Tài liệu UNITS AND CONVERSION FACTORS E.J. ROSCHKE PROPULSION DIVISION JET PROPULSION LABORATORY doc

UNITS AND CONVERSION FACTORS E.J ROSCHKE PROPULSION DIVISION JET PROPULSION LABORATORY NOTE: Many years ago I was given a copy of this document, prepared in handwriting, some time in the early 1960’s I did not know the author, E.J Roschke I have found it to be such a useful reference that I decided to have an electronic version prepared Recently, I spoke with Dr Roschke, now retired from the Jet Propulsion Laboratory to learn of the document’s origin In the early 1960’s a group of research engineers, largely having backgrounds in mechanical engineering, were engaged in the new field of electric propulsion They experienced practical annoyances with the mingling of units from mechanical engineering, electrical engineering and physics That situation motivated Dr Roschke to assemble this material Although I have carefully checked the values given here, it is quite possible that some typographical errors remain I will appreciate learning any corrections that should be made F.E.C Culick Mechanical Engineering California Institute of Technology October 2001 UNITS AND CONVERSION FACTORS Table of Contents Section I II III IV V VI VII Page References Decimal Multiples and Submultiples Description of Units Mechanical, Electric, Magnetic Equivalent Units mksq System Dimensions of esu and emu Electric and Magnetic Quantities Dimensions and Units for Physical Quantities — mksq System A Mechanical B Thermal C Electric and Magnetic Conversion of mksq Units to Gaussian Units Conversion Factors A Plane Angle B Solid Angle C Length D Area E Volume F Mass G Density H Time I Speed J Force K Pressure L Energy, Work, Heat M Specific Energy N Specific Energy Per Unit Temp O Power P Heat Flux Q Heat Transfer Coefficient R Thermal Conductivity S Absolute Viscosity T Kinematic Viscosity AA Electric Charge BB Electric Current CC Electric Potential DD Electric Resistance EE Electric Resistivity FF Capacitance GG Inductance 4 5 6,7 7 8-23 8 9 10 10 11 11 11 12 13 14 15 16 17 17 18 19 19 20 20 20 21 21 21 22 Table of Contents – continued Section VIII IX X XI XII Page HH Magnetix Flux I I Magnetomotive Force J J Magnetic Field Strength, B KK Magnetic Vector, H Electromagnetic Constants of Free Space Electromagnetic Constants of Materials Some Important Dimensional Constants Some Important Dimensionless Groups The Perfect Gas Law A Nomenclature, Definitions and Equations B Values of Universal Gas Constant, Boltzmann’s Constant and Avogadro’s Number in Different Units 22 22 23 23 24 24 25 26 27,28 27 28 References used in compiling these charts and tables are listed below in the order of “most usage” Halliday, D & Resnick, R., Physics – For Students of Science and Engineering, John Wiley, New York, 1960 Forsythe, W.E., Smithsonian Physical Tables, 9th Revised Edition, Publ 4169, Smithsonian Institution, Washington, D.C., 1954 Scott, R.B., Cryogenic Engineering, D Van Nostrand Inc., Princeton, New Jersey, 1959 Hall, N.A., Thermodynamics of Fluid Flow, Second Printing with revisions, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1956 Gray, D.E (coordinating