A1 The International System of Units, Fundamental Constants, and Conversion Factors Nitin Goel IntelTechnologyIndiaPvt.Ltd. TheInternationalsystemofunits(SI)isbasedonsevenbaseunits.Otherderivedunitscanberelatedto thesebaseunitsthroughgoverningequations.Thebaseunitswiththerecommendedsymbolsarelisted inTableA1.1.DerivedunitsofinterestinsolarengineeringaregiveninTableA1.2. Standardprefixes canbe usedintheSIsystem to designatemultiples ofthebasicunits and thereby conservespace.ThestandardprefixesarelistedinTableA1.3. Table A1.4 lists some physical constants that arefrequently used in solarengineering, together with theirvaluesintheSIsystemofunits. Conversion factors between the SI and English systems for commonly used quantities are given in TableA1.5. A1-1 q2007byTaylor&FrancisGroup,LLC A1-2 HandbookofEnergyEfficiencyandRenewableEnergy TABLEA1.1 TheSevenSIBaseUnits Quantity NameofUnit Symbol Length Meter m Mass Kilogram kg Time Second s Electriccurrent Ampere A Thermodynamictemperature Kelvin K Luminousintensity Candela cd Amountofasubstance Mole mol TABLEA1.2 SIDerivedUnits Quantity NameofUnit Symbol Acceleration Meterspersecondsquared m/s2 Area Squaremeters m2 Density Kilogrampercubicmeter kg/m3 Dynamicviscosity Newton-secondpersquaremeter Ns/m2 Force Newton(Z1kgm/s2) N Frequency Hertz Hz Kinematicviscosity Squaremeterpersecond m2/s Planeangle Radian rad Potentialdifference Volt V Power Watt(Z1J/s) W Pressure Pascal(Z1N/m2) Pa Radiantintensity Wattspersteradian W/sr Solidangle Steradian sr Specificheat Joulesperkilogram–Kelvin J/kgK Thermalconductivity Wattspermeter–Kelvin W/mK Velocity Meterspersecond m/s Volume Cubicmeter m3 Work,energy,heat Joule(Z1N/m) J TABLEA1.3 EnglishPrefixes Multiplier Symbol Prefix Multiplier MultiplierSymbol 1012 T Tera 103 M(thousand) 109 G Giga 106 MM(million) 106 m Mega 103 k Kilo 102 h Hecto 101 da Deka 10K1 d Deci 10K2 c Centi 10K3 m Milli 10K6 m Micro 10K9 n Nano 10K12 p Pico 10K15 f Femto 10K18 a Atto q2007byTaylor&FrancisGroup,LLC TheInternationalSystemofUnits,FundamentalConstants,andConversionFactors A1-3 TABLEA1.4 PhysicalConstantsinSIUnits Quantity Symbol Value Avogadroconstant N 6.022169!1026kmolK1 Boltzmannconstant k 1.380622!10K23J/K Firstradiationconstant CZ2phC2 3.741844!10K16Wm2 1 Gasconstant R 8.31434!103J/kmolK Planckconstant h 6.626196!10K34Js Secondradiationconstant CZhc/k 1.438833!10K2mK 2 Speedoflightinavacuum C 2.997925!108m/s Stefan–Boltzmannconstant s 5.66961!10K8W/m2K4 