# EXAMPLES

Design Phase LCC calculations can be either for a single device or a whole system. Comparison of different systems is a typical consideration for the de­sign phase. In the tender phase, the supplier can use LCC calculations to show the improved economy of a single device. Figure 16.5 shows that the present value of investment and energy cost are the most significant. Typically, invest­ment in a heat recovery system reduces the total cost. Maintenance costs in this case are not significant. The proportion of disposal costs is also small, but could be a more significant factor in the future.

Different filter areas and types are compared in Fig. 16.6. Due to the short annual operating time in this case, the optimum area was rather small. In the sensitivity analysis the variation of the interest rate did not significantly influ­ence the ranking of the alternatives. An increase in operating time results in larger filter areas becoming more cost-effective. L. ife cycle costs (present value). EUR

TABLE 16.1 Example of a Spreadsheet for Calculating Energy and Maintenance Costs in the Procurement Process: a Liquid Cooling Unit

 Cooling power dissipa­tion per year, kW Operating Time at Partial Cooling Power, H/y Cooling Energy, MWh/y COP,* Quoted Estimate Of Supplier Electric Power, Quoted Estimate Of Supplier, KW Electric Energy, Quoted Estimate Of Supplier, MWh/y Energy Costs, Quoted Estimate Of Supplier, EUR/y Estimated maint­enance costs, quoted estimate of supplier, EUR/y I. 000 500 500 6.2 160 80 4 000 2 000 3.50 700 .5,9 340 120 6 000 — 3 000 250 750 5.2 580 145 7 250 — 4 000 200 800 4.7 850 170 8 500 5 000 50 250 3.9 1 280 64 3 200 Total 1 350 3 000 — — 579 28 950 5 200

 COP, Coefficient of Performance, is equal to cooling power per needed electric power.

Procurement Phase In LCC calculations the energy consumption is of prime importance. Table 16.1 gives an example of the energy calculations for consumption guarantee in the procurement process. In this case, the designer has estimated the power dissipation for a liquid cooling unit and the supplier defines the performance of his equipment by means of COP and energy consumption. The maintenance costs and guaranteed costs are given.

The tender with the lowest total costs (sum of investment, energy and maintenance costs) is the best and the supplier guarantees energy, and mainte­nance costs for, say, a three-year period. If the target costs are exceeded, the supplier pays a penalty; if the operating costs are lowered, the supplier and the customer share the bonus. TABLE A. I SI Basic Units

Term Name Symbol

 Length Meter M Mass Kilogram Kg Time Second S Electric current Ampere A Temperature Kelvin К Luminous intensity Candela Cd Amount of substance Mole Mol Magnitude Term Symbol K)-u Pi CO P 10-9 Nano N 10-6 Micro (j, m KVi Milli M 11)2 Cenri C 10-‘ Deci D I 10 Deca Da II)2 Hecto H 101 Kilo K 10" Mega M 10" G’ga G 1012 Tera T 10!S Peta P 10!B Exa E

TABLE A.3 Heat

 Quantity Name Symbol Dimension Heat, work, or energy Joule J N m Heat flow rate, power Wart W I s~’ Temperature Kelvin K K (thermodynamic unit) Temperature Celsius E °C (customary unit) Heat flow rare 4- W nr2 Thermal transmittance Transmittance V Wrrr2K-‘ Coefficient Thermal conductivity A W in“1 K-‘ TABLE A.4 Force and Pressure Quantity Name Symbol Dimension Force newton N Kg m s‘2 Pressure, stress pascal Pa N m‘2

 Quantity Name Symbol Dimension

 1 O’“4 rrr S"1 10-1 N s nr2 Kinematic viscosity stokes St

Dynamic viscosity poise P

TABLE A.6 Mass and Density Quantity Name Symbol Dimension

Mass kilogram M kg

Density—————- p kg m ’