editor), American Institute of Physics Handbook, McGraw Hill Inc., New York, 1957 Additional Note on Use of Conversion Tables, Part VII Multiply units appearing in left-hand column by appropriate numerical factor to obtain units appearing in upper row I DECIMAL MULTIPLES AND SUB-MULTIPLES Name tera giga mega kilo hecto deca II Symbol Equivalent Name Symbol Equivalent T G M k h − 1012 109 106 103 102 10 deci centi milli micro nano pico d c m µ n p 10-1 10-2 10-3 10-6 10-9 10-12 DESCRIPTION OF UNITS MECHANICAL UNITS Quantity cgs mks Length Mass Time Force Work, Energy Power Dynamic Viscosity Kinematic Viscosity centimeter gram second dyne erg − poise stoke meter kilogram second newton joule watt − − ELECTRIC AND MAGNETIC UNITS The esu and emu unit systems are cgs systems esu denotes “electrostatic unit”, sometimes given prefix “stat”, e.g statcoulomb emu denotes “electromagnetic unit”, sometimes given prefix “ab”, e.g abcoulomb Some emu units have special names: Quantity emu line maxwell gauss gilbert oersted Magnetic Flux, φ Magnetic Field Strength, B Magnetomotive Force, F Magnetic Vector, H mksq weber weber/m2 amp-turn amp-turn/m mksq DIMENSIONS Length Mass Time Current Charge III L M T Q/T Q EQUIVALENT UNITS mksq SYSTEM newton volt amp joule weber farad henry ohm watt kilogram-meter/(second)2 newton-meter/coulomb coulomb/second newton-meter = volt-second coulomb/volt weber/amp volt/amp joule/sec = = = = = = = = = coulomb-volt IV DIMENSIONS OF esu AND emu ELECTRIC AND MAGNETIC QUANTITIES The fundamental dimensions in both systems are M, L, T cgs units used esu emu Symbol MxLyTz Quantity MxLyTz x y z x y z Charge Field Intensity Elec Displacement Charge Density Current Density Elec Potential Total Current Mag Field Strength Mag Vector Permittivity Permeability Conductivity Capacitance Inductance Resistance q E D ρ j V I B H ε µ σ C L R ½ ½ ½ ½ ½ ½ ½ ½ ½ 0 0 0 -½ -½ − -½ ½ − 2 ½ -2 -1 -1 -1 -1 -1 -1 -2 -1 -2 -2 -1 ½ ½ ½ ½ ½ ½ ½ ½ ½ 0 0 0 *c = velocity of light (free space) in cm/sec ≈ × 1010 Thus: emu of charge = 2.998 × 1010 esu of charge or abcoulomb = 2.998 × 1010 statcoulomb ½ − ½ − − 3 2 ½ -½ -½ -2 -2 -1 1 0 -2 -1 -2 -1 -1 -1 2 -1 emu∗ esu c 1/c c c c 1/c c 1/c c c2 1/c2 c2 c2 1/c2 1/c2 V DIMENSIONS AND UNITS FOR PHYSICAL QUANTITIES mksq SYSTEM A MECHANICAL QUANTITIES Quantity Acceleration Angle Angular Accleration Angular Momentum Angular Velocity Area Energy Force Frequency Gravitational Field Strength Length Mass Mass Density Momentum Power Pressure Time Torque Velocity Viscosity (Dynamic) Viscosity (Kinematic) Volume Wave Length Work Dimensions LT-2 T-2 ML2T-1 T-1 L2 ML2T-2 MLT-2 T-1 LT-2 L M ML-3 MLT-1 ML2T-3 ML-1T-2 T ML2T-2 LT-1 ML-1T-1 L2T-1 L3 L ML2T-2 Derived Units meter/sec2 radian radian/sec2 kgm-meter2/sec radian/sec meter2 joule newton cycle/sec newton/kgm meter kilogram kgm/meter2 kgm-meter/sec watt newton/meter2 second newton/meter meter/sec kgm/meter-sec meter2/sec meter3 meter joule B THERMAL QUANTITIES* Quantity Dimensions ML2T-2 ML2T-2θ-1 L2T-2θ-1 ML2T-2 L2T-2θ-1 θ MLT-3θ-1 L2T-1 MT-3θ-1 Enthalpy Entropy Gas Constant Internal Energy Specific Heat Temperature Thermal Conductivity Thermal