high-pressure side (feed), cm Hg, Pa (atm) |
| pl | total pressure in low-pressure side (permeate) cm Hg, Pa (atm) |
| pM | permeance in solid, m/s (ft/h) |
| P | parameter in Eq. (5.5-12), dimensionless |
| P | total pressure, N/m2, Pa (lbf/ft2, atm, psia, mm H) |
| P | power, W (ft · lbf/s, hp) |
| P | flow rate, kg/h, kg/min; also number of phases at equilibrium |
| P | momentum vector, kg · m/s (lbm · ft/s) |
| PA | vapor pressure of pure A, N/m2, Pa (lbf/ft2, atm, psia, mm Hg) |
 | permeability of A, cm3 (STP) · cm/s · cm2cm Hg |
 /t | permeance of A, cm3 (STP)/s · cm2 · cm Hg, m3 (STP)/s · m2 · Pa |
| Pw | solvent membrane permeability, kg solvent/s · m · atm (lbm/h · ft · atm) |
| PM | permeability, m3(STP)/(s · m2 C.S. · atm/m) |
| q | heat-transfer rate, W (btu/h); also net energy added to system, W (btu/h); also J (btu) |
| q | flow rate, m3/s (ft3/s) |
| q | heat flux vector, W/m2 (btu/h · ft2) |
 | rate of heat generation, W/m3 (btu/h · ft3) |
| q | feed condition defined by Eq. (11.4-12) |
| q' | flow rate in Darcy's law, cm3/s |
| q | kg adsorbate/kg adsorbent (lbm/lbm) |
| qc | condenser duty, kJ/h, kW (btu/h) |
 ,m | residual defined by Eq. (4.5-11), K (°F) |
| qR | reboiler duty, kJ/h, kW (btu/h) |
| qAR | concentration of A in bulk bed volume, equiv/L volume |
| Q | total concentration of A and B in bulk bed volume, equiv/L volume |
| Q | outflow in crystallizer, L/h |
| Q | circulation rate, m3/s (ft3/h) |
| Q | amount absorbed, kg mol/m2; also heat loss, W (btu/h); also heat absorbed, J/kg (btu/lbm, ft · lbf/lbm) |
| r | radius, m (ft) |
| r | ratio of pressures, ρl/ρh |
| rA | rate of generation, kg A/s · m3 (lbmA/h · ft3) |
| rH | hydraulic radius, m (ft) |
| (r2)cr | critical value of radius, m (ft) |
| R | rate of drying, kg/h · m2 (lbm/h · ft2) |
| R | solute rejection, dimensionless |
| R | scaleup ratio, dimensionless |
| R | radius, m (ft); also resistance, K/W (h · °F/btu) |
| R | parameter in Eq. (5.5-12), dimensionless; also resistance, ohms |
| R | gas constant (see Appendix A.1); also reflux ratio = Ln/D, dimensionless |
| RA | rate of generation, kg mol A/s · m3 (lb mol A/h · ft') |
| Rb | radius of spindle, m (ft) |
| Rc | radius of outer cylinder, m (ft) |
| Rc | contact resistance, K/W (h · °F/btu) |
| Rg | gel layer resistance, s · m2 · atm/kg |
| Rm | resistance of filter medium, m−1(ft−1) |
| Rm | membrane resistance, m2/kg |
| Rc | cake resistance, m2/kg |
| Ri | rate of generation of i, kg/s (lbm/h) |
| R× | x component of force, N (lbf, dyn) |
| s | compressibility constant, dimensionless |
| s | mean surface renewal factors, s−1 |
| S | conduction shape factor, m (ft) |
| S | solubility of a gas, m3 solute(STP)/m3 solid · atm [cc solute(STP)/cc solid · atm] |
| S | distance between centers, m (ft); also steam flow rate, kg/h, kg mol/h (lbm/h) |
| S | volume of feed solution, m3 (ft3) |
| S | cross-sectional area of tower, m2 (ft2); also stripping factor, 1/A |
| S | length of side in structured packing, cm (in.) |
| S0 | specific surface area, m2/m3 volume (ft2/ft3 volume) |
| Sp | surface area of particle, m2 (ft2) |
| t | fin thickness, m (ft) |
| t | time, s, min, or h |
| t | temperature, K, °C (°F) |
| t | membrane thickness, cm, m (ft) |
| tb | break-point time, h |
| tt | time equivalent to total capacity, h |
| tT | mixing time, s |
| tu | time equivalent to usable capacity up to break-point time, h |
| T | tray spacing, m (ft) |
| T | torque, kg · m2/s2 |
| T | temperature. K, °C (°F, °R); also feed rate, ton/min |
| TS | temperature at STP, K |
| T' | deviation of temperature from mean temperature  , K (°F) |
 | average velocity, m/s (ft/s) |
| U | overall heat-transfer coefficient, W/m2 · K (btu/h · ft2 · °F) |
| U | internal energy, J/kg (btu/lbm) |
| ν | velocity, m/s (ft/s) |
| ν | velocity vector, m/s (ft/s) |
| νA | velocity of A relative to stationary coordinates, m/s (ft/s, cm/s) |
