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HVAC & Hydronics formula solvers

Hydronic Heat Transfer (Water)

Q˙=ρwcwV˙ ΔT\dot{Q} = \rho_w c_w \dot{V} \, \Delta T

HVAC & HydronicsThermodynamicsFluid MechanicsHeat carried by a water loop from flow rate and supply-to-return ΔT — the SI form of the trade rule BTU/hr = 500 × GPM × ΔT.

Glycol Loop Heat Transfer (Capacity Derate)

Q˙=ρcV˙ ΔT\dot{Q} = \rho c \dot{V} \, \Delta T

HVAC & HydronicsThermodynamicsWater TreatmentHeat carried by a glycol loop using the actual mix density and specific heat, which is how the 500 constant derates for antifreeze.

Air Sensible Heat (1.08 Rule)

Q˙s=ρacaV˙ ΔT\dot{Q}_s = \rho_a c_a \dot{V} \, \Delta T

HVAC & HydronicsThermodynamicsSensible heat carried by an airstream from CFM and dry-bulb ΔT, assuming standard air — the trade rule BTU/hr = 1.08 × CFM × ΔT.

Air Latent Heat (0.68 Rule)

Q˙l=ρaV˙hfg ΔW\dot{Q}_l = \rho_a \dot{V} h_{fg} \, \Delta W

HVAC & HydronicsThermodynamicsLatent heat from dehumidifying an airstream, set by airflow and the change in humidity ratio — the trade rule BTU/hr = 0.68 × CFM × Δgrains.

Air Total Heat (4.5 Rule)

Q˙t=ρaV˙ Δh\dot{Q}_t = \rho_a \dot{V} \, \Delta h

HVAC & HydronicsThermodynamicsTotal (sensible plus latent) heat carried by an airstream from airflow and enthalpy change — the trade rule BTU/hr = 4.5 × CFM × Δh.

Tons of Refrigeration from BTU/hr

T=Q˙12,000 BTU/hrT = \frac{\dot{Q}}{12{,}000\ \text{BTU/hr}}

HVAC & HydronicsThermodynamicsConverts a cooling load in BTU/hr (or kW) to tons of refrigeration, where one ton is 12,000 BTU/hr or 3.5169 kW.

Coefficient of Performance (COP)

COP=Q˙W˙\mathrm{COP} = \frac{\dot{Q}}{\dot{W}}

HVAC & HydronicsThermodynamicsEfficiency of a heat pump or chiller: useful heating or cooling delivered divided by the electrical power drawn to deliver it.

Energy Efficiency Ratio (EER)

EER=Q˙ [BTU/hr]W˙ [W]\mathrm{EER} = \frac{\dot{Q}\ [\text{BTU/hr}]}{\dot{W}\ [\text{W}]}

HVAC & HydronicsThermodynamicsCooling efficiency as BTU/hr of capacity per watt of electrical input, a deliberately mixed-unit ratio equal to 3.412 times the COP.

EER to COP Conversion

EER=3.412×COP\mathrm{EER} = 3.412 \times \mathrm{COP}

HVAC & HydronicsThermodynamicsConverts between the two efficiency scales, since one watt of input equals 3.412 BTU/hr and both ratios describe the same machine.

Chiller Efficiency (kW per Ton)

kW/ton=W˙ [kW]Q˙ [tons]\mathrm{kW/ton} = \frac{\dot{W}\ [\text{kW}]}{\dot{Q}\ [\text{tons}]}

HVAC & HydronicsThermodynamicsThe chiller-plant efficiency metric: kilowatts drawn per ton of cooling produced, where lower is better and 0.5 kW/ton is excellent.

Condenser Water Flow Rate

V˙=Q˙⋅HRFρwcw ΔT\dot{V} = \frac{\dot{Q} \cdot \mathrm{HRF}}{\rho_w c_w \, \Delta T}

HVAC & HydronicsFluid MechanicsWater TreatmentTower water flow needed to reject a chiller's load plus compressor heat, the physics behind the 3 gpm per ton at 10 °F rule of thumb.

Round Duct Air Velocity

v=4V˙πd2v = \frac{4 \dot{V}}{\pi d^{2}}

HVAC & HydronicsFluid MechanicsAir velocity in a round duct from the volume flow and the duct diameter, the check that keeps branches quiet and mains efficient.