Diffusivity Heat Transfer Coefficient Derived Units joule joule/K° joule/kgm- K° joule joule/kgm-K° K° watt/meter- K° meter2/sec watt/meter2- K° *The dimension of temperature is θ; the unit is K° C ELECTRIC AND MAGNETIC QUANTITIES Quantity Charge Field Intensity Elec Displacement Charge Density Current Density Elec Potential Total Current Mag Field Strength Mag Vector Permittivity Permeability Conductivity Capacitance Inductance Resistance Symbol Dimensions Derived Units q E D ρ j V I B H ε µ σ C L R Q MLT-2Q-1 L-2Q L-3Q L-2T-1Q ML2T-2Q-1 T-1Q MT-1Q-1 L-1T-1Q M-1L-3T2Q2 MLQ-2 M-1L-3TQ2 M-1L-2T2Q2 ML2Q-2 ML2T-1Q-2 coulomb volt/meter coulomb/meter2 coulomb/meter2 amp/meter2 volt coulomb/sec weber/meter2 amp(turn)/meter farad/meter henry/meter 1/ohm-meter farad henry ohm VI CONVERSION OF mksq UNITS TO GAUSSIAN UNITS Quantity q E D ρ j V I B H µ ε σ C L R Conversion Factor × Gaussian Unit* mksq Unit coulomb volt/meter coulomb/meter2 coulomb/meter3 amp/meter2 volt coulomb/sec : = amp weber/meter2 amp-turn/meter farad/meter henry/meter 1/ohm-meter farad henry ohm 10-1 c 106/c 4π × 10-5 c 10-7 c 10-5 108/c 10-1 104 4π × 10-3 4π × 10-11c2 107/4π 10-11 10-9c2 109 109 = = = = = = = = = = = = = = = statcoulomb statvolt/cm lines/cm2 statcoulomb/cm3 abamp/cm2 statvolt abamp gauss oersted   1/abohm-cm statfarad abhenry abohm (esu) (esu) (esu) (esu) (emu) (esu) (emu) (emu) (emu) (esu) (emu) (emu) (esu) (emu) (emu) *c = vel of light (free space) in cm/sec ≈ × 1010 Use of table: coulomb = 10-1 (3 × 1010) statcoulomb = × 109 statcoulomb VII CONVERSION FACTORS NOTE: mksq UNITS ARE CAPITALIZED USE OF TABLES: EXAMPLE degree = 2.778 × 10-3 revolutions so, 16.7o = 16.7 × 2.778 × 10-3 revolutions A PLANE ANGLE o degree minute second RADIAN revolution = = = = = ′ ′′ RADIAN rev 1.667 × 10-2 2.778 × 10-4 57.30 360 60 1.667 × 10-2 3438 2.16 × 104 3600 60 2.063 × 105 1.296 × 105 1.745 × 10-2 2.909 × 10-4 4.848 × 10-4 6.283 2.778 × 10-3 4.630 × 10-5 7.716 × 10-7 0.1592 1 revolution = π RADIANS = 360o , 1o = 60′ = 3600′′ B SOLID ANGLE sphere = π steradians = 12.57 steradians meter – kgf = 9.807 joule, watt-sec = joule = nt-meter, cm-dyne = erg Some conversions used in spectroscopy: eV = 8065.7 cm-1 cm-1 = 0.000124 eV eV ≈ 6000°K At 300°K, kT ≈ 0.05 eV NOTES FOR TABLE L: The electron volt is the kinetic energy an electron gains from being accelerated through the potential difference of one volt in an electric field The units enclosed by heavy lines are not properly energy units; they arise from the relativistic mass-energy equivalent formula E = mc2 M SPECIFIC ENERGY cal gm JOULE KGM 1 calorie per gram = erg gm 4.186 × 107 4.186 × 103 Btu ft - lbf hp - hr lbm lbm lb m 1.800 1.400 × 103 7.072 × 10-4 3.346 × 10-5 1.690 × 10-11 2.389 × 10-8 10 4.299 × 10-8 2.389 × 10-4 104 4.299 × 10-4 0.3346 1.690 × 10-7 Btu per pound (mass)= 0.5557 2.326 × 107 2.326 × 103 777.9 3.929 × 10-4 foot-pound per pound (mass)= 7.142 × 10-4 2.990 × 104 2.990 1.285 × 10-3 5.051 × 10-7 horsepower-hour per pound (mass)= 1.414 × 103 5.920 × 1010 5.920 × 106 2.545 1.980 × 106 erg per gram = JOULE per KILOGRAM = -4 (SEE NOTE FOR TABLE N) 14 N SPECIFIC ENERGY PER UNIT TEMPERATURE cal gm°C