2.0 KEY EQUATIONS. Evaporator Net Refrigeration Effect. Compressor Work. Net Condenser Effect

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1 2.0 KEY EQUATIONS Evaporator Net Refrigeration Effect Q net refrigeration effect [] = (H 1 H 4 ) lb (Refrig Flow Rate) (60) min lb min hr H 1 = leaving evaporator enthalpy lb ; H 4 = entering evaporator enthalpy [ lb ] Compressor Work W compressor [] = (H 2 H 1 ) lb (Refrig Flow Rate) (60) min lb min hr H 2 = leaving compressor enthalpy lb ; H 1 = entering condneser enthalpy [ lb ] Net Condenser Effect Q net condenser effect [] = (H 2 H 4 ) lb (Refrig Flow Rate) (60) min lb min hr H 2 = entering condenser enthalpy lb ; H 4 = leaving condneser enthalpy [ lb ] Net Condenser Effect Function of Compressor Work and Net Refrigeration Effect Q net condenser effect [] = W compressor [] + Q net refrigeration effect [] Coefficient of Performance COP = W out W in = Q net refrigeration effect [] W compressor [] Refrigeration Room Ventilation Rate Q[CFM] = 100XG 0.5, where G = lbs of refrigerant. Refrigeration - 4

2 2.0 KEY EQUATIONS AND TERMS Relationship of Enthalpy of Vaporization, Enthalpy of Saturated Vapor and Liquid Water h g = h f + h fg h g = enthalpy of saturated vapor[ lbm ] h f = enthalpy of saturated liquid h fg = enthalpy of vaporization all enthalpies at constant temperature & pressure Enthalpy of Wet Steam (Mixed Region) as a Function of Steam Quality h mix = h f + x h fg h mix = enthalpy of wet steam (mix of liquid & vapor) x = steam quality, drnyess fraction, % vapor Relationship of Entropy of Vaporization, Entropy of Saturated Vapor and Liquid Water s g = s f + s fg s g = entropy of saturated vapor[ s f = entropy of saturated liquid s fg = entropy of vaporization Entropy of Wet Steam (Mixed Region) as a Function of Steam Quality s mix = s f + x s fg s mix = entropy of wet steam (mix of liquid & vapor) x = steam quality, drnyess fraction, % vapor Heat Available from Condensing Steam Q = m h fg m = mass flow rate [ lbm hr ] Q = energy [ hr ] Throttling: Irreversible Adiabatic [Constant Enthalpy] or Isenthalpic h initial = h final Steam - 3

3 Tank Heating/Cooling: Isometric [Constant Volume] v initial = v final v = specific volume [ ft3 lb ] Turbine Expansion: Isentropic [Constant Entropy] or Reversible Adiabatic s initial = s final Compressor: Isentropic [Constant Entropy] or Reversible Adiabatic s initial = s final Boiler Heating: Isobaric [Constant Pressure] P initial = P final P = pressure [psia] Heat Exchanger (Boiling or Condensing): Isothermal [Constant Temperature] T initial = T final Boiler Efficiency ε boiler = (m feedwater) (H steam,out H feedwater,in) m fuel HHV Convert Feed-Water Flowrate in GPM to Steam Flowrate in lbs/hr gallon of water 1 minute 1 ft 3 [ 7.48 gallon 62.4 lb ft 3 60 minute ] = 500 lbs hour hr Simplified Steam Heating Coil: Steam to Water Heat Transfer m steam h fg = 500 GPM water T Steam - 4

4 Simplified Steam Heating Coil: Steam to Air Heat Transfer m steam h fg = 1.08 CFM air T Steam - 5

2.0 KEY TERMS 1 Dry Bulb Temperature Dry bulb temperature indicates the amount of energy independent of the amount of water in

Units = [ ] 2 Wet Bulb Temperature Wet bulb temperature indicates the amount of water in the air.

Units = [ ] 3 Dew Point The temperature at which moist air must be cooled to, in order for water to condense out of the air.

5 2.0 KEY TERMS 1 Dry Bulb Temperature Dry bulb temperature indicates the amount of energy independent of the amount of water in the air. Measured with a thermometer. Units = [ ] 2 Wet Bulb Temperature Wet bulb temperature indicates the amount of water in the air. Measured with a sling psychrometer or hygrometer. Units = [ ] 3 Dew Point The temperature at which moist air must be cooled to, in order for water to condense out of the air. Units = [ ] 4 Humidity Ratio Humidity ratio or specific humidity is the measure of the amount of water in air. lb of Water Varpor Units = [ ] lb of Dry Air 5 Relative Humidity Relative Humidity indicates the amount of water in the air relative to the total amount of water the air can hold. Units = [%] Psychrometrics - 4

6 Sensible Heat 7 Latent Heat 8 Enthalpy Sensible heat indicates the amount of dry heat. It indicates the amount of energy either absorbed or released to change the dry bulb temperature of the air.