Note: I metric ton = 10-’ k

UNIT CONVERSION FACTORS ■■I TABLE A.7 Electrical

 Quantity Name Symbol Dimension Potential Volt V W A-1 Resistance Ohm A V A‘1 Magnetomotive force ampere A A Charge Coulomb C A s Capacitance Farad F A s V‘1 Inductance Henry H V s A-‘ Frequency Hertz Hz S*1 ■ TABLE A.8 Light Quantity Name Symbol Dimensions Luminous flux . lumen lm Cd sr Illuminance Lux lx Lm m-2 TABLE A.9 Length (L) Km M mm Mile Foot Inch ftm Km 1 103 10S 6.214 X 10"1 3.281 X 103 — ———— M 10"5 1 103 6.214 X 10^4 3.281 3.937×10 10s Mm 10-1, 10~3 1 —— 3.281 x 10~3 3.937x 10-2 103 Mile 1.609 1.609 X 105 ———— 1 5.28 X 103 — ———— Foot 3.048 x 10-4 .3.048 x 10"1 3.048 x 102 ——————- 1 1.2X10 —————- Inch———- 2.54 xlO"2 2.54 x 10 ——————— — 1 2.54 X 104 Jim —— Io-fi U)"3 — — — 1

 M1 Ft2 In2 M2 1 1.076 x 10 1.55 x 1
 APPENDIX TABLE A. 11 Volume (V = L3)

 M3 L Ft3 Gallon M3 1 To’ 3.531 x 10 2.200 x 102 L 10-* 1 3.53 1 x 10“2 2.200 x 10-’ It * 2,832 x 10~2 2.832 x 10 1 6.229 Gallon 4.546 x 10~3 4.546 1.605 x 10-‘ 1

 Note: The U. S. gallon is 3.78.5 x 10 ‘ m3. TABLE A. 12 Mass (m)

 H G Lb Grains Kg I 10’ 2.205 K UH 1 —— 1.543 x 10 Lb 4.536 x 10-‘ 4..536 x 102 1 7.0 x 103

TABLE A. 13 Mass per Unit Length (m L~’)

 Kg nrr1 Lb ft-1 Kg nr’ 1 6.720 x 10-‘ Lb fr] 1.488 1 TABLE A. 14 Mass per Unit Area (m L~2) Kg nrr2 Lb ft-2 Kg nr2 1 2.048 x 10-‘ Lb fr2 4.882 1 TABLE A. IS Force (N = Kg m s-2) N (kg m sp -J) kN Ibf N 1 Io-3 2.248 x 10-‘ KN 103 1 2.248 x 102 Lb f 4.448 4.448x 10-* 1 Note: 1 kg f = 9.807 N = 2.205 Lb F.

■■ TABLE A. 16 Power (W = J r1)

W (J s_l) Horsepower

W 1 1.341 x 10-’

Horsepower 7.4.57xl02 1

TABLE A. 17 Quantity of Heat (W)

 M] KWh Btu Mj 1 2.778 x 10-‘ 9.478 x 102 KWh 3,6 1 3.412 x U>5 Btu 1.055 x IO—1 —— 1
 Note: 1 Kcal = 4.187KJ = 3.968 Btu and 1000 Kcal = 1 Thermic.

 TABLE A. 18 Specific Heat (c) Kj kg-1 Btu lb-‘ “F-1 Kj kg-‘ 1 2.388 x 10-’ Btu lb“1 °F 4.187 1

TABLE A. 19 Heat Flow Rate (\$)

 W Btu h-1 Refrigeration (Ton) W 1 3.412 2.843 x 10^ Btu h_l 2.9.31 X 101 1 8.333 x 10-’ Refrigeration (Ton) 3.517×10’ 1.200 X 104 1
 Note: 1 Kcal Lr1 = 1.163 W = 3.96 Btu h~’.