Equivalent Round Duct Diameter

De=1.30(ab)0.625(a+b)0.25D_e = 1.30 \frac{(ab)^{0.625}}{(a+b)^{0.25}}

HVAC & HydronicsFluid MechanicsHuebscher's equation for the round duct that has the same friction loss and airflow as a given rectangular duct of sides a and b.

Air Changes per Hour (ACH)

ACH=3600 V˙Vroom\mathrm{ACH} = \frac{3600 \, \dot{V}}{V_{room}}

HVAC & HydronicsFluid MechanicsHow many times per hour a ventilation rate replaces the air in a room, the ventilation yardstick behind BTU/hr = 60 × CFM ÷ room volume.

Sensible Heat Ratio (SHR)

SHR=Q˙sQ˙s+Q˙l\mathrm{SHR} = \frac{\dot{Q}_s}{\dot{Q}_s + \dot{Q}_l}

HVAC & HydronicsThermodynamicsThe fraction of a cooling coil's total load that is sensible, the number that decides whether a room ends up cool or merely cold and clammy.

Mixed Air Temperature

Tm=f Toa+(1−f) TraT_m = f \, T_{oa} + (1-f) \, T_{ra}

HVAC & HydronicsThermodynamicsTemperature of the blend leaving a mixing box, weighted by the outdoor air fraction — the reading that verifies an economizer's damper position.

Expansion Tank Acceptance Volume

Vt=Vs e1−P1P2V_t = \frac{V_s \, e}{1 - \dfrac{P_1}{P_2}}

HVAC & HydronicsFluid MechanicsDiaphragm expansion tank size for a closed hydronic loop from system volume, water expansion and the absolute fill and relief pressures.

Loop Water Expansion Volume

ΔV=V0 β ΔT\Delta V = V_0 \, \beta \, \Delta T

HVAC & HydronicsFluid MechanicsThermodynamicsVolume a hydronic loop's water gains when heated, from the starting volume, the volumetric expansion coefficient and the temperature rise.

Hydronic Static Fill Pressure

P=ρwgH+PmarginP = \rho_w g H + P_{margin}

HVAC & HydronicsFluid MechanicsCold fill pressure a closed loop needs to lift water to its highest point plus a safety margin, the SI form of the 2.31 ft per psi rule.

Radiator Output at Non-Rated Temperature

Q˙=Q˙r(ΔTΔTr)n\dot{Q} = \dot{Q}_r \left(\frac{\Delta T}{\Delta T_r}\right)^{n}

HVAC & HydronicsThermodynamicsCorrects a radiator or baseboard's catalogue output to the actual water-to-air temperature difference using the emitter exponent n.

Seasonal Heating Energy (Degree-Day Method)

E=Q˙d ΔTm tΔTd ηE = \frac{\dot{Q}_d \, \Delta T_m \, t}{\Delta T_d \, \eta}

HVAC & HydronicsThermodynamicsEstimates seasonal fuel energy by scaling the design heat loss with the average temperature deficit, season length and equipment efficiency.

Boiler or Furnace Output from Input

Q˙out=Q˙in η\dot{Q}_{out} = \dot{Q}_{in} \, \eta

HVAC & HydronicsThermodynamicsUsable heat delivered by a boiler or furnace from its fuel input rate and its efficiency rating, the nameplate arithmetic behind AFUE.

Combustion (Stack) Efficiency — Siegert Formula

η=100−A ΔTCO2\eta = 100 - A \, \frac{\Delta T}{\mathrm{CO_2}}

HVAC & HydronicsThermodynamicsClassic flue-gas efficiency estimate from net stack temperature and flue CO₂ percentage, with a fuel constant A of about 0.66 for gas.

Refrigerant Superheat

SH=Tsuction−Tsat\mathrm{SH} = T_{suction} - T_{sat}

HVAC & HydronicsThermodynamicsDegrees of superheat at the compressor suction: how much warmer the vapour is than its saturation temperature at the same pressure.

Refrigerant Subcooling

SC=Tsat−Tliquid\mathrm{SC} = T_{sat} - T_{liquid}

HVAC & HydronicsThermodynamicsDegrees of subcooling at the condenser outlet: how much colder the liquid is than its saturation temperature at the same pressure.