6 6 Sensible Heat 7 Latent Heat 8 Enthalpy Sensible heat indicates the amount of dry heat. It indicates the amount of energy either absorbed or released to change the dry bulb temperature of the air. Units = [ lb of air ] Latent heat indicates the amount of energy in the air due to moisture. It is the amount of heat released when water in the air condenses out or the amount of heat absorbed by water in order to vaporize the water. Units = [ lb of air ] Enthalpy is an indication of the total amount of energy in the air, both sensible and latent. Units = [ lb of air ] Exam Tip #1: Do not spend enormous amounts of time trying to interpolate the exact value on the psychrometric chart. The psychrometric chart is provided as part of the NCEES exam, but the chart is small and unclear compared to the ones typically used in practice. It is the opinion of the writer that this fact should indicate to the test taker that it is not important to get the values to the nearest (exaggeration) because it is impossible. In addition, the exam writer would not provide possible multiple choice answers that are fairly close together because of the confusion that would arise. Exam Tip #2: During the exam, do not write on anything that is not part of the exam, including your own psychrometric chart. This may result in disqualification. Psychrometrics - 5

7 3.0 KEY EQUATIONS Sensible Heat Equation Q sensible = 1.08 T DB CFM Q sensible = sensible heat [ hr ] T DB = difference in dry bulb temperature between entering and leaving CFM = volumetric flow rate, cubic feet per minute Latent Heat Equation Q latent = W GR CFM Q latent = latent heat [ hr ] gains of water vapor W GR = change in humidity ratio [ ] lb of dry air CFM = volumetric flow rate, cubic feet per minute Latent Heat Equation Q latent = 4, 840 W LB CFM Q latent = latent heat [ hr ] lbs of water vapor W lb = change in humidity ratio [ ] lb of dry air CFM = volumetric flow rate, cubic feet per minute Total Heat Equation Q total = 4. 5 ( h) CFM Q total = total heat [ hr ] h = change in enthalpy between entering and leaving CFM = volumetric flow rate, cubic feet per minute Air Mixing Equation - Dry Bulb T mix,db = T 1,DB % 1 + T 2,DB % 2 T mix,db = mixed air dry bulb temperature T 1,DB = air stream 1 dry bulb temperature % 1 = air stream 1 percent by mass T 2,DB = air stream 2 dry bulb temperature % 2 = air stream 2 percent by mass Psychrometrics - 6

8 Air Mixing Equation - Dry Bulb T mix,db = T 1,DB CFM 1 + T 2,DB CFM 2 CFM 1 + CFM 2 CFM 1 = air stream 1 volumetric flow rate CFM 2 = air stream 2 volumetric flow rate Air Mixing Equation - Enthalpy Air Mixing Equation - Enthalpy h mix = h 1,DB % 1 + h 2,DB % 2 h mix = mixed air enthalpy h 1 = air stream 1 enthalpy % 1 = air stream 1 percent by mass h 2 = air stream 2 enthalpy % 2 = air stream 2 percent by mass h mix = h 1 CFM 1 + h 2 CFM 2 CFM 1 + CFM 2 Relative Humidity as a Function of Humidity Ratio and Partial Pressures RH = p w p SAT x 100% W w W SAT x 100% RH = relative humidity p w = partial pressure of water vapor in the air stream p SAT = saturated vapor pressure of water at the temperature in question W w = humidity ratio of the air stream W SAT = humidity ratio of the air stream at saturation at the temperature in question Psychrometrics - 7

9 2.0 IMPORTANT TERMS & EQUATIONS Convert U-Factor to R-Value U = 1 R U = heat transfer coefficient [ hr ft 2 ] R = thermal resistance [ hr ft2 ] Addition of R-Values R total = R 1 + R 2 + R 3 + R n Addition of U-Factors 1 U total = 1 U U U U n Thermal Conductivity Units k = hr ft Convert Thermal Conductivity to R-Value and U-Factor R = t k t = thickness of material [ft] k = thermal conductivity [ hr ft U = k t Heat Transfer Equation Q = U A T U = overall heat transfer coefficient[ hr ft 2 ] A = area of heat transfer [ft 2 ] T = temperature difference between hot and cold areas of heat transfer [ ] Heat Transfer - 4

10 Log Mean Temperature Difference (LMTD) LMTD = T a T b ln ( T a) T b T a = temperature difference at entrance T b = temperature difference at exit Counter-flow Heat Exchanger Heat Transfer - 5