erg gm°C JOULE KGM °K Btu lb m °F ft - lb f lb m ° F hp - hr lb m ° F = 4.186 × 107 4.186 × 103 1.000 777.9 3.929 × 10-4 = 2.389 × 10-8 10-4 2.388 × 10-8 1.859 × 10-5 9.376 × 10-12 JOULE per KGM per DEGREE K = 2.389 × 10-4 104 2.388 × 10-4 0.1859 9.376 × 10-8 Btu per lb (mass) per degree F 1.000 4.187 × 107 4.187 × 103 777.9 3.929 × 10-4 foot-lb per lb (mass) per degree F = 1.286 × 10-3 5.382 × 104 5.382 1.285 × 10-3 5.051 × 10-7 horsepower-hour per lb (mass) per degree F= 2.546 × 103 1.066 × 1011 1.066 × 107 2.545 1.980 × 106 1 calorie per gram per degree C erg per gram per degree C = NOTE FOR TABLES M & N: The engineering units enclosed within the heavy lines have been properly related to the pound mass rather than the pound force because these specific thermal quantities depend on unit mass and have nothing to with weight However, in engineering practice it is customary to relate energy and energy per degree to weight Thus we speak of Btu/lb, ft-lb/lb and hp-hr/lb of weight The conversion factors given in Tables M & N are equally valid for this purpose if the local acceleration of gravity if the earth standard value of g = 32.174 ft/sec2 = 9.80665 meter/sec2 This is true because the pound-force and the pound-mass are numerically equal at standard gravity It should be realized that relating specific quantities to weight, rather than mass, involves a change of concept because weight and mass are not dimensional equivalents The relation between units of mass and weight is not a relation between the concepts of mass and weight The units are related by lbf = 32.174 lbm ft/sec2 15 O POWER Btu hr 12.97 0.2161 3.929 × 10-4 7.000 × 10-2 2.930 × 10-4 0.2930 3600 = 2.778 × 10-4 4.669 × 104 777.9 1.414 252.0 1.055 1.055 × 103 7.713 × 10-2 2.142 × 10-5 1.667 × 10-2 3.030 × 10-5 5.399 × 10-3 2.260 × 10-5 2.260 × 10-2 4.628 1.286 × 10-3 60 1.818 × 10-3 0.3239 1.356 × 10-3 1.356 = foot-pound per minute ft - lb sec = British thermal unit per second ft - lb 1 British thermal unit per hour Btu sec hp cal sec kw WATT foot-pound per second = horsepower = 2545 0.7069 3.3 × 104 550 178.2 0.7457 745.7 calorie per second 0.3950 1.852 × 102 3.087 5.613 × 10-3 4.186 × 10-3 4.186 = 14.29 kilowatt = 3413 0.9481 4.425 × 104 737.6 1.341 238.9 1000 WATT = 3.413 9.481 × 10-4 44.25 0.7376 1.341 × 10-3 0.2389 0.001 16 P HEAT FLUX* kilocal cal sec - cm hr − m M Btu watt WATT in 2 hp Btu hr- ft sec- in ft 3.600 × 104 4.185 × 104 27.00 1.327 × 104 2.560 × 10-2 5.212 kilocalorie per hour per meter2 = 2.778 × 10-5 1.163 7.500 × 10-4 0.3687 7.112 × 10-7 1.448 × 10-4 WATT per METER2 = 2.390 × 10-5 0.8602 6.452 × 10-4 0.3171 6.117 × 10-7 1.246 × 10-4 watt per inch2 = 3.704 × 10-2 1.333 1550 491.5 9.481 × 10-4 0.1931 British thermal unit per hour per foot2 = 7.535 × 10-5 2.713 3.153 2.035 × 10-3 1.929 × 10-6 3.928 × 10-4 British thermal unit per sec per inch2 = 39.06 1.406 × 106 1.635 × 106 1.055 × 103 5.184 × 105 203.6 horsepower per foot2 0.1918 6.905 8027 5.179 × 102 *Also power per unit area 2.546 × 103 4.911 × 10-3 1 calorie per sec per centimeter2 = = Q HEAT TRANSFER COEFFICIENT, h cal WATT sec− cm °C watt Btu hr - ft °F M °K in °C calorie per sec per