TABLE A.20 Heat Emission or Gain

W m-J Btu Ft~2 H-‘

W nr2 1 3.170 x 10-1

Btufr2H-1 3.155 1

 ■■ TABLE A.2I Heat Transfer Coefficient, U W m-2 K-‘ Btu ft-2 h-‘ °F-‘ W m-’ K-1 Btu fr2 h-‘ °F-‘ 1 1.761 X 10-‘ 5.678 1 ■■ TABLE A.22 Heat Flow per Unit Volume W m 3 Btu ft-3 h-‘ W (n ‘■ Btu ft-‘ hr1 1 9.662 x IQ-2 1.035 x 10 1 ■■ TABLE A.23 Heat Flow per Unit Length W M 1 kW m“1 Btu ft“1 h"1 Wm-1 1 UH 1.040 kWm-1 10’ 1 1.040 x10′ Btu fr1 h"1 9.615 x 10-‘ 9.615 x 10-4 1 ■■ TABLE A.24 Thermal Conductivity (a) W m-‘ K-‘ Btu in ft-2 h-‘ “F-1 W m-1 K-‘ Btu in ft"2 H~’ 0F" I 6.933 1 1.442x 10-‘ 1 ■■1 TABLE A.25 Mass Calorific Value, Latent Heat Kj kg-1 Btu lb-‘ Kj kg ‘ Btu lb*1 1 4.29.9×10-‘ 2.326 1 ■■ TABLE A.26 Volume Calorific Value
 MJ m"3 Btu ft-3

TABLE A.27 Pressure (p)

 KN trr2 (kPa) MN m-2 (MPa) B (bar) Lbf in*2 Atm Ft Head KN nr2 1 1 ()-;i 10~2 1.450 x 10~l 9.869 x 10 3.346 x KH (kPa) MN M ’ 10’’ 1 10 1.450 x 102 9.869 3.346 x I ‘■1 — (MPa) B (bar) 10’ Io-1 J 1.450 x 10 9.869 x 10-‘ 3.346 x 10 Lbf in—’ 6.895 6.895 x 10—1 6.895 x 1(H 1 6.805 x 10~2 2.307 Atm 1.013 x 102 1.013 xlO"1 1.013 1.470 x 10 1 3.390 x 10 Ft head 2.989 2.989 x IO“3 2.989 x lO“2 4.3.35 x 10-‘ 2.950 x IO-2 1

 Note: 1 kg f/cm2 = 98.07 kN/m2 (kPa) = 14.22 Ibf/m’.

TABLE A.28 Pressure (p)

 N m-2 (Pa) mb In Hg In H20 N m-2 (Pa) mb in Hg in H20 1 Io-2 102 1 3.386 xlO3 .3.386 x 10 2.491 xlO2 2.491 2.953 X IO"4 2.953 X IO 2 1 7.356 x 10-2 4.15 X IO"3 4.15 X 10*1 1.360 x 10 1 TABLE A.29 Density (p) Kg rrr3 (g L’1) kg L_l Lb ft’3 Lb gal-1 Kg nr’ Kg L_1 Lb fr’ lb gal-1 1 10-3 103 1 1.602 x 10 1.602 xlO-2 9.978 x 10 9.978 xlO-2 6.243 X 10-2 6.243 X 10 1 6.229 1.2 X IO-2 1.2 X 10 1.605 x 10-‘ 1 TABLE A.30 Specific Volume M3 kg —■ (L g -•) L kg-1 Ft3 Lb“1 Gal lb"1 M3 kg _1 L kg-1 Ft 5 lb-1 Gal lb-i 1 IO3 Io-3 1 6.243 x IO“2 6.243 x 10 1.002 xlO“2 1.002 x 10 1.602 X 10 1.602 X IO-2 1 1.605 x 10-‘ 9.978 X 10 9.978 X 10“2 6.229 1

 G m‘3 Grain ft-3 Oz gal G nr-’ grain fr3 Oz gal-1 1 2.229 6.236 x 10’ 4.370 x 10-‘ 1 2.725 x 10’ 1.604 x 10-4 3.670 x 10-4 1 TABLE A.32 Concentration, Mass per Unit Mass Kgkg-‘ G^r1 Grain lb-1 Kg kg“1 G kgr1 Grain lb"’ 1 Io-:} 1.429 x 10"4 10’ 1 1.429 x 10-‘ 7000 x 10’ 7.0 1