q2007byTaylor&FrancisGroup,LLC A1-4 HandbookofEnergyEfficiencyandRenewableEnergy TABLEA1.5 ConversionFactors PhysicalQuantity Symbol ConversionFactor Area A 1ft.2Z0.0929m2 1acreZ43,560ft.2Z4047m2 1hectareZ10,000m2 1squaremileZ640acres Density r 1lb /ft.3Z16.018kg/m3 m Heat,energy,orwork QorW lBtuZ1055.1J 1kWhZ3.6MJ 1ThermZ105.506MJ lcalZ4.186J 1ft.lbZ1.3558J f Force F 1lbZ4.448N f Heatflowrate,refrigeration q 1Btu/hZ0.2931W 1ton(refrigeration)Z3.517kW lBtu/sZ1055.1W Heatflux q/A 1Btu/hft.2Z3.1525W/m2 Heat-transfercoefficient h 1Btu/hft.2FZ5.678W/m2K Length L 1ft.Z0.3048m 1in.Z2.54cm 1miZ1.6093km Mass m 1lb Z0.4536kg m 1tonZ2240lbm 1tonne(metric)Z1000kg Massflowrate m_ 1lb /hZ0.000126kg/s m Power W_ 1hpZ745.7W 1kWZ3415Btu/h 1ft.lb/sZ1.3558W f 1Btu/hZ0.293W Pressure p 1lb/in.2(psi)Z6894.8Pa(N/m2) f 1in.HgZ3,386Pa 1atmZ101,325Pa(N/m2)Z14.696psi Radiation l 1langleyZ41,860J/m2 1langley/minZ697.4W/m2 Specificheatcapacity c 1Btu/lb 8FZ4187J/kgK m Internalenergyorenthalpy eorh 1Btu/lb Z2326.0J/kg m 1cal/gZ4184J/kg Temperature T T(8R)Z(9/5)T(K) T(8F)Z[T(8C)](9/5)C32 T(8F)Z[T(K)K273.15](9/5)C32 Thermalconductivity k 1Btu/hft.8FZ1.731W/mK Thermalresistance R 1h8F/BtuZ1.8958K/W th Velocity V 1ft./sZ0.3048m/s 1mi/hZ0.44703m/s Viscosity,dynamic m 1lb /ft.sZ1.488Ns/m2 m 1cPZ0.00100Ns/m2 Viscosity,kinematic n 1ft.2/sZ0.09029m2/s 1ft.2/hZ2.581!10K5m2/s Volume V 1ft.3Z0.02832m3Z28.32L 1barrelZ42gal(U.S.) 1gal(U.S.liq.)Z3.785L 1gal(U.K.)Z4.546L Volumetricflowrate Q_ 1ft.3/min(cfia)Z0.000472m3/s 1gal/min(GPM)Z0.0631l/s q2007byTaylor&FrancisGroup,LLC A2 Solar Radiation Data Nitin Goel IntelTechnologyIndiaPvt.Ltd. A2-1 q2007byTaylor&FrancisGroup,LLC A2-2 HandbookofEnergyEfficiencyandRenewableEnergy FIGUREA2.1 Descriptionofmethodforcalculatingtruesolartime,togetherwithaccompanyingmeteorological charts, for computing solar-altitude and azimuth angles, (a) Description of method; (b) chart, 258N latitude; (c)chart,308Nlatitude;(d)chart,358Nlatitude;(e)chart,408Nlatitude;(f)chart,458Nlatitude;(g)chart,508N latitude.Descriptionandchartsreproducedfromthe“SmithsonianMeteorologicalTables”withpermissionfromthe SmithsonianInstitute,Washington,D.C. q2007byTaylor&FrancisGroup,LLC SolarRadiationData A2-3 350 North 10 340 0 20 330 30 10 NW 320 20 40 NE 310 50 30 300 40 60 290 6 p.m. 5600 6 a.m. 70 We2s8t0 5 p.m.S4 p.mO.3 pL.m.2A p.m.R1 p.m. No78o00n 11 a.m.10 a.