centimeter2 - ºC = 4.185 × 104 27.00 7.372 × 103 WATT per METER2 per DEG KELVIN = 2.390 × 10-5 6.452 × 10-4 0.1762 watt per inch2 per deg Centigrade = 1550 273.1 Btu per hour per per foot2 - ºF = 3.704 × 10-2 1.356 × 10-4 5.675 = 70.31 3.663 × 10-3 1.899 × 103 = 0.3452 Btu per sec per inch2 - ºF horsepower per foot2 - ºF 2.943 × 106 1.445 × 104 17 9.322 5.184 × 105 2.546 × 103 Btu sec - in °F 1.422 × 10-2 3.398 × 10-7 5.267 × 10-4 1.929 × 10-6 hp ft °F 2.895 6.922 × 10-5 0.1073 3.928 × 10-4 203.6 4.911 × 10-3 R R THERMAL CONDUCTIVITY, k cal WATTS watts Btu Btu hp sec− cm °C METER ° K in ° C hr - ft °F sec - in ° F ft ° F calorie per sec per centimeter-deg C = 418.5 10.63 241.9 5.600 × 10-3 9.503 × 10-2 WATT per METER per DEG KELVIN = 2.390 × 10-3 2.540 × 10-2 0.5781 1.338 × 10-5 2.271 × 10-4 watt per inch per deg Centigrade 39.37 22.76 = 9.407 × 10-2 5.269 × 10-4 8.939 × 10-3 1.730 4.394 × 10-2 = 4.134 × 10-3 2.315 × 10-3 3.929 × 10-4 = 1.786 × 102 7.474 × 104 1.898 × 103 4.320 × 104 16.97 = 10.52 4403 111.8 2546 5.894 × 10-2 1 Btu per hour per foot-deg F Btu per sec per inch-deg F horsepower per foot-deg F 18 S ABSOLUTE OR DYNAMIC VISCOSITY, µ centipoise kgm f −sec poise meter lb − sec ft KGM M−SEC 10-3 lb m ft − sec centipoise = 10-2 1.020 × 10-4 2.089 × 10-5 poise = 100 1.020 × 10-2 2.089 × 10-3 0.100 6.720 × 10-2 kg (force) – sec per meter2 = 9.807 × 103 98.07 0.2048 9.807 6.590 lb (force) – sec per foot = 4.788 × 104 4.788 × 102 4.882 47.88 32.174 103 10 0.1020 2.089 × 10-2 0.6720 1.488 × 103 14.88 0.1518 3.108 × 10-2 1.488 1 KILOGRAM per METER-SEC = lb (mass) per foot – sec = 6.720 × 10-4 NOTE FOR TABLE S: The absolute viscosity µ is properly expressed in force units according to its definition In heat transfer and fluid mechanics it is usually expressed in massequivalent units to avoid the use of a conversion factor in Reynolds Number Mass units have been used in the portion of the table enclosed in heavy lines The proper force units for µ in the mksq system are NEWTON-SEC per METER2; they are seldom used The poise is the cgs force unit and is defined by dyne - second poise = centimeter T KINEMATIC VISCOSITY, ν = µ⁄ρ centistoke stoke METER2/SEC ft2/sec centistoke = 10-2 10-6 1.076 × 10-5 stoke = 100 10-4 1.076 × 10-3 METER2/SEC = 106 104 10.76 = 9.290 × 104 929.0 9.290 × 10-2 ft /sec stoke = centimeter2/sec 19 AA ELECTRIC CHARGE abcoul amp-hr COUL faraday statcoul 2.778 × 10-3 10 1.036 × 10-4 2.998 × 1010 abcoulomb (1 emu) = ampere-hour = 360 3600 3.730 × 10-2 1.079 × 1013 COULOMB = 0.100 2.778 × 10-4 1.036 × 10-5 2.998 × 109 faraday = 9.652 × 103 26.81 9.652 × 104 2.893 × 1014 statcoulomb (1 esu) = 3.336 × 10-11 9.266 × 10-14 3.336 × 10-10 3.456 × 10-15 1 electronic charge = 1.602 × 10-19 coulombs = (1.602 × 10-19)(2.998 × 109) statcoulomb = 4.8 × 10-10 esu BB ELECTRIC CURRENT abamp AMP statamp abampere (1 emu) = 10 2.998 × 1010 AMPERE = 0.100 2.998 × 109 statampere (1 esu) = 3.336 × 10-11 3.336 × 10-10 CC ELECTRIC POTENTIAL, ELECTROMOTIVE FORCE abv VOLT statv abvolt (1 emu) = 10-8 3.336 × 10-11 VOLT = 108 3.336 × 10-3 statvolt (1 esu) = 2.998 × 1010 299.8 20 DD ELECTRIC RESISTANCE abohm OHM statohm abohm (1 emu) = 10-9 