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Mathamatical & Physical Formulae

pine1

Nick Pine **< nick_pine@verizon.net>** wrote:

cfm = 16.6Asqrt(HdT) (airflow up a chimney) E = NTU/(NTU+1) (counterflow heat exch. efficiency) E = (Tco-Tci)/(Thi-Tci) (heat exchanger I/O temps) E = (Thi-Tho)/(Thi-Tci) (heat exchanger I/O temps) NTU = AU/Cmin (number of heat transfer units) Pa = 29.921/(1+0.62198/w) (vapor pressure in air) Pe = VIF (power in electical load) Pe/A = 0.00509Vw^3 (wind power density) Ph = (Ti-To)U (Ohm's law for heatflow) Ph = cfmdT (heat power carried by airstream) Ph = 100A(Ps-Pa) (heat loss from uncovered pool) Ph = 0.1714x10^-8Ae(Th^4-Tc^4) (radiation heat loss) Ps = exp(17.863-9621/(460+T)) (vapor pressure at 100% RH) R = Rv/A = d/(kA) (thermal resistance of a wall) RH = 100Pa/Pw (relative humidity) Rv = d/k (US "R-value") Q = C(Th-Tc) (stored heat energy) Trc = Tc+460 (absolute temp of cold object) Trdp = Trc/(1+Trcln(RH/100)/9621) (absolute dew point) Trh = Th+460 (absolute temp of hot object) T(t) = Tf+(Tf-Ti)exp(-t/RC) (temp after t hours in Tf air) Trwb = 9621/(22.47+ln(100Pa+Tra-Twrb)) (abs. wet bulb temp, iterate) U = kA/d = A/Rv (thermal conductance of a wall) Definitions: A area (ft^2) C heat capacitance (Btu/F) cfm airflow (ft^3/min) Cmin heat capacity flow rate (Btu/h-F) d thickness (inches) dT temp diff (F) e emissivity of surface (shiny => 0, dull => 1) E heat exchanger efficiency F power factor (DC =>1) H height difference (ft) I current (A) k thermal conductivity (Btu-in/h-F-ft^2) P power (watts) Pa water vapor pressure in air ("Hg) Pe heat power (Btu/h) Pw water vapor pressure near pool ("Hg) Q heat energy (Btu) R thermal resistance (F-h/Btu) RC time constant (hours) RH relative humidity (%) Rv US "R-value" in ft^2-F-h/Btu t time delay (hours) T temperature (F) Tc cold temperature (F) Tci cold fluid temp entering heat exchanger (F) Tco cold fluid temp leaving heat exchanger (F) Trdp absolute dew point (R) Tf final temp (F) Thi hot fluid temp entering heat exchanger (F) Tho hot fluid temp leaving heat exchanger (F) Ti initial temp (F) Trc cold absolute temperature (R) Th hot temperature (F) Trh hot absolute temperature (R) Trwb absolute wet bulb temp (R) U thermal conductance (Btu/h-F) V voltage (V) Vw windspeed (mph) w humidity ratio (#water/#dry air) Conductivities (k, in Btu-in/h-F-ft^2): still air, 0.18; Styrofoam, 0.2; water, 4.2 (for downward heatflow); ice, 1.1; concrete, 5; soil, 5-15; glass, 7; steel, 314; copper, 2724 R-values (Rv in Btu/h-F-ft^2): slow-moving air, 2/3; single-pane window, 1; double-pane, 2; double foil with large airspaces & downward heatflow, 10 Densities (lb/ft^3): air, 0.075; ice, 57.2; water, 62.3; concrete, 150; steel, 450 Specific heats by volume (Btu/F-ft^3): air, 0.02; concrete, 25; ice, 28; steel, 59; water, 63 Latent heats (Btu/lb): ice melts, 144; water evaporates, 970 Metric equivalents: 1 m = 3.281 ft 1 m/s = 2.24 mph 1 kg = 2.205 lb 1 kJ = 0.948 Btu 1 kWh = 3412 Btu 1 kW = 1.341 HP 1 L = 0.264 gal Rvm = Rv/5.68 (W/m^2C) deg C = 5/9(deg F-32) Long-term average Phila weather: Jan July daily min temp 22.8 67.2 F 24-h avg 30.4 76.7 F daily max 37.9 86.1 F sun on S wall 1000 820 Btu/ft^2 E/W " 425 1030 Btu/ft^2 N " 190 580 Btu/ft^2 horiz surf 620 1890 Btu/ft^2 humidity ratio w 0.0025 0.0133 windspeed 10.3 8.0 mph Betz (wind efficiency) limit: 0.593