| νAd | diffusion velocity of A relative to molar average velocity, m/s (ft/s, cm/s) |
| νp | volume of particle, mm3/particle |
| ν'mb | minimum bubbling velocity, m/s (ft/s) |
| νM | molar average velocity of stream relative to stationary coordinates, m/s (ft/s, cm/s) |
| νH | humid volume, m3/kg dry air (ft3/lbm dry air) |
| νt | terminal settling velocity, m/s (ft/s) |
| ν+ | dimensionless velocity defined by Eq. (3.10-34) |
| ν* | velocity defined by Eq. (3.10-42), dimensionless |
 | deviation of velocity in x direction from mean velocity  , m/s (ft/s) |
| ν' | superficial velocity based on cross section of empty tube, m/s (ft/s, cm/s) |
 | velocity at minimum fluidization, m/s (ft/s) |
 | terminal settling velocity, m/s (ft/s) |
| VA | solute molar volume, m3/kg mol |
| V | flow rate, kg/h, kg mol/h, m3/s (lbm/h, ft3/s) |
| V | volume, m3 (ft3, cm3); also specific volume, m3/kg (ft3/lbm) |
| V | volume of crystallizer, L |
| V | velocity, m/s (ft/s); also total amount, kg, kg mol (lbm) |
| V | flow rate of permeate, cm3 (STP)/s, m3/s (ft3/h) |
| Vp | outlet permeate flow rate, m3 (STP)/s, m3/s (ft3/h) |
| V' | inert flow rate, kg/h, kg/s, kg mol/h (lbm/h) |
| VC, VD | superficial velocities of continuous and dispersed phase, ft/h |
| wA | mass fraction of A |
 | work done on surroundings, W (ft · lbf/s) |
| W | free water, kg (lbm) |
 | mechanical shaft work done on surroundings, W (ft · lbf/s) |
| W | flow rate, kg/h, kg mol/h (lbm/h) |
| W | work done on surroundings, J/kg(ft · lbf/lbm) |
| W | weight of wet solid, kg (lbm) |
| W | height or width, m (ft); also power, W (hp); also mass dry cake, kg (lbm) |
| W | width of paddle, m (ft) |
| WS | mechanical shaft work done on surroundings, J/kg(ft · lbf/lbm) |
| Wp | shaft work delivered to pump, J/kg(ft · lbf/lbm) |
| (1 − Wƒ) | cumulative wt fraction |
| × | distance in x direction, m (ft) |
| × | mass fraction or mole fraction; also fraction remaining of original free moisture |
| ×A | mass fraction of A, mole fraction of A, dimensionless |
 | inert mole ratio, mol B/mol inert |
| xƒ | mole fraction of A in feed, dimensionless |
| xo | mole fraction of A in reject, dimensionless |
| xoM | mole fraction of minimum reject concentration, dimensionless |
| xBM | log mean mole fraction of inert or stagnant B given in Eq. (6.3-4) |
| (1 − ×A)*M | log mean inert mole fraction defined by Eq. (10.4-27) |
| (1 − ×A)iM | log mean inert mole fraction defined by Eq. (10.4-7) |
| X | particle size, m (ft); also parameter =  , dimensionless |
| X | parameter = Dt/×2, dimensionless; also free moisture, kg water/kg dry solid (lb water/lb dry solid) |
| y | distance in y direction, m (ft); also mole fraction |
| y' | mole fraction in permeate at interface, dimensionlesss |
| yA | mass fraction of A or mole fraction of A; also kg A/kg solution (lb A/lb solution) |
| yBM | log mean mole fraction of inert or stagnant B given in Eq. (7.2-11) |
| y+ | dimensionless number defined by Eq. (3.10-35) |
| yp | mole fraction of A in permeate, dimensionless |
| (y − yi)M | log mean driving force defined by Eq. (10.6-27) |
| (1 − yA)iM | log mean inert mole fraction defined by Eq. (10.4-6) |
| (y − y*)M | log mean driving force defined by Eq. (10.6-28) |
| Y | temperature ratio defined by Eq. (4.10-2), dimensionless |
| Y | fraction of unaccomplished change in Table 5.3-1 or Eq. (4.9-3) |
| Y | expansion correction factor defined in Eqs. (3.2-9) and (3.2-11) |
| z | distance in z direction, m (ft); also tower height, m (ft) |
| z | temperature range for 10:1 change in DT, °C (°F) |
| Z | height, m (ft); also temperature ratio in Eq. (4.9-2) |
| Greek letters | |
| α | correction factor = 1.0, turbulent flow and  , laminar flow |
| α | absorptivity, dimensionless; also flux ratio = 1 + NB/NA |
| α | thermal diffusivity = k/ρcp, m2/s (ft2/h, cm2/s) |