11 Parallel-flow Heat Exchanger Conduction Heat Transfer Equation Q = k A (T hot T cold ) t where Q = quantity of heat transfered hr k = thermal conductivity of material hr ft T hot T cold = temperature difference between indoors and outdoors [ ] t = thickness of material [ft] A = area of heat transfer [ft 2 ] Convective Heat Transfer Equation Q = h A T h = convective heat transfer coefficient[ hr ft 2 ] A = area of heat transfer [ft 2 ] T = temperature difference between hot and cold areas of heat transfer [ ] Heat Transfer - 6

12 Radiative Heat Transfer Equation Q = h rad A T h rad = radiation heat transfer coefficient[ hr ft 2 ] A = area of heat transfer [ft 2 ] T = temperature difference between hot and cold areas of heat transfer [ ] Heat Transfer - 7

13 2.0 KEY EQUATIONS AND TERMS Mechanical Horsepower of a Fan CFM TSP[in. wg] MHP = 6,356 MHP = mechanical horse power [HP] CFM = airflow TSP = total static pressure [in. wg] Convert Mechanical Horsepower to Brake Horsepower 1 BHP = MHP ( fan efficiency ) Convert Brake Horsepower to Electric Horsepower 1 HP = BHP motor efficiency Velocity Pressure as a Function of Air Velocity VP = FPM [in. wg] 4005 FPM = air velocity in feet per minute VP = velocity pressure [in. wg] Simplified Sensible Heat Equation Q = 1.08 CFM T[ ] h air conditions at 70 and 1 atm. Friction loss due to length of duct F duct [in. wg] = L[ft] f[ in. wg 100 ft ] Equipment and Systems - 5

14 Fan Affinity Laws CASE 1: N old = N new CFM new = RPM new RPM old P new = RPM new RPM old BHP new = RPM new RPM old 1 CFM old 2 P old 3 BHP old Fan Affinity Laws CASE 2: RPM old = RPM new CFM new = N new N old P new = N new N old BHP new = N new N old 1 CFM old 2 P old 3 BHP old Bypass Factor Equation for Coils h entering coil h leaving coil Bypas Factor = h entering coil h apparatus dew point where h is equal to the enthalpy Bypass Factor Equation for Coils T entering coil T leaving coil Bypas Factor = T entering coil T apparatus dew point where T is equal to the dry bulb temperature Bypass Factor Equation for Coils W entering coil W leaving coil Bypas Factor = W entering coil W apparatus dew point where W is equal to the humidity ratio Equipment and Systems - 6

15 Moisture Transfer Equation H = 60 ρ Q (W exit W enter ) [lb of water] W = the humidity ratio entering or leaving the system [lb of dry air] ρ = density of air [ lb ft 3] Q = air flow rate [ ft3 min ] H = moisture transferred [ lb hr ] Energy Recovery Device Efficiency Equations ε sensible = q sensible,actual q sensible,max ε latent = q latent,actual q latent,max ε total = q total,actual q total,max Energy Recovery Device Determine Actual Sensible Heat Transferred q sensible,actual = 1.08 CFM outdoor (T outdoor T supply ) q sensible,actual = 1.08 CFM return (T return T exhaust ) Energy Recovery Device Determine Maximum Possible Sensible Heat Transferred q sensible,max = 1.08 CFM min (T outdoor T return ) Energy Recovery Device Determine Actual Latent Heat Transferred q latent,actual = 4,770 CFM outdoor (W outdoor W supply ) q latent,actual = 4,770 CFM return (W return W exhaust ) Energy Recovery Device Determine Maximum Possible Latent Heat Transferred q latent,max = 4,770 CFM return (W outdoor W return ) Equipment and Systems - 7

16 Energy Recovery Device Determine Actual Enthalpy Transferred q total,actual = 4.5 CFM outdoor (h outdoor h supply ) q stotal,actual = 4.5 CFM return (h return h exhaust ) Energy Recovery Device Determine Maximum Possible Enthalpy Transferred q total,max = 4.5 CFM outdoor (h outdoor h return ) Darcy Weisbach Equation h = flv2 [Darcy Weisbach Equation] 2Dg where h = ft of head; f = Darcy friction factor; v = velocity ft sec, D = inner diameter [ft], g = gravity [32.2 ft sec 2] Darcy Weisbach Equation h = flv2 [Darcy Weisbach Equation] 2Dg where h = ft of head; f = Darcy friction factor; v = velocity ft sec, D = inner diameter [ft], g = gravity [32.2 ft sec 2] Positive Suction Head Equation P suct = ±P elev P fric + P vel Pressure Drop due to Velocity Equation [Pump] V 2 ft [ft of head]; velocity in 2g sec ; gravity = 32.2 ft sec 2 Equipment and Systems - 8