1.113 × 10-21 OHM = 109 1.113 × 10-12 statohm (1 esu) = 8.987 × 1020 8.987 × 1011 EE ELECTRIC RESISTIVITY, RECIPROCAL CONDUCTIVITY abohm-cm abohm-centimeter (1 emu) = ohm-cm OHM-M statohm-cm 10-9 10-11 1.113 × 10-21 ohm-circ mil/ft 6.015 × 10-3 ohm-centimeter = 109 0.0100 1.113 × 10-12 6.015 × 106 OHM-METER = 1011 100 1.113 × 10-10 6.015 × 108 statohm-centimeter (1 esu) = 8.987 × 1020 8.987 × 1011 8.987 × 109 5.406 × 1018 ohm-circular mil per foot 166.2 1.662 × 10-7 1.662 × 10-9 1.850 × 10-19 = FF CAPACITANCE abf FARAD µf statf abfarad (1 emu) = 109 1015 8.987 × 1020 FARAD = 10-9 106 8.987 × 1011 microfarad = 10-15 10-6 8.987 × 105 statfarad (1 esu) = 1.113 × 10-21 1.113 × 10-12 1.113 ì 10-6 21 GG INDUCTANCE abhenry HENRY àh stathenry 10-9 0.001 1.113 × 10-21 abhenry (1 emu) = HENRY = 109 106 1.113 × 10-12 microhenry = 103 10-6 1.113 × 10-18 stathenry (1 esu) = 8.987 × 1020 8.987 × 1011 8.987 × 1017 HH MAGNETIC FLUX maxwell kiloline WEBER 0.001 10-8 maxwell (1 line or emu) = kiloline = 1000 10-5 WEBER = 108 105 1 esu = 2.998 webers II MAGNETOMOTIVE FORCE abamp-turn AMP-TURN gilbert abamp-turn = 10 12.57 AMP-TURN = 0.100 1.257 gilbert = 7.958 × 10-2 0.7958 1 pragilbert = π amp-turn esu = 2.655 × 10-11 amp-turn 22 JJ MAGNETIC FIELD STRENGTH, B kiloline gauss in WEBER METER milligauss gamma 6.452 × 10-2 10-4 1000 105 155.0 1.550 × 10-2 1.550 × 105 1.550 × 107 104 64.52 107 109 = 10-3 6.452 × 10-6 10-7 100 = 10-5 6.452 × 10-8 10-9 10-2 oersted gauss (line per cm2) = kiloline per in2 = WEBER PER METER2 = milligauss gamma esu = 2.998 × 106 weber/meter2 104 gauss = tesla KK MAGNETIC VECTOR, H amp − turn AMP − TURN amp − turn cm cm METER in 10 1000 25.40 12.57 0.100 100 2.54 1.257 10-3 10-2 2.540 × 10-2 1.257 × 10-2 3.937 × 10-2 0.3937 39.37 0.4947 7.958 × 10-2 0.7958 79.58 2.021 abamp − turn abampere-turn per centimeter = ampere-turn per centimeter = AMPERE-TURN PER METER = ampere-turn per inch = oersted = oersted = gilbert/cm esu = 2.655 × 10-9 amp-turn/meter praoersted = π amp-turn/meter 23 VIII ELECTROMAGNETIC CONSTANTS OF FREE SPACE Maxwell was able to show analytically that the constant appearing in a wave equation derived for free space (perfect vacuum), for the case ρ e = σ c = , was the square of the velocity of propagation of electromagnetic waves in free space The experiments of Hertz verified that this velocity was the velocity of light in free space and that c2 = µ0ε0 where µ0 is the permeability of free space and ε0 is the permittivity of free space This equation is true for any system of units; in the mksq system c µ0 ε0 IX = = = 2.997925 × 108 meter/sec 1.256637 × 10-6 henry/meter 8.85416 × 10-12 farad/meter ELECTROMAGNETIC CONSTANTS OF MATERIALS The permeability and permittivity of materials are usually given relative to the values of free space Relative permeability µ κm = µ0 Magnetic Susceptibility Relative permittivity ε κe = ε0 (Dielectric constant) Electric Susceptibility κm = + χm κe = + χe When looking up values of electromagnetic constants of materials care must be taken to be sure what values are specified, i.e µ, κm or χm and ε, κe or χe The usual values given are κe and χm κm is a number near unity