TABLE A.33 Mass Fluid Flow (qm)

 Ib h — Kg s- Kgh-

Kgs-1 1 3.6×10’ 7.937 x 10’

Kg h‘1 2.778 x 10‘4 1 2.205

Ibh-1 1.260×10′-‘ 4.536 x 10-1 1

TABLE A.34 Volumetric Flow of Fluids (qv)

 M3 s_l M3 H“1 Ft3 min-1 L s-1 Lh-‘ Gal min-1 Gal H*1 M * s-1 1 3.6 x 10’ 2.119 x 10’ 10‘ 3.6 x 10,; 1.320 x 104 7.919 x IO5 M* h ~1 2.778 x 10-4 1 5.886 x IQ-1 2.778 x 10-‘ 10’ 3.666 2.20 x 102 Ft3 min-1 4.719 x IO‘4 1.699 I 4.719 x Io-‘ 1.699 x 10’ 6.229 3.737 x 10j L s-1 10‘ ’ 3.6 2.119 1 3.6 x 10-’ 1.320 x 10 7.919 x 10- L h-1 2.778 x 10-7 10-’ 5.886 x 10-4 2.778 x 1Q-4 1 3.666 x IO” 2.220 x J O‘1 GaJ min‘1 7.577 x :i0-J 2.728 x 10-‘ 1.605 x IO‘4 7.577 x Io-2 2.728 x 102 1 6.0 x 10 Gal h-‘ 1.263 x 10-6 4.546 x 10-’ 2.676 x 10—’ 1.263 x Io-’ 4.546 1.667 x 10“2 1
 Fts- TABLE A.35 Velocity (v)

Ft min"

Ms“1 1 3.21 1.968 xlO2

Ft s-‘ 3.048 x 10“’ 1 6.0×10

Ftinin-‘ 5.080 x 10—’ 1.667 X 10-2 1

TABLE A.36 Pressure Drop per Unit Length

 Pa rrr1 Mm H20 m_l In HjO ftr1 In HjO 100 Ftr1 Ibf in-21 OOfr1 Pa nr’ Mm H20 nr 1 In H20 fr1 In H20 100 fr1 Ibf iir2100 fr1 1 9.807 8.172 X 102 8.172 2.262 x 102 1.020 x 10-‘ 1 8.333 X 10 8.333 X 10‘1 2.307 x 10 1.224 x 10-‘ 1.200 x 10-2 1 Io-2 2.768 x 10-‘ 1,224 x 10‘1 1.200 102 1 2.768 x 10 4.421 x 10 4.335 x 10"2 3.613 3.613 X 10-2 1

TABLE A.37 Absolute (Dynamic) Viscosity (/l)

 P (poise) = 10"1 N s Rrr1 CP (centipoise) Ibf s Ftr2 Ibf h ftr2 P (poise) 1 102 2.089 x 10-’ 5,802 x IO“7 CP Io-2 1 2.089 x 10-5 5.802 x IO"9 Ibf s fr2 4.788 x 102 4.788 x 104 1 2.778 x 10-4 Ibf h fr2 1.724 x 10 1.724 x 10* 3.600 x 103 1 TABLE A.38 Kinematic Viscosity (v) St (stokes) = 10-4 m2 s-1 CSt (centistokes) Ft2 s-1 Ft2h-‘ St 1 102 1.076 x 10-J 3.875 CSt Io-2 1 1.076 x 10-5 3.875 x 10— Ft2 S"1 9.290 x 102 9.290 x 104 1 3.600 x 105 Ft2 h"1 2.581 x IO*1 2.581 x 10 2.778 x 10-4 1 GREEK ALPHABET, AND ABBREVIATIONS TABLE A.39 Symbols Term Units Symbol A Absolute radiant heat flow Wnr2 % bs Absolute static pressure Pa Psa Absolute total pressure (stagnation pressure) Pa Pta Acceleration M s‘2 A Acceleration due to gravity M s-2 S Air, gas, vapor, or 1 fluid flow rate Mass flow volume flow Kg s-< M1 s 4m