+mT2+3.2.2097° I°a.mM.8 a.mE.7 a.m. 8E0ast 80 +15° 260 70 +1+05°° 100 0° 60 250 −5° 110 50 −10° −15° 240 40 −20° 120 −23.27° 230 30 130 Decli- SW 220 20 140 SE nation Approx. dates +23° 27° June 22 210 10 150 +20° May 21, July 24 +15° May 1, Aug. 13 (b) 200 190 Sou0th 170 160 ++1 05°° AApprr.. 136, ,S Aeupgt. . 1208 0° Mar. 21, Sept. 23 350 North 10 − 5° Mar. 8, Oct. 6 340 0 20 − 10° Feb. 23, Oct. 20 330 30 − 15° Feb. 9, Nov. 3 10 − 20° Jan. 21, Nov. 22 NW 320 20 40 NE − 23° 27° Dec. 22 310 50 30 300 40 60 50 290 6 p.m. 60 6 a.m. 70 We2s8t0 5 p.m.4S p.mO.3 p.Lm.2A p.m.R1 p.m. No788o000n 11 a.m.10 a+.T2m+3+2..120597°° °Ia.m.M8 a.Em.7 a.m. 8E0ast 260 70 +1+05°° 100 0° 250 60 −5° 110 50 −10° −15° 240 40 −20° 120 −23.27° 230 30 130 SW 220 20 140 SE 10 210 150 200 0 160 (c) 190 South 170 FIGUREA2.1 (continued) q2007byTaylor&FrancisGroup,LLC A2-4 HandbookofEnergyEfficiencyandRenewableEnergy 350 North 10 340 0 20 330 30 10 320 40 NW 20 NE 310 50 30 3007 p.m. 4500 5 a.m.60 290 6 p.m. 60 6 a.m. 70 We22s68t00 5 p.m.S4 p.mO. 3 pL.m.2A p.m.R1 p.m.No787o000n 11 a.m.10 a+.T2m+3+2.+.120195°70 I°°a°.m.M8 a.mE.7 a.m. 18E00a0st +5° 60 0° 250 110 −5° 50 −10° 240 −15° 120 40 −20° −23.27° 230 30 130 SW 220 20 140SE Dnaetciolin- Approx. dates 210 10 150 ++2203°° 27° JMuanye 2 212, July 24 200 0 160 +15° May 1, Aug. 13 (d) 190 South 170 +10° Apr. 16, Aug. 28 + 5° Apr. 3, Sept. 10 350 North 10 0° Mar. 21, Sept. 23 340 0 20 − 5° Mar. 8, Oct. 6 330 30 − 10° Feb. 23, Oct. 20 10 − 15° Feb. 9, Nov. 3 NW 320 20 40 NE −− 2230°° 27° JDaenc.. 2212, Nov. 22 310 50 30 300 7 40 m. 60 p.m 50 5 a. . 290 6 p.m. 60 6 a.m. 70 We22s68t00 5 p.m.4S p.m.O3 p.mL. 2 Ap.m.1R p.m. No7887o0000n11 a.m.10 a.mT+2.+3+2.9210 7I5°a°°.m.M8 a.Em. 7 a.m. 18E00a0st +10° 60 +5° 250 0° 110 50 −5° 240 40 −−1105°° 120 −20° 230 30 −23.27° 130 SW 220 20 140 SE 10 210 150 200 0 160 (e) 190 South 170 FIGUREA2.1 (continued) q2007byTaylor&FrancisGroup,LLC SolarRadiationData A2-5 350 North 10 340 0 20 330 30 10 320 40 NW 20 NE 310 50 30 300 40 60 m. 290 7 p.m. 5600 m.5 a. 70 280 6 p.m. 70 m.6 a. 80 5 p.S 80 E 7 a. We2s6t0 m.4 p.mO.3 pL.m.2A p.m.1R p.m. N8o0on 11 a.m.10 aT.+m2+.3+2.1209I 57°a°°.m.M8 a.m. 1E0a0st 60 +10° 250 +5° 110 50 0° 240 40 −−150°° 120 −15° 230 30 −20° 130 −23.27° SW 20 SE Decli- 220 140 nation Approx. dates 10 +23° 27° June 22 210 150 +20° May 21, July 24 200 0 160 +15° May 1, Aug. 13 (f) 190 South 170 +10° Apr. 16, Aug. 28 + 5° Apr. 3, Sept. 10 0° Mar. 21, Sept. 23 350 North 10 340 0 20 − 5° Mar. 8, Oct. 6 330 30 − 10° Feb. 23, Oct. 20 10 − 15° Feb. 9, Nov. 3 320 40 − 20° Jan. 21, Nov. 22 NW 20 NE − 23° 27° Dec. 22 310 50 300 .m.p 8 3400 .m.a 4 60 m. 290 7 p.m 50 5 a. 70 . 