Refrigerant Mass Flow Rate

m˙=Q˙Δh\dot{m} = \frac{\dot{Q}}{\Delta h}

HVAC & HydronicsThermodynamicsRefrigerant circulated per unit time from the cooling capacity and the enthalpy change across the evaporator, the basis of compressor sizing.

Pump Affinity Law — Flow vs Speed

Q2Q1=N2N1\frac{Q_2}{Q_1} = \frac{N_2}{N_1}

HVAC & HydronicsFluid MechanicsWater TreatmentFirst affinity law: a centrifugal pump's capacity changes in direct proportion to shaft speed when the impeller diameter is unchanged.

Pump Affinity Law — Head vs Speed

H2H1=(N2N1)2\frac{H_2}{H_1} = \left(\frac{N_2}{N_1}\right)^{2}

HVAC & HydronicsFluid MechanicsWater TreatmentSecond affinity law: pump head varies with the square of shaft speed, so a 20% speed cut costs 36% of the developed head.

Pump Affinity Law — Power vs Speed

P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}

HVAC & HydronicsFluid MechanicsWater TreatmentThird affinity law: absorbed power varies with the cube of shaft speed — the single relation that pays for every variable-frequency drive.

Pump Affinity Law — Flow vs Impeller Diameter

Q2Q1=D2D1\frac{Q_2}{Q_1} = \frac{D_2}{D_1}

HVAC & HydronicsFluid MechanicsWater TreatmentCapacity scales directly with trimmed impeller diameter at constant speed, the classic way to de-rate an oversized centrifugal pump permanently.

Pump Affinity Law — Head vs Impeller Diameter

H2H1=(D2D1)2\frac{H_2}{H_1} = \left(\frac{D_2}{D_1}\right)^{2}

HVAC & HydronicsFluid MechanicsWater TreatmentDeveloped head falls with the square of the trimmed impeller diameter, so a 10% trim sheds about 19% of the head at constant speed.

Fan Affinity Law — Airflow vs Speed

Q2Q1=N2N1\frac{Q_2}{Q_1} = \frac{N_2}{N_1}

HVAC & HydronicsFluid MechanicsPhysicsFan airflow in CFM changes in direct proportion to wheel speed, the first law used when re-sheaving a belt-driven air handler.

Fan Affinity Law — Static Pressure vs Speed

SP2SP1=(N2N1)2\frac{SP_2}{SP_1} = \left(\frac{N_2}{N_1}\right)^{2}

HVAC & HydronicsFluid MechanicsPhysicsFan static pressure rises with the square of wheel speed, the reason a modest re-sheave can overpressurise ductwork and blow out flex connections.

Fan Affinity Law — Power vs Speed

P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}

HVAC & HydronicsFluid MechanicsPhysicsFan brake power varies with the cube of wheel speed — the law behind variable-air-volume energy savings and behind burnt-out re-sheaved motors.

Pump Water Horsepower

WHP=Q H SG3960WHP = \frac{Q \, H \, SG}{3960}

HVAC & HydronicsFluid MechanicsWater TreatmentUseful power delivered to the liquid; the 3960 divisor assumes US gallons per minute, feet of head and horsepower output.

Pump Brake Horsepower

BHP=Q H SG3960 ηBHP = \frac{Q \, H \, SG}{3960 \, \eta}

HVAC & HydronicsFluid MechanicsWater TreatmentShaft power the motor must actually supply; the 3960 constant assumes gpm, feet of head and horsepower, with efficiency as a fraction.

Pump Efficiency from Hydraulic and Shaft Power

η=PhydPshaft\eta = \frac{P_{hyd}}{P_{shaft}}

HVAC & HydronicsFluid MechanicsWater TreatmentPump efficiency is the ratio of hydraulic power delivered to the liquid over the mechanical power absorbed at the shaft.

Fan Brake Horsepower

BHP=Q⋅SP6356 ηBHP = \frac{Q \cdot SP}{6356 \, \eta}

HVAC & HydronicsFluid MechanicsPhysicsShaft power a fan absorbs; the 6356 divisor assumes cubic feet per minute, inches of water gauge and horsepower at the given efficiency.

Total Dynamic Head

TDH=hs+hf+hvTDH = h_s + h_f + h_v

HVAC & HydronicsFluid MechanicsWater TreatmentThe head a pump must develop: static lift plus friction losses plus velocity head, all expressed in feet or metres of the pumped liquid.