 Term Units Symbol Air leakage factor M1 S ‘ Ni — P Air leakage rate Tit ’ S"’1 ‘■1, i Air temperature °C Air velocity M s’ V a Air velocity at time T M s‘1 T’. Allowable exposure time H AET Angle (plane) Radian (rad) or degree (°) O’ Angle (solid) Steradian (Sr) Ft Angular acceleration Rad s-2 Angular velocity Rad s-’ Ft) Approach velocity M S ’ Area M2 (O Area, actual (filter face) M2 (Of Area, duct cross section M2 ADc< Area (filter medium) M2 AIm Area (filter surface) M2 Atmospheric pressure Pa Pa B Basal metabolic rate W Ra­ BM Blade (fan) tangential velocity In s_l U Body heat storage W in-2 S Body height M H;> Body mass Kg MH Body surface area M2 >n Body surface area covered with % Anv Clothing Boundary layer insulation Clo Ia Breadth M B Bulge or sag of a duct or enclo­ M S Sure C Capacity (dust-holding) Kg kg“1 Qh Carbon dioxide production L C02 h-« CLv. ca. Cartesian coordinates —— X, y, z Celsius temperature °C 0 Chilling temperature °c 0* Coefficient of cuhical K“1 /3 Expansion

SYMBOLS, GREEK ALPHABET, AND ABBREVIATIONS TABLE A.39 (continued)

 Term Units Symbol Counting rate S-‘ N Clothing insulation M2 °C W-1 Clo Clothing mass variation Kg A MAn Clothing surface temperature °C T»clo Coefficient of thermal conductivity W m 1 °C A Component of air velocity along the X axis M s~’ V* Component of air velocity along the >’ Axis M s‘1 L Component of air velocity along the Z axis M s^1 V, Compressibility factor of a gas —— Z Conductive heat exchange Witt2 V Com) Convective heat exchange Wnr2 V ronv Convective heat exchange (±) From globe thermometer to Wnr2 Air Convective heat transfer coefficient Witt2 Kt1 H. Core temperature °C Ec Cross section area M2

D

 Darcy friction factor —— A Deflection M 8 Density Kg m-3 P Dew point temperature °C Orf Diameter ratio of a flow —— P Measuring device Diameter Outer —— D Inner —— D Differential pressure Pa p Distance to V m s-1 isovelocity M Line Draft rating % DR Drop of air jet from its leaving M Hv Center line Dry heat loss Wnr2 V Dry Dryness fraction, steam % X Duration, limited exposure H

 Term Units Symbol Dynamic pressure Pa Pj Dynamic viscosity N s m-2 E Effective area of a device M2 Effective clothing insulation M2 ° C W“1 Effective length M / Effective mechanical power Wm-2 W Effective radiant heat flow Wm-2 V r eff Effective radiating area of a Body M2 Ar Efficiency —— V Efficiency average —— Vav Emissivity of a surface or sensor —— Es Emissivity of black globe —— Energy J E Energy loss per unit mass J kg"’ Ay Enthalpy per Unir Mass J kg"’ H Entropy per unit mass J kg“’ K-i S Equivalent diameter of a rectangular duct M De Evaporative heat transfer coefficient W nr2 Pa -‘ He Exposed area M2 F Face loading (filter) Kg m2 —— Fan air power W P, Fan or pump efficiency —— Vr Fan equivalent orifice M2 Ofe Fan or pump head M, Pa H Fan or pump impeller power W P<, Fan or pump work per unit mass J kg"1 Y Fan pressure Pa Pf Fan or pump shaft power W Ps Flow coefficient of leakage M3 (s Pa")’1 C. Flow coefficient of subsonic flow in an orifice —— A Flow mass M 5 s*1 Qm Flow volumetric M 3 s_1

TABLE A.39 (continued)