60 m. 280 6 p.m. 70 m.6 a. 80 5 p. S 80 E 7 a. We2s62t050 m.4 p.m.O3 p.Lm.2A p.m.R1 p.m.N876o000on 11 a.m. 10T a.+m2.+3I+2.9+2 1017a5°.0°°mM°. 8 a.m. 1110E0a0st 50 +5° 0° 240 40 −5° 120 −10° 230 30 −−1250°° 130 SW 220 20 −23.27° 140 SE 10 210 150 200 0 160 (g) 190 South 170 FIGUREA2.1 (continued) q2007byTaylor&FrancisGroup,LLC A2-6 HandbookofEnergyEfficiencyandRenewableEnergy TABLEA2.1 SolarIrradianceforDifferentAirMasses Wavelength AirMass;aZ0.66;bZ0.085a 0 1 4 7 10 0.290 482.0 0.0 0.0 0.0 0.0 0.295 584.0 0.0 0.0 0.0 0.0 0.300 514.0 4.1 0.0 0.0 0.0 0.305 603.0 11.4 0.0 0.0 0.0 0.310 689.0 30.5 0.0 0.0 0.0 0.315 764.0 79.4 0.1 0.0 0.0 0.320 830.0 202.6 2.9 0.0 0.0 0.325 975.0 269.5 5.7 0.1 0.0 0.330 1059.0 331.6 10.2 0.3 0.0 0.335 1081.0 383.4 17.1 0.8 0.0 0.340 1074.0 431.3 24.9 1.8 0.1 0.345 1069.0 449.2 33.3 2.5 0.2 0.350 1093.0 480.5 40.8 3.5 0.3 0.355 1083.0 498.0 48.4 4.7 0.5 0.360 1068.0 513.7 57.2 6.4 0.7 0.365 1132.0 561.3 68.4 8.3 1.0 0.370 1181.0 603.5 80.5 10.7 1.4 0.375 1157.0 609.4 89.0 13.0 1.9 0.380 1120.0 608.0 97.2 15.6 2.5 0.385 1098.0 609.8 104.5 17.9 3.1 0.390 1098.0 623.9 114.5 21.0 3.9 0.395 1189.0 691.2 135.8 26.7 5.2 0.400 1429.0 849.9 178.8 37.6 7.9 0.405 1644.0 992.8 218.7 48.2 10.6 0.410 1751.0 1073.7 247.5 57.1 13.2 0.415 1774.0 1104.5 266.5 64.3 15.5 0.420 1747.0 1104.3 278.9 70.4 17.8 0.425 1693.0 1086.5 287.2 78.9 20.1 0.430 1639.0 1067.9 295.4 81.7 22.6 0.435 1663.0 1100.1 318.4 92.2 26.7 0.440 1810.0 1215.5 368.2 111.5 33.8 0.445 1922.0 1310.4 415.3 131.6 41.7 0.450 2006.0 1388.4 460.3 152.6 50.6 0.455 2057.0 1434.8 486.9 165.2 56.1 0.460 2066.0 1452.2 504.4 175.2 60.8 0.465 2048.0 1450.7 515.7 183.3 65.1 0.470 2033.0 1451.2 527.9 192.0 69.8 0.475 2044.0 1470.3 547.3 203.7 75.8 0.480 2074.0 1503.4 572.6 218.1 83.1 0.485 1976.0 1443.3 562.4 219.2 85.4 0.490 1950.0 1435.2 572.2 228.2 91.0 0.495 1960.0 1453.6 592.9 241.9 98.7 0.500 1942.0 1451.2 605.6 252.7 105.5 0.505 1920.0 1440.1 607.6 256.4 108.2 0.510 1882.0 1416.8 604.4 257.8 110.0 0.515 1833.0 1384.9 597.3 257.6 111.1 0.520 1833.0 1390.0 606.1 264.3 115.2 0.525 1852.0 1409.5 621.3 273.9 120.7 0.530 1842.0 1406.9 626.9 279.4 124.5 0.535 1818.0 1393.6 627.7 282.8 127.4 0.540 1783.0 1371.7 624.5 284.4 129.5 0.545 1754.0 1354.2 623.2 286.8 132.0 0.550 1725.0 1336.6 621.7 289.2 134.5 0.555 1720.0 1335.7 625.5 293.0 137.3 (continued) q2007byTaylor&FrancisGroup,LLC