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NEBB Fundamental Formulas Approved NEBB

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NEBB Fundamental Formulas Approved NEBB NEBB Fundamental Formulas A = Area (ft²) IP, (m²) SI M = Mass (lb) IP, (kg) SI ACH = Air Changes per Hour ma = Mixed Air Ak = Effective Area m = meter (metre) AV = Average m³/s = Volumetric Flow: Cubic Meters Per Second BHP = Brake Horsepower (IP) HP NLA = No Load Amperage BP = Brake Power (SI) kW NPSHA = Net Positive Suction Head Available Btu = British Thermal Unit oa = Outside Air Btu/h = Btuh = BTUH = BTU/Hour % oa = % of Outside Air ℄ = Center Distance (used in belt formula) Ω = Ohm °C = Degrees Celsius, °C P = Pressure C = Friction Loss Coefficient (For Duct Fittings) Pa = Atmospheric Pressure CCF = 100 Cubic Feet Pab = Absolute Pressure (Atmospheric Pressure + Gauge Pressure) CFM = Volumetric Flow: Cubic Feet Per Minute Pa = Pascals, Pressure SI Cp = Specific Heat π = 3.14 Cv = Flow Constant (IP) PD = Sheave Pitch Diameter ρ = Density (lb/ft³) IP, (kg/m³) SI P℄ = Pressure at Pump Centerline d = Diameter (in.) IP, (mm) SI ppm = parts per million Δ = Difference or Change (Final - Initial) psi = Pounds Per Square Inch dimp = Impeller Diameter psia = Pounds Per Square Inch Absolute E = Volts psig = Pounds Per Square Inch Gauge Eff = Efficiency Pvp = Absolute Vapor Pressure EP = Pump Efficiency Q (flow) = Volumetric Fluid Flow Rate: (i.e. CFM, GPM, m³/s, l/s, etc.) °F = Degrees Fahrenheit, °F Q (heat) = Heat Flow Rate (BTU/Hour) IP, (W or kW) SI f = Friction Factor °R = °Rankin = Degrees Rankin, °R FLA = Full Load Amps r = Radius (in) IP, (mm) SI fpm = Feet per Minute (fpm) % ra = % of Return Air ft = Foot R = Resistance g = Acceleration of Gravity ra = Return Air gal = Gallons rad = Radians GPM = Gallons Per Minute (GPM) RH = Relative Humidity h = Enthalpy (BTU/lb dry air) IP, (kJ/kg dry air) SI RPM = Revolutions Per Minute H = Head (in wc, ft wc, psi) IP, (Pa, kPa) SI Rvalue = Thermal Resistance Hg = Mercury s = second hma = Mixed Air Enthalpy SHR = Sensible Heat Ratio hoa = Outside Air Enthalpy SME = Sash Movement Effect Performance Rating (SME-XX yyy) HP = Horsepower SP = Static Pressure hr = Hour Sp Gr = Specific Gravity (for water use 1.00) hra = Return Air Enthalpy T = Temperature HT = Height (in) IP, (mm) SI Ta = Absolute Temperature (460˚ + T) or °R I = Amps Tma = Mixed Air Temperature J = Joules Toa = Outside Air Temperature K = Kelvin, K TP = Total Pressure Kv = Flow constant (SI) Tra = Return Air Temperature kg = Kilogram TS = Tip Speed (fpm) IP, (m/s) SI kJ = Kilojoule U = Heat Transfer Coefficient kPa = Kilopascal µ = viscosity, dynamic kW = Kilowatt = 1000 Watts V = Velocity l = Liter (Litre) VP = Velocity Pressure l/s = Volumetric Flow: Liters Per Second W = Watt lb = Pounds WD = Width (in) IP, (mm) SI lm = Lumens wg = wc = water gauge = water column ln = natural log WHP = Water Horsepower (IP) LG = Length (in) IP, (mm) SI WP = Water Power (SI) lx = Lux ω = Humidity Ratio (lb or grains of water/lb of dry air) (g H2O/kg dry air) Approved NEBB - May 11, 2016 Page 1 of 8 Version 1.2 NEBB Fundamental Formulas Airflow & Velocity Equations Q = V × A Q = V x A TP(in wg) = VP + SP TP(Pa) = VP + SP V( std air) = 4005 × √VP V(std air) = √(1.66 × VP) VP VP V = 1096 × √( ) V = 1.414 × √( ) 휌 휌 Q × 60 Q × 3600 ACH = ACH = (LG x WD x HT ) (LG x WD x HT ) d 2 d 2 π × ( ) 2 π × ( ) 2 2 (π × r ) 2 (π × r ) Area = = Area = = Round 144 144 Round 1,000,000 1,000,000 (HT × WD) (HT × WD) Area = Area( ) = (square/rectangular) 144 square/rectangular 1,000,000 2 HT HT 2 ((HT x WD) + (π × ( ) )) ((HT × WD) + (π × ( ) )) 2 2 Area = AreaOval = Oval 144 1,000,000 Air Temperature Equations ℉ = (1.8 × ℃) + 32° ℃ = (℉ − 32) ÷ 1.8 °R = (℉ + 460) K = (℃ + 273) Tma = (%oa × Toa) + (%ra × Tra) hma = (%oa × hoa) + (%ra × hra) (Tra − Tma) (hra − hma) %oa = ( ) × 100 %oa = ( ) × 100 (Tra − Toa) (hra − hoa) Heat Transfer Calculations l Qtotal = 4.5 × CFM × ∆h Qtotal = 1.2 × ⁄s × ∆h l Qsensible = 60 × Cp × ρ × CFM × ∆Tair Qsensible = Cp × ρ × ⁄s × ∆Tair l Qsensible = 1.08 × CFM × ∆Tair Qsensible = 1.23 × ⁄s × ∆Tair Qlatent = 0.69 × CFM × ∆휔gr of H2O ⁄lb dry air l Qlatent = 3.0 × ⁄s × ∆휔g H2O ⁄kg dry air Qlatent = 4840 × CFM × ∆휔lb of H2O ⁄lb dry air SHR = Qsensible ÷ Qtotal Qtotal = Qlatent + Qsensible Fan Equations 3 l⁄ m ⁄ rad⁄ CFM2 RPM2 s2 ss s2 = = 3 = CFM1 RPM1 l⁄ m ⁄ rad⁄ s1 s1 s1 2 2 3 2 l⁄ m ⁄ P2 CFM2 P2 s2 s2 = ( ) = ( ) = ( 3 ) P1 CFM1 P1 l⁄ m ⁄ s1 s1 3 3 3 3 l⁄ m ⁄ BHP2 CFM2 kW2 s2 s2 = ( ) = ( ) = ( 3 ) BHP1 CFM1 kW1 l⁄ m ⁄ s1 s1 (π × d × rpm) (π × d × rpm) Tip Speed = TP = Tip Speed = TP = 12 60 Approved NEBB - May 11, 2016 Page 2 of 8 Version 1.2 NEBB Fundamental Formulas Sheave Equations PDmotor RPMfan PDmotor RPMfan = ( ) × RPMmotor = PDfan RPMmotor PDfan 2 (PDlarge − PDsmall) Fan Belt Length = (℄ × 2) + (1.57 × (PD + PD )) + ( ) large small 4 × ℄ Electrical Equations Power(Watts) = E × I 1 kW = 1000 Watts I = E ÷ Ω Ω = E ÷ I 1 HP = 746 Watts 1 Watt = 3.413 Btu/hr Power Equations (E × I × PF × Eff) (E × I × PF) BHP = kW = 1 phase 746 1 phase 1000 PF=Power Factor PF=Power Factor (E × I × PF × Eff × 1.732) (E × I × PF × 1.732) BHP = kW = 3 phase 746 3 phase 1000 PF=Power Factor = 0.8 & Eff=0.9; if not given (I − (NLA × 0.5) BHP = HP × ( actual ) (FLA − (NLA × 0.5) (FLAtag × Etag) FLAactual = Eactual (CFM × TP × SpGr) Fan HP = (6356 × Eff) Resistance Series Circuit: total resistance: Ω = Rtotal Parallel Circuit: total resistance: Ω = Rtotal 1 1 1 1 RTotalSeries = R1 + R2 + R3 + ⋯ + Rn = + + ⋯ + RTotalParallel R1 R2 Rn Eprimary × Iprimary = Esecondary × Isecondary Voltage Drop = I × RTotal Conversions kilowatts (Kw) Btu / hr 413 horsepower (HP) Btu / hr 2545 joules Btu / hr 0.000948 kilogram calories Btu / hr 3.968 tons of cooling (chiller) Btu / hr 12000 tons of cooling (cooling tower) Btu / hr 15000 gallons U.S. (water) pounds U.S. (lb.) 8.33 millimeters inches U.S. 25.4 centimeters inches U.S. 2.54 bar pounds per square inch (PSI) 14.5 inches of water pounds per square