 Term Units Symbol Fluid density upstream of a Kg nr3 Pu Measuring device Force N Ґ Frequency S’1 F G Globe temperature °C % Gross body mass loss Kg Am H Heat capacity JK-> C Fleat flux W

J

 Jet angle 0 Jet drop M HD Jet rise M Hr Jet spread 0 P Jet temperature °C Jet throw M L,

 Term Units Symbol K Kinematic viscosity M2 s 1 F Kinetic energy (mass) J kg”1 EK L Latent heat (mass) J kg’1 I Length M L Lewis relationship °C kPa‘1 LR Limit value for body heat gam W h m 2 Qlirn Or ioss Local skin temperature °C O*
 M

 Mach number —— Ma Mass Kg M Mass of dry air Kg MDa Mass flow rate (gas or fluid) Kg s-‘ Mass of water vapor Kg Maximum body heat storage W h nr- Qmvix Maximum evaporative heat transfer from skin WnT2 E Max Mean penetration (filter) —— P,„ Mean pressure drop Pa H’n, Mean skin temperature °C Mean velocity of flow in a conduit M s"1 Metabolic rate Wnr2 M (met! Molar mass Kg moH MM Momentum Kg m s‘1 P Motor input power W Pf. Motor output fan efficiency —— Vm Motor power output W Pm

N

 Natural wet bulb temperature °C ®wb Nominal volume air flow L ‘■/I n’JIIl O Operative temperature °C Flop Overall fan efficiency —— %

TABLE A.39 (continued)

 Term Units Symbol Overall hear transfer coefficient Overlap length (ductwork) W nr2 K-1 Rn U K P Partial pressure Pa Pv Particle production rate S-1 Qi> Particle size |j. m Dp Percentage dissatisfied % PD Periodic rime S T Permeability index for clothing —— Jcl„ Layer Plane angle Rad or 0 A, Я, 7 Plane radiant temperature K T,. Polytropic coefficient —— N Position of control setting % or ° S Power W P Predicted mean vote —— PMV Predicted percentage dissatisfied % PPD Pressure difference between Pa AP,. Points psetc. Pressure loss coefficient —— Pressure total Pa Pt Primary’ air flow rate M3 s_l or 1 s“1 or kg s*1 *?vp nip Q Quantity of hear J E
 R

 Radiation heat transfer coefficient W nr 2 K-4 Br Radiation temperature asymmetry °c: Radiative heat exchange Wnr2 Radiative heat exchange between globe thermometer and surroundings W m-2 VG Radiative heat transfer coefficient Radius W irr2K Br Inner M R Outer M R

 Term Units Symbol Radius of curvature M Rm Ratio of specific heat —— Y Capacities Relative fluid velocity to an M sr‘1 Tv Impeller Relative humidity —
 S

 Saturation pressure of a vapor KPa Pv, i Saturated water vapor pressure at skin temperature KPa Pa, Saturated water vapor pressure at wet bulb temperature KPa Pas. w Secondary air flow rate Mass flow Kg S-‘ <7«. Volume flow In1 s“1 Or 1 S"1 Shatt fan power efficiency — Va Solid angle Sr (I Sound power level DB Lu, Sound pressure level DB Lp Specific heat capacity J kg-’ K"’ C Specific heat capacity at constant pressure Jkg-lK-i CP Specific heat capacity at constant volume J kg"1 K-’ Spread of a jet M K Stagnation pressure Pa Pu Static gauge pressure Pa PS Stefan-Boltzmann constant Wnr2 K-4 (J STPD reduction factor —— Ґ Surface area Rn2 A, Surface heat transfer coefficient W rrr2 K-1 H Surface temperature °C Es Surface tension N m-2 A
 T

 Tangential component relating to a Ms1 Cu Fan, or pump impeller, or fluid Temperature difference K or °C* AT or A 0* Thermal diffusivity M 2 S-1 A

TABLE A.39 (continued)