17 Pump Affinity Laws Q 1 = D 1 ; if speed is held constant Q 2 D 2 Q 1 = N 1 ; if diameter is held constant Q 2 N 2 Pump Affinity Laws H 1 H 1 2 = D 1 ; if speed is held constant H 2 2 D 2 2 = N 1 ; if diameter is held constant H 2 N 2 2 Pump Affinity Laws P 1 P 1 3 = D 1 ; if speed is held constant P 2 3 D 2 3 = N 1 ; if diameter is held constant P 2 N 2 3 Heat Transfer Between Pipe to Outer Surface in k[ h ft Q pipe to outer surface = 2 ] A[ft 2 ] (T X[in] outer surface T pipe )[ ] Where k is equal to the conductivity of the insulation and X is equal to the thickness of the insulation. K can vary depending on the temperature of the pipe. Heat Transfer Between Pipe Surface and Air Q outer surface to air = h[ ft 2 h ] A[ft2 ] (T ambient T outer surface )[ ] Where h is equal to the surface coefficient of the insulation. This value is a measure of how well the surface of the material in question is at conducting heat to the ambient air. The value can increase for higher wind speeds and varying surface and air temperatures. Equipment and Systems - 9

18 Cooling Tower Range Range = T water,in [ ] T water,out [ ] Cooling Tower Apprach Approach = T water,out [ ] T air in,wb [ ] Cooling Tower Effectiveness Effectiveness = Range Range + Approach Cooling Tower Evaporation Rate cooling tower flow rate gal min T water,in T water,out = evaporation rate gal min Combining the Sound Levels of Multiple Sources L A = 10 log 10 (10 DB DB DB DB DB DB v10 DB DB 8 100) Sound Level at a Distance from a Point Source (Spherical Propagation) L db = L equip 20 log 10 x 1 L db = Sound level at a distance of x [DB] L equip = Sound level of equipment [DB] x = distance from equipment [ft ] Sound Level at a Distance from a Point Source (Half-Spherical Propagation) L db = L equip 20 log 10 x + 2 Sound Level at a Distance from a Point Source (Quarter-Spherical Propagation) L db = L equip 20 log 10 x + 5 Equipment and Systems - 10

19 Sound Level at a Distance from a Point Source (Eighth-Spherical Propagation) L db = L equip 20 log 10 x + 8 Equipment and Systems - 11

20 2.0 EQUATIONS/TERMS Ohm s Law I = V R I = current [amps] V = voltage [volts] R = resistantce [amps] Resistors in series R eq,series = R 1 + R 2 + R 3 + R n Resistors in parallel 1 R eq = 1 R R R R n Power Equations P = I V P = V2 R P = I 2 R Pump Water Horsepower Equations P mech work,pump[hp] = h ft Q gpm (SG) ; 3956 Q = volumetric flow rate [gallons per minute] h = pressure [feet of head] P = power [horesepower] SG = specific gravity P mech work,pump,[hp] = p psi Q gpm (SG) ; 1,714 p = pressure [psi] Support -4

21 Fan Mechanical Horsepower Equation P mech work,fan[hp] = Q cfm TP in wg ; 6356 Q cfm = volumetric flow rate of air [cubic feet per minute] TP in wg = total pressure [inches water gauge] P mech work,fan[hp] = fan mechanical horsepower Pump or Fan Brake Horsepower Equation P fan/pump[hp] = P mech work[hp]] ε fan/pump ; Motor Horsepower Equation P motor = P mech work[hp]] ε motor ; Electrical Power Supplied to Motor P supplied to motor[hp] = P motor[hp] PF Support -5

22 Conversion Formula Factor Value Present Value to Future Value FV = PV x (1 + i) n Multiply PV by (F/P, i, n) Future Value to Present Value PV = FV (1 + i) n Multiply FV by (P/F, i, n) Present Value to Annual Value i (1 + i)n A = PV ( (1 + i) n 1 ) Multiply PV by (A/P, i, n) Annual Value to Present Value 1 (1 + i) n PV = A ( ) i Multiply A by (P/A, i, n) Future Value to Annual Value i A = FV( (1 + i) n 1 ) Multiply FV by (A/F, i, n) Annual Value to Future Value FV = A ( (1 + i)n 1 ) i Multiply A by (F/A, i, n) Support -6

NEBB Fundamental Formulas

NEBB Fundamental Formulas Approved NEBB - May 1, 17 Page 1 of 8 Version 1.3 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