inch (PSI) 0.036 inches of Mercury (Hg) pounds per square inch (PSI) 0.491 Approved NEBB - May 11, 2016 Page 3 of 8 Version 1.2 NEBB Fundamental Formulas Hydronic Pump Equations 3 l⁄ m ⁄ rad⁄ GPM2 RPM2 s2 s2 s2 = = 3 = GPM1 RPM1 l⁄ m ⁄ rad⁄ s1 s1 s1 3 d m ⁄ GPM2 imp2 s2 dimp2 = 3 = GPM1 dimp1 m ⁄ dimp1 s1 3 2 2 2 m ⁄ rad H2 GPM2 H2 h ⁄s = ( ) = ( 2 ) = ( 2 ) 3 rad H1 GPM1 H1 m ⁄ ⁄s h1 1 3 3 3 3 m ⁄ rad⁄ BHP2 GPM2 BP2 s2 s2 = ( ) = ( 3 ) = ( ) BHP1 GPM1 BP1 m ⁄ rad⁄ s1 s1 3 (GPM × H푓푡 푤푔 × SpGr) m ⁄ WHP = WPkW = 9.81 × s × Hm × SpGr 3960 l ( ⁄s × HPa × SpGr) WP = SpGr = 1.0, unless given, EP use 0.7 if not given W 1002 (GPM × H푓푡 푤푔 × SpGr) BHP = ( ) WP 3960 × EP BP = EP SpGr = 1.0, unless given, EP use 0.7 if not given (WHP × 100) (WP × 100) EP = EP = in % BHP in % BP Hydronic Calculations P 3 3 P √ 2 m m √ 2 Coil ∆P: GPM2 = GPM1 × ( ) Coil ∆P: ⁄h = ⁄h × ( ) P1 2 1 P1 GPM m3 Cv = ⁄h SpGr Kv = √( ) SpGr ∆Ppsi √( ) ∆PBar ∆Ppsi 3 ∆PBar GPM = C × √( ) m ⁄ = K × √( ) v SpGr h v SpGr SpGr = 1.0, unless given, EP use 0.7 if not given SpGr = 1.0, unless given, EP use 0.7 if not given 2 3 2 GPM m ⁄ ∆Ppsi = SpGr × ( ) h Cv ∆PBar = SpGr × ( ) Kv SpGr = 1.0, unless given, EP use 0.7 if not given SpGr = 1.0, unless given, EP use 0.7 if not given V2 NPSHA = P ± P + ( ) − P − P a s 2g vp f Heat Transfer Calculations 푄퐵푡푢 = 퐶푝 × ρ × 퐺푃푀 × ∆푇℉ 푄푘푊 = 퐶푝 × ρ × 푙푠 × ∆푇℃ 푚3 푄푘푊 = 4190 × ⁄푠 × ∆푇℃ 푄퐵푡푢 = 500 × 퐺푃푀 × ∆푇℉ 푙 푄푊 = 4190 × ⁄푠 × ∆푇℃ Boiler Calculations Input Btu Fire Rate = Output Btu = Input Btu × %Eff Fuel Btu gal⁄ hr $Cost Boiler Operating Cost = Fire Rate × hrs Burned × ⁄ gal⁄ Btu = lb of water × 500 × ∆Twater hr gal Approved NEBB - May 11, 2016 Page 4 of 8 Version 1.2 NEBB Fundamental Formulas Metric Equivalents acceleration m/s2 meters per second squared 1m/s2 = 3.281 ft/sec2 m3/s cubic meters per second 1 m3/s = 2118.88 cfm airflow volumetric l/s liters per second 1 l/s = 2.12 cfm flow rate m3/hr cubic meters per hour 1 m3/hr = 0.589 cfm m2 square meter 1 m2 = 10.764 ft2 area mm2 square millimeters 1 mm2 = 0.0016 in2 atmospheric kPa kiloPascals 101.325 kPa = 29.92 in Hg = 14.696 psi pressure Bar Barometers 1 Bar = 100kPa = 29.53 in Hg = 14.504 psi m meter 1 m = 3.281 ft distance. length, or m meter 1 m = 39.370 in distance mm millimeter 1 mm = 0.039 in lx Lux 1 lx = 0.093 fc lighting intensity lm/m2 Lumens/square meter 1lm/m2 = 0.0931 fc kPa kiloPascals = 1000 Pascals 1 kPa = 0.296 in Hg = 0.145 psi pressure Pa Pascals 1 Pa = 0.004 in wg temperature °C degrees Celsius °C = (°F - 32) / 1.8 velocity m/s meters per second 1 m/s = 196.9 fpm volume m3 cubic meters 1 m3 = 35.31 ft3 1 Btu = Energy required to heat 1 lb of H2O from 39 ˚F to 40 ˚F 1 CCF = 100000 Btu 1 ft = inches ÷ 12 1 ft wc = 0.434 psi 1 ft Hg = 5.89 psi inches = ft x 12 1 mm Hg = 0.535 in wc 1 in Hg = 1.133 ft 1 kW/hr = 3413 Btu 1 lb(moisture) = 7000 grains 1 psi = 2.307 ft wc 1 psi = 27.681 in wc 1 psi = 2.036 in Hg 1 Ton refrigeration = 12000 Btu/hr Atmospheric.
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