 Term Units Symbol Thermodynamic (absolute) K* T* Temperature Thickness M T or D Thickness of dynamic boundary M 8 Layer Thickness of thermal boundary Laver M 8T Throw of a jet M L> Time S T Time constant, exponential S R Change Tip Reynolds number of a fan —— Impeller Tip speed of a fan impeller M s-1 U Torque N m T Total gas or air flow rate Mass flow Kg s"1 ?mr Volume flow M1 s-1; L s"1 ?vr Total gauge pressure Pa Pt Total heat transfer coefficient W rrr2 0C-‘ H Turbulence intensity % T 1 u U Universal gas constant I Kg“1 K-i R V Velocity M s“1 V Velocity components in the X. y, M s“1 U, V, w Z directions Velocity of sound M s‘1 C Volume M3 V Volume flow rare In’ s_1 or L s_l <1V W Water vapor latent heat of Win"2 ‘Pi. Vaporization Water vapor partial pressure KPa P„ Water vapor pressure at skin KPa Pa Temperature Wave length M A Weight N G Weighted sound pressure level DB A L PA DBB DB C LrC

 Term Units Symbol Wet bulb globe temperature °C Wetted duct perimeter M A’ Width M B Wind chill index W nr2 WCI Work .1 W Y Young’s modulus Nm"2 E
 *In normal work, "C is used in preference to the absolute temperature K. However, it is essential that K be used when working with the gas laws, radiation, and the coefficient of cubical expansion. The symbol for normal temperature is 0 followed by a suffix, while T always denotes absolute temperature.

 APPENDIX TABLE A.40 The Greek Alphabet

 Narne Symbols Alpha A A Beta B /3 Gamma R Y Delta A A Epsiion E F Zeta 7. L Eta H V Thкta 0 E Iota I L Kappa K K Lambda A A Mu M P Nu N Xi X X Omicron O O Pi N 7T Rho P P Sigma 2 Chi X X Psi Џ •P Omйga N U)

TABLE A.41 Symbols for Operations

 Symbol Definition K Is identical to * Does not equal = or « Is approximately equal to Is directly proportional to Tends to Is less than > Is greater than S Is less than or equal to A Is greater than or equal to Ax Finite increase in X Sx Variation in X Dx Total differential in X Grad Gradient Div Divergence Curl Curl V2 Laplacian 1 Factorial ( ) Parentheses Exp or Ex Exponential of X In a; Logarithm to base E of X Log,,) X Logarithm to base 10 of X [ J Brackets [1J One-dimensional  Three-dimensional V Summation

TABLE A.42 Abbreviations

 Meaning Abbreviation About Ca. Absolute Abs Alternating current A. c. Apparatus dew point Adp Atomic weight At. wr. Boiling point B. p. Boundary layer B. l. Centerline C. l. Compare Cf.

 Meaning Abbreviation Direct current D. c. Dry bulb temperature D. b.t. Electromotive force Cmf Equation Fq. For example E. g. High pressure H. P. Hydrogen ion concentration PH Fiquid (specified) I, (followed by the appropriate chemical symbol) Liquid oxygen LOX Liquefied petroleum gas LPG Melting point M. p. Molecular weight Mol. wt. Namely Viz. Note well N. b. Outside diameter OD Parts per million Ppm Per cent % Relative humidity RH Research and development R & D Specific Sp. That is I. e. Latin terms In the place cited (reference to an earlier quote) He. cit. In the work cited (a further reference to a book Op. cit. Previously mentioned, but this time in a different Passage) In the same place (a reference to a topic covered in a Ibid. Preceding reference) And another or and others Et al. (e. g., Burgess et al. rather than Burgess, Ellenbecker, and Treitman)

Mean molecular weight of dry air Ma = 28.969 kg kmol~J Mean molecular weight of water Mv = 18.02 kg kmol-1 Density of dry air at 101.325 kPa and 0 °C = 1.293 kg m-3 Density of water at 4 °C = 1000 kg m~3 Density of water at 20 °C = 998.23 kg m-3