| α, αAB | relative volatility of A with respect to B, dimensionless |
| α | specific cake resistance, m/kg (ft/lbm) |
| α | angle, rad |
| α | kinetic-energy velocity correction factor, dimensionless |
| α* | ideal separation factor =  / , dimensionless |
| αG | gas absorptivity, dimensionless |
| αT | eddy thermal diffusivity, m2/s (ft2/h) |
| ß | concentration polarization, ratio of salt concentration at membrane surface to the salt concentration in bulk feed stream, dimensionless |
| ß | momentum velocity correction factor, dimensionless |
| ß | volumetric coefficient of expansion, 1/K (1/°R) |
| ß | ratio D2/D1 of diameters, dimensionless |
| γ | viscosity coefficient, N · sn'/m2 (lbm/ft · s2−n') |
| γ | ratio of heat capacities = cp/cν, dimensionless |
| Γ | flow rate, kg/s · m (lbm/h · ft) |
| Γ | concentration of property, amount of property/m3 |
| δ | molecular diffusivity, m2/s |
| δ | boundary-layer thickness, m (ft); also distance, m (ft) |
| δ | constant in Eq. (4.12-2), dimensionless |
| δƒ | film thickness for film theory, m (ft) |
| Δ | difference; also difference operating-point flow rate, kg/h(lbm/h) |
| ΔL | growth of crystals, mm |
| ΔTa | arithmetic temperature drop, K, °C(°F) |
| ΔT1m | log mean temperature driving force, K, °C(°F) |
| ΔH | enthalpy change, J/kg, kJ/kg, kJ/kg mol(btu/lbm, btu/lb mol) |
| ∇ | design criterion for sterilization, dimensionless |
| Δp | pressure drop, N/m2, Pa (lbf/ft2) |
| ε | roughness parameter, m (ft); or void fraction, dimensionless |
| ε | emissivity, dimensionless; also volume fraction, dimensionless |
| εM | mass eddy diffusivity m2/s (ft2/h, cm2/s) |
| ε | heat-exchanger effectiveness, dimensionless |
| ε | void fraction of packing, dimensionless |
| εG | gas emissivity, dimensionless |
| εt | momentum eddy diffusivity, m2/s (ft2/s) |
| εmf | void fraction at minimum fluidization, dimensionless |
| ηƒ | fin efficiency, dimensionless |
| ηt | turbulent eddy viscosity, Pa · s, kg/m · s (lbm/ft · s) |
| η | efficiency, dimensionless |
| θ | angle, rad |
| θ | parameter in Eq. (11.7-19) |
| θ | cut or fraction of feed permeated, dimensionless |
| θ* | fraction permeated up to a value of x = 1 − L/Lf, dimensionless |
| λ | wavelength, m (ft) |
| λ | latent heat, J/kg, kJ/kg (btu/lbm); also mean free path, m (ft) |
| λ+ | limiting ionic conductance in water of cation, (A/cm2)(V/cm) (g equiv/cm2) |
| λ− | limiting ionic conductance in water of anion, (A/cm2)(V/cm) (g equiv/cm2) |
| λAb | latent heat of A at normal boiling point, J/kg, kJ/kg mol (btu/lbm) |
| μ | viscosity, Pa · s, kg/m · s, N · s/m2 (lbm/ft · s, lbm/ft · h, cp) |
| μa | apparent viscosity, Pa · s, kg/m · s (lbm/ft · s) |
| ν | momentum diffusivity μ/ρ,m2/s (ft2/s, cm2/s) |
| ν | kinematic viscosity, centistokes |
| π1 | dimensionless group, dimensionless |
| π | osmotic pressure, Pa, N/m2 (lbf/ft2, atm) |
| ρ | crystal density, g/mm3 |
| ρ | density, kg/m3 (lbm/ft3); also reflectivity, dimensionless |
| σ | interfacial tension of liquid, dyn/cm |
| σ | constant, 5.676 × 10−8 W/m2 · K4 (0.1714 × 10−8 btu/h · ft2 · °R4); also collision diameter, Å |
| Σ | sigma value for centrifuge, m2 (ft2) |
| τzx | flux of x-directed momentum in z direction, (kg · m/s)/s · m2 or N/m2 (lbf/ft2, dyn/cm2) |
| τ | shear stress, N/m2 (lbf/ft2, dyn/cm2) |
| τ | holdup time, h |
| τ | tortuosity, dimensionless |
| φ | velocity potential, m2/s (ft2/h) |
| φ | angle, rad; also association parameter, dimensionless |
| φ | osmotic coefficient, dimensionless |
| φS | shape factor of particle, dimensionless |
| Ψz | flux of property, amount of property/s · m2 |
| ψ | correction factor, dimensionless |
| ψ | stream function, m2/s (ft2/h) |
| ψp | parameter defined by Eq. (14.3-13), dimensionless |
| ω | angular velocity, rad/s |
| ω | solid angle, sr |
| ΩD,AB | collision integral, dimensionless |
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