and may be greater or less than unity; χm may be positive or negative but is small compared to unity κe is always greater than unity and may be significantly larger than unity; χe is always positive and may be large compared to unity: κm ≶ 1, κm ~ κc ≥ χm χe ≥ ≶ 0, χ m > 24 X SOME IMPORTANT DIMENSIONAL CONSTANTS (mksq units) Name Speed of light Universal Gravitational Const Avogadro’s Number Universal Gas Constant Standard Volume of Ideal Gas Planck’s Constant Boltzmann’s Constant Mechanical Equiv of Heat Triple Point of Water Ice Point of Water Maximum Density of Water (at 3.98°C, atm) Permeability of Free Space Permittivity of Free Space Electronic Charge Electronic Rest Mass Proton Rest Mass Neutron Rest Mass Mass-Energy Relation Magnetic Moment of Electron Compton Wavelength of Electron First Bohr Orbit Radius in Hydrogen Atom Stefan-Boltzmann Const Symbol Computational Value Best Experimental Value 3.00 × 108 meter/sec 6.67 × 10-11 nt-m2/kgm2 6.02 × 1023 /mole 8.32 joule/mole °K 2.24 × 10-2 meter3 6.63 × 10-34 joule/sec 1.38 × 10-23 joule/°K 4.19 joule/cal 273.16 °K 273.16 °K gm/cm3 (2.997930 ± 0.000003) × 108 (6.673 ± 0.003) × 10-11 (6.02486 ± 0.00016) × 1023 8.31696 ± 0.00034 (2.24207 ± 0.00006) × 10-2 (6.62517 ± 0.00023) × 10-34 (1.38044 ± 0.00007) × 10-23 4.1855 ± 0.0004 273.16 °K exactly 273.16 °K ± 0.0002 0.999973 λc a0 1.26 × 10-6 henry/meter 8.85 × 10-12 farad/meter 1.60 × 10-19 coulomb 9.11 × 10-31 kgm 1.67 × 10-27 kgm 1.67 × 10-27 kgm 8.99 × 1016 meter2/sec2 9.28 × 10-32 joule-m2/weber 2.43 × 10-12 meter 5.29 × 10-11 meter 4π × 10-7 exactly (8.85415 ± 0.00002) × 10-12 (1.60206 ± 0.00003) × 10-19 (9.1083 ± 0.0003) × 10-31 (1.67239 ± 0.00004) × 10-27 (1.67470 ± 0.00004) × 10-27 (8.98758 ± 0.00003) × 1016 (9.2837 ± 0.0002) × 10-32 (2.42626 ± 0.00002) × 10-12 (5.29172 ± 0.00002) × 10-11 σ 5.67 × 10-8 joule/sec(°K)4 meter2 (5.6687 ± 0.0019) × 10-8 c G N0 R h k J Σ0 µ0 ε0 e me mp mn c = E/m 25 XI SOME IMPORTANT DIMENSIONLESS GROUPS Name Group Field of Use Biot Euler Fourier (Bi) = hL/k (Eu) = p/ρV2 (Fo) = ατ/L2 Conduction heat transfer Fluid mechanics Conduction heat transfer Froude Graetz Grashof Hartmann (Fr) = V Lg & (Grz) = w cp/kL (Grf) = L3 ρ2gβ∆t/µ2 2 1/ (Ha) = ( σ c B0 L / µ ) Fluid mechanics Heat transfer, free convection Heat transfer, free convection MHD Knudsen Lewis Mach Nusselt Péclet Prandtl Reynolds Magnetic Reynolds Schmidt Stanton Weber (Kn) = λ/L (Le) = (Sc)/(Pr) = α/D (M) = V/a (Nu) = hL/k (Pe) = (Re)(Pr) (Pr) = µcp/k (Re) = VLρ/µ (Re)m = µσc VL (Sc) = µ/ρD (St) = h/cp Vρ (We) = ρV2L/σ Fluid mech., rarified gas flow Conv heat & mass transfer High speed flow Convection heat transfer Convection heat transfer Convection heat transfer Fluid mech., heat transfer MHD Conv heat & mass transfer Convection heat transfer Fluid mechanics, free surface (N) = (Ha)2/(Re) (S) = (Ha)2/(Re)(Re)m MHD MHD Symbols: B0 – Applied mag field D – Diffusion coefficient L – Characteristic length V – Fluid velocity a – Acoustic velocity g – Gravity h – Heat transfer coefficient k – Thermal conductivity p – Static pressure ρ – Density λ - Mean free path (molecular) ∆t – Temperature difference & w - Mass rate of flow cp – Specific heat (const pressure) α - Thermal diffusivity β - Thermal expansion coefficient σ - Surface tension σc – Electric conductivity µ - Viscosity or magnetic permeability τ - Time interval 26 XII THE PERFECT GAS LAW A NOMENCLATURE, DEFINITIONS, AND EQUATIONS In the following discussion the elementary particle under consideration is the molecule Care must be taken to use consistent units, especially to make the proper distinction between mass and weight units The units of the gas constant must be consistent with those used for density or specific volume NOMENCLATURE: Symbol ρ k m n p υ υN M N N0 R R0 T V W Definition in cgs Units Density in grams per cm3 Boltzmann’s Constant in ergs/molecule K° Mass of molecule in grams Particle Number Density in molecules/cm3 Pressure in dynes/ cm2 Specific Volume in cm3 per gram Specific Molar Volume in cm3 /gm-mole Molecular Weight in gm/gm-mole Number of moles Avogadro’s Number, no of molecules per gm-mole Gas Constant in ergs/gm K° Universal Gas Constant in ergs/gm-mole K° Absolute Temperature, degrees Kelvin Total Volume in cubic centimeters “Weight” of Gas in grams Avogadro’s Law: All ideal gases at the same temperature and pressure have the same specific molar volume At STP (0°C, atm), υN = 22.4 liters/gm-mole = 22400 cm3/gmmole = 359 ft3/lb-mole At the same temperature and pressure all ideal gases contain the same number of molecules per unit volume Definition of the mole: The gm-mole is the amount of an ideal gas which will occupy the same volume as 32 gm of oxygen at STP; the pound-mole is similarly related to 32 lb of oxygen The weight of a mole of gas is numerically equal to the molecular weight of the gas Forms of the Perfect Gas Law: pυ = RT pυN =R0T Useful Relations: ρ = nm m = M/N0 R = R0/M R0 = N0 k p = ρRT = nkT pV = WRT = N R0T N0 = nυN υN = V/N N = W/M 27 B VALUES OF UNIVERSAL GAS CONSTANT, BOLTZMANN’S CONSTANT AND AVOGADRO’S NUMBER IN DIFFERENT UNITS Units ft-lb/lb-mole R° ft-lb/lb-mole K° ft-lb/lb-mole R° Btu/lb-mole R° ft3 atm/lb-mole R° ft3 atm/lb-mole K° R0 1544 2779 3.407 1.987 0.729 1.315 Units ergs/molecule K° JOULES/MOLECULE K° ft-lb/molecule R° Btu/molecule R° Units cal/gm-mole K° cm3 atm/gm-mole K° liter atm/gm-mole K° ergs/gm-mole K° JOULES/KGM-MOLE K° psia ft3/lb-mole R° k 1.38 × 10-16 1.38 × 10-23 5.655 × 10-24 7.267 × 10-27 R0 1.987 82.06 0.08206 8.313 × 107 8313 10.71 Units N0 molecules/gm-mole 6.023 × 1023 MOLECULES/KGM-MOLE 6.023 × 1026 molecules/lb-mole 2.73 × 1026 atm = 1.013 × 106 dynes/cm2 erg = dyne-cm erg = 10-7 joule ft-lb = 1.356 107 ergs 28 ... and emu Electric and Magnetic Quantities Dimensions and Units for Physical Quantities — mksq System A Mechanical B Thermal C Electric and Magnetic Conversion of mksq Units to Gaussian Units Conversion. .. UNITS AND CONVERSION FACTORS Table of Contents Section I II III IV V VI VII Page References Decimal Multiples and Submultiples Description of Units Mechanical, Electric, Magnetic Equivalent Units. .. have an electronic version prepared Recently, I spoke with Dr Roschke, now retired from the Jet Propulsion Laboratory to learn of the document’s origin In the early 1960’s a group of research engineers,