Barometric pressure at standard temperature and pressure = 101.325 kPa Standard temperature and pressure (STP) = 0 °C at 101.325 kPa (also known as normal temperature and pressure)

Universal gas constant Rgas = MR = 8.3143 J mol 1 K 1 Volume of 1 mol of the permanent gases (at 101.325 kPa and 0 °C) =22.4136 m3 Characteristic gas constant for dry air Ra = 287 J kg-1 K~J Characteristic gas constant for steam Rv = 462 J kg-1 K_1 Mean specific heat of air at constant pressure cpa = 1005 J kg-1 K-1 Mean specific heat of air at constant volume Cva = 718 j kg-1 K-1 Mean specific heat of steam of air at constant pressure cpv = 4210 J kg’1 K_l Mean specific heat of steam at constant volume cvv = 1810 J kg-1 K-1 Adiabatic index for air at room temperature and pressure =1.4 Latent heat of steam at 0 °C = 2500 kj kg-1 K-1 Standard gravity = 9.806 65 m s~2

Velocity of sound in air at normal temperature and pressure c = 331.46 m s"1 Stefan’s Constant A = 5.67 x 10~8 W nr2 K 4

The following dimensionless numbers may be expressed in various forms due to the use of other relevant parameters.

Archimedes Number

Ar = = Buoyancy force

Fj pV2 Inertia force

The ratio A p/p can be replaced by AT/T. Ar relates the influence of ve­locity and temperature of a jet when discharged into an environment of a dif­ferent temperature. In some instances the Froude number, Galileo number, or Grashof number may replace the Archimedes number.

Colburn j-Factor

 Re Pr0 33 Colburn j-factor = —^un,, = St ■ Pr0’66 Used in heat-transfer applications.

Colburn j-factor = g^-A-Sc0,66 ’ Re Se

 ( ‘0.33 2 . 3 P gX, Used in mass-transfer applications. Condensation Number

Co = B

Eu = = Pressure force

Py1 Inertia force

Froude number

GL Gravity force See Archimedes number.

Graetz number

F7 _ ЧтС XI

Same as Peclet number except ^ considered (entrance region).

Grashof number

П___ j8gp2/3A0 _ (Buoyancy forces)(Inertia force)

— ■■ ■……………. ■ 7

T)~ (Viscous forces)“

Kn = ^ = Molecular mean free path

0. 5D Characteristic length

Used for particulate movement in a gas.

Lewis number

Le = — = —

Pr D

Where

K = = Thermal diffusivity Cp Mass diffusivity

Used for calculations involving the vaporization of a fluid.

Mach number

Ma = EtlLi = Y. nr JL. = Inertia force

Kl2 K [K Compressibility force

P 4p

Nusselt number

Nu = -&L = —

АЛ0 A

Ratio of temperature gradients, used for heat transfer taking place with fluid flow.

Peclet number

P _ VlCpP _ R p Heat convection A Heat conduction

Pe = Hi = Mass transfer D Mass diffusivity

Used in mass transfer applications involving aerosols.

Pr = Ј22 = E = Molecular diffusivity of momentum A K Molecular diffusivity of heat

Used for heat transfer with fluid flow.

Re = = — = Lnert’a f°rce

R v Viscous force

Relates the nature of the fluid flow in and around bodies. Richardson Number

 ( 80 Dz
 Dv
 / aj Dz
 + G
 ~g Ri = —
 Dv
 T1 Schmidt number   Sc = — = Momentum diffusivity D Mass diffusivity

Used for mass transfer = Pr number for mass transfer = Colburn number. Sherwood number

Sh = j3 _ §1 — (Mass transfer coefficient ) ( Length )

D D Diffusion coefficient

This is the Nusselt number for mass transfer.

St = Nu _ 4> _ H _ Wall heat-transfer rate

Re • Pr VpcAO V pc Heat transfer by convection

Used for convective heat transfer applications.

Stk = V^f Stopping distance 18 T]L Characteristic length

Where Cf = Cunningham’s factor. Used for particulate settling calcula­tions.