Net Positive Suction Head Available (NPSHa)

NPSHa=hatm+hs−hf−hvpNPSH_a = h_{atm} + h_s - h_f - h_{vp}

HVAC & HydronicsFluid MechanicsWater TreatmentAbsolute head available at the pump suction above the liquid's vapour pressure — the margin that keeps a pump from cavitating.

Darcy–Weisbach Head Loss

hf=f LD v22gh_f = f \, \frac{L}{D} \, \frac{v^{2}}{2g}

HVAC & HydronicsFluid MechanicsPhysicsThe rigorous pipe friction equation: head loss from friction factor, length-to-diameter ratio and velocity head, with g = 9.80665 m/s².

Laminar Friction Factor (f = 64/Re)

f=64Ref = \frac{64}{Re}

HVAC & HydronicsFluid MechanicsPhysicsIn laminar pipe flow the Darcy friction factor depends only on Reynolds number — roughness plays no part below about Re = 2300.

Swamee–Jain Friction Factor

f=0.25[log⁡10 ⁣(ε3.7D+5.74Re0.9)]2f = \frac{0.25}{\left[\log_{10}\!\left(\frac{\varepsilon}{3.7D} + \frac{5.74}{Re^{0.9}}\right)\right]^{2}}

HVAC & HydronicsFluid MechanicsPhysicsAn explicit turbulent friction factor within about 1% of the implicit Colebrook–White equation, valid for Re from 5000 to 10⁸.

Hazen–Williams Head Loss

hf=10.67 L Q1.852C1.852D4.8704h_f = \frac{10.67 \, L \, Q^{1.852}}{C^{1.852} D^{4.8704}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe waterworks head-loss equation in SI form, with Q in m³/s and D in m; the 10.67 constant is 4.727 when working in feet and cubic feet per second.

Hazen–Williams Velocity

v=0.849 C R0.63S0.54v = 0.849 \, C \, R^{0.63} S^{0.54}

HVAC & HydronicsFluid MechanicsWater TreatmentMean water velocity from hydraulic radius and hydraulic gradient; the 0.849 SI constant becomes 1.318 when R is in feet and v in feet per second.

Minor Loss from K Factor

hL=K v22gh_L = K \, \frac{v^{2}}{2g}

HVAC & HydronicsFluid MechanicsWater TreatmentHead lost through a valve or fitting as a multiple of velocity head, with g = 9.80665 m/s² and K taken from a fitting table.

Equivalent Length of a Fitting

Leq=KDfL_{eq} = \frac{K D}{f}

HVAC & HydronicsFluid MechanicsWater TreatmentConverts a fitting's K factor into the length of straight pipe that would cause the same friction loss at the same friction factor.

Valve Flow Coefficient (Cv)

Q=CvΔPSGQ = C_v \sqrt{\frac{\Delta P}{SG}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe US valve-sizing relation: Cv is the gpm of 60 °F water a valve passes at 1 psi drop, so Q is in gpm and ΔP in psi.

Valve Flow Coefficient (Kv, metric)

Q=KvΔpSGQ = K_v \sqrt{\frac{\Delta p}{SG}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe metric valve-sizing relation: Kv is the m³/h of water a valve passes at 1 bar drop, related to Cv by Cv ≈ 1.156 Kv.

Pipe Internal Volume

V=πD24LV = \frac{\pi D^{2}}{4} L

HVAC & HydronicsFluid MechanicsWater TreatmentThe liquid a run of pipe holds, from inside diameter and developed length — the starting point for every flush, fill or chemical dose.

Partially Filled Horizontal Cylindrical Tank

V=L[r2cos⁡−1 ⁣(r−hr)−(r−h)2rh−h2]V = L \left[ r^{2} \cos^{-1}\!\left(\frac{r-h}{r}\right) - (r-h)\sqrt{2rh - h^{2}} \right]

HVAC & HydronicsFluid MechanicsGeometryLiquid volume in a horizontal cylinder from the wetted depth, using the circular segment area times the tank length.

Pipe Velocity from Flow and Diameter

v=4QπD2v = \frac{4Q}{\pi D^{2}}

HVAC & HydronicsFluid MechanicsWater TreatmentAverage velocity in a full round pipe from volumetric flow and inside diameter — the first check on any piping design.

Barlow's Formula (Pipe Pressure Rating)

P=2StDP = \frac{2 S t}{D}

HVAC & HydronicsFluid MechanicsMechanicsInternal pressure a pipe can hold from wall stress, wall thickness and outside diameter — the thin-wall hoop-stress relation used by pipeline codes.

Expansion Loop Leg Length (Guided Cantilever)

L=3ED ΔSaL = \sqrt{\frac{3 E D \, \Delta}{S_a}}

HVAC & HydronicsFluid MechanicsMechanicsLeg length an expansion loop or offset needs to absorb a given thermal movement without exceeding the pipe's allowable stress.

Water Hammer Surge (Joukowsky Equation)

ΔP=ρ a Δv\Delta P = \rho \, a \, \Delta v

HVAC & HydronicsFluid MechanicsPhysicsPeak pressure surge from a sudden change in flow velocity: fluid density times pressure-wave celerity times the velocity change.

Pump Specific Speed (Ns)

Ns=NQH0.75N_s = \frac{N \sqrt{Q}}{H^{0.75}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe dimensional index that classifies impeller type, evaluated in US units with N in rpm, Q in gpm and H in feet at the best efficiency point.

Chiller Heat Rejection

Qr=Qe HRFQ_r = Q_e \, \mathrm{HRF}

Water TreatmentThermodynamicsHVAC & HydronicsHeat a chiller's tower has to reject: the evaporator load times the heat rejection factor that adds the compressor's own work to the load.

Energy Cost from a Utility Rate

Ce=E peC_e = E \, p_e

Water TreatmentThermodynamicsHVAC & HydronicsCost of the energy a system consumes: kilowatt-hours or fuel BTUs times the utility rate, for tower fans, pumps and boiler gas.

Newton's Law of Cooling (Q = hAΔT)

Q˙=hA ΔT\dot{Q} = h A \, \Delta T

Heat TransferThermodynamicsHVAC & HydronicsConvective heat rate from a surface, set by the film coefficient, the wetted area and the surface-to-fluid temperature difference.

Overall Heat Transfer Coefficient (U)

1U=1hi+Lk+1ho\frac{1}{U} = \frac{1}{h_i} + \frac{L}{k} + \frac{1}{h_o}

Heat TransferThermodynamicsHVAC & HydronicsOverall coefficient U for a plane wall with fluid on both sides, adding the inside film, the wall and the outside film as resistances in series.

Convection Film Resistance

R=1hAR = \frac{1}{h A}

Heat TransferThermodynamicsHVAC & HydronicsThermal resistance of a boundary-layer film in kelvin per watt, the reciprocal of the film coefficient times the wetted surface area.

Heat Flow from Thermal Resistance

Q˙=ΔTR\dot{Q} = \frac{\Delta T}{R}

Heat TransferThermodynamicsHVAC & HydronicsOhm's law for heat: the flow through an assembly equals the temperature difference across it divided by its total thermal resistance.

Overall U from Total Resistance

U=1RtotAU = \frac{1}{R_{tot} A}

Heat TransferThermodynamicsHVAC & HydronicsConverts an assembly's total resistance in kelvin per watt into the overall coefficient U quoted on exchanger and envelope datasheets.

Conduction Through a Pipe Wall

Q˙=2πkL ΔTln⁡(r2/r1)\dot{Q} = \frac{2 \pi k L \, \Delta T}{\ln(r_2 / r_1)}

Heat TransferThermodynamicsHVAC & HydronicsRadial conduction through a cylindrical pipe or insulation layer, where the area grows outward so the resistance follows a logarithm.

Log Mean Temperature Difference (Counterflow)

ΔTlm=ΔT1−ΔT2ln⁡(ΔT1/ΔT2)\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}

Heat TransferThermodynamicsHVAC & HydronicsEffective driving temperature difference in a counterflow exchanger, from the terminal differences at the hot and cold ends of the shell.

Log Mean Temperature Difference (Parallel Flow)

ΔTlm=ΔT1−ΔT2ln⁡(ΔT1/ΔT2)\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}

Heat TransferThermodynamicsHVAC & HydronicsEffective driving temperature difference when both streams enter at the same end, pairing the two inlets and the two outlets.

Heat Exchanger Duty (Q = U·A·F·LMTD)

Q˙=UAF ΔTlm\dot{Q} = U A F \, \Delta T_{lm}

Heat TransferThermodynamicsHVAC & HydronicsThe LMTD design equation with the correction factor F, which derates the counterflow driving force for shell-and-tube or crossflow arrangements.

Stream Duty from Mass Flow (Q = ṁcΔT)

Q˙=m˙ cp ΔT\dot{Q} = \dot{m} \, c_p \, \Delta T

Heat TransferThermodynamicsHVAC & HydronicsHeat picked up or given off by one exchanger stream, from its mass flow, specific heat and the temperature change across the unit.

Heat Exchanger Effectiveness (ε = Q/Qmax)

ε=Q˙Q˙max\varepsilon = \frac{\dot{Q}}{\dot{Q}_{max}}

Heat TransferThermodynamicsHVAC & HydronicsEffectiveness as the ratio of actual duty to the thermodynamic maximum, the performance figure that needs no outlet temperatures to interpret.

Fouled Overall Coefficient

1Uf=1Uc+1hf\frac{1}{U_f} = \frac{1}{U_c} + \frac{1}{h_f}

Heat TransferThermodynamicsHVAC & HydronicsAdds a fouling deposit as one more resistance in series, reducing the clean overall coefficient to the fouled value used for design margin.

Fin Heat Transfer Rate

Q˙f=ηf hAf ΔTb\dot{Q}_f = \eta_f \, h A_f \, \Delta T_b

Heat TransferThermodynamicsHVAC & HydronicsDuty of a fin or finned surface: the ideal convective rate over the whole fin area, derated by the fin efficiency.

Combined Convection and Radiation Coefficient

ht=hc+εσ(Ts+Tsur)(Ts2+Tsur2)h_t = h_c + \varepsilon \sigma (T_s + T_{sur})(T_s^2 + T_{sur}^2)

Heat TransferThermodynamicsHVAC & HydronicsTotal surface coefficient adding a linearised radiation term to the convective film, so one h covers both mechanisms over a modest ΔT.

R-Value of an Insulation Layer (R = L/k)

R=LkR = \frac{L}{k}

Heat TransferHVAC & HydronicsThermodynamicsArea-specific thermal resistance of one layer, from its thickness and thermal conductivity — the RSI or R-value quoted on every insulation label.

Total R-Value of an Assembly

Rtot=R1+R2+R3R_{tot} = R_1 + R_2 + R_3

Heat TransferHVAC & HydronicsThermodynamicsTotal R-value of a wall, roof or floor built up from three layers in series, where the same heat crosses each layer so the R-values simply add.

U-Factor from Total R-Value (U = 1/R)

U=1RtotU = \frac{1}{R_{tot}}

Heat TransferHVAC & HydronicsThermodynamicsConverts an assembly's total R-value into the U-factor used by energy codes and window labels, and back — the two are simple reciprocals.

Heat Loss Through an Assembly (Q = A·ΔT/R)

Q˙=A ΔTRtot\dot{Q} = \frac{A \, \Delta T}{R_{tot}}

Heat TransferHVAC & HydronicsThermodynamicsSteady heat loss through a wall, roof or floor from its area, the inside-to-outside temperature difference and the assembly's total R-value.

Heat Flux Through Insulation (q = ΔT/R)

q′′=ΔTRq'' = \frac{\Delta T}{R}

Heat TransferHVAC & HydronicsThermodynamicsHeat flow per unit area through an insulated assembly, straight from the temperature difference and the R-value, with no area needed.

Effective R-Value with Framing (Parallel Path)

1Reff=ffrRfr+1−ffrRcav\frac{1}{R_{eff}} = \frac{f_{fr}}{R_{fr}} + \frac{1 - f_{fr}}{R_{cav}}

Heat TransferHVAC & HydronicsThermodynamicsWhole-wall R-value once the studs are counted, area-weighting the framing and cavity paths as parallel conductances rather than averaging their R-values.

Fouling Factor on an Overall Coefficient

1Uf=1Uc+Rf\frac{1}{U_f} = \frac{1}{U_c} + R_f

Heat TransferThermodynamicsHVAC & HydronicsService-condition U of a heat exchanger, adding the TEMA fouling factor as an extra area-specific resistance on top of the clean coefficient.