HVAC Design Formulas and Calculations Guide

HVAC design relies heavily on accurate calculations to ensure systems operate efficiently, maintain comfort, and meet performance requirements. From determining heating and cooling loads to sizing equipment and distribution systems, engineers and technicians depend on a wide range of formulas to make informed design decisions. This guide brings together essential HVAC equations used across airside and waterside systems, helping professionals better understand how airflow, temperature differences, and energy transfer interact within a building.

The article covers fundamental relationships such as sensible, latent, and total heat calculations, along with air change rates, fluid flow equations, and psychrometric principles. It also explores critical concepts like fan and pump laws, duct and pipe sizing, energy efficiency metrics, and heat transfer through building envelopes. By presenting both English and metric formulations, the guide supports a wide range of applications and design standards used globally.

In addition to core system calculations, this resource extends into specialized areas such as steam and condensate systems, humidification, cooling towers, and refrigeration-related ventilation. Whether you are performing load calculations, analyzing system performance, or designing complete HVAC systems, these equations serve as a practical reference to support accurate, efficient, and reliable engineering work.

Airside System Equations

$$\text{Sensible Heat} = H_S = 1.08 \times \text{CFM} \times \Delta T$$

$$\text{Latent Heat} = H_L = 0.68 \times \text{CFM} \times \Delta \text{WGR}$$

$$\text{Total Heat} = H_T = 4.5 \times \text{CFM} \times \Delta h$$

$$\mathrm{SHR} = \frac{H_s}{H_T} = \frac{H_s}{H_s + H_L}$$

Waterside System Equations

$$\text{Total Heat}=H = 500 \times \text{GPM} \times \Delta T$$

$$\text{Evaporator Water Flow Rate= } \text{ GPM}_{\text{EVAP}} = \frac{\text{TONS} \times 24}{\Delta T}$$

$$\text{Condenser Water Flow Rate} = \text{GPM}_{\text{COND}} = \frac{\text{TONS} \times 30}{\Delta T}$$

Air Change Rate Equations

$$\text{Air Change Rate Per hour} = \frac{\text{CFM} \times 60}{\text{VOLUME}}$$

$$\text{Air Flow Rate} = \text{CFM} = \frac{\text{AC}}{\text{HR}} \times \frac{\text{VOLUME}}{60}$$

English/Metric Airside System Equations Comparison

Sensible Heat Equations

$$\text{Sensible Heat (Btu/h)} = H_s = 1.08\,\frac{\text{Btu}\cdot\text{min}}{\text{Hr}\cdot\text{ft}^3\cdot{}^\circ\text{F}} \times \text{CFM} \times \Delta T$$

$$\text{Sensible Heat (kJ/h)} = H_{SM} = 72.42\,\frac{\text{kJ}\cdot\text{min}}{\text{Hr}\cdot\text{m}^3\cdot{}^\circ\text{C}} \times \text{CMM} \times \Delta T_M$$

Latent Heat Equations

$$\text{Latent Heat (Btu/h)} = H_L = 0.68\,\frac{\text{Btu}\cdot\text{min}\cdot\text{lb DA}}{\text{Hr}\cdot\text{ft}^3\cdot\text{Gr H}_2\text{O}} \times \text{CFM} \times \Delta W$$

$$\text{Latent Heat (kJ/h)} = H_{LM} = 177{,}734.8\,\frac{\text{kJ}\cdot\text{min}\cdot\text{kg DA}}{\text{Hr}\cdot\text{m}^3\cdot\text{kg H}_2\text{O}} \times \text{CMM} \times \Delta W_M$$

Total Heat Equations

$$\text{Total Heat (Btu/h)} = H_T = 4.5\,\frac{\text{lb}\cdot\text{min}}{\text{Hr}\cdot\text{ft}^3} \times \text{CFM} \times \Delta h$$

$$\text{Total Heat (kJ/h)} = H_{TM} = 72.09\,\frac{\text{kg}\cdot\text{min}}{\text{Hr}\cdot\text{m}^3} \times \text{CMM} \times \Delta h_M$$

$$H_T = H_s + H_L$$

$$H_{TM} = H_{SM} + H_{LM}$$

English/Metric Waterside System Equation Comparison

$$\text{Total Heat (Btu/h)} = H = 500\,\frac{\text{Btu}\cdot\text{min}}{\text{Hr}\cdot\text{gal}\cdot{}^\circ\text{F}} \times \text{GPM} \times \Delta T$$

$$\text{Total Heat (kJ/h)} = H_M = 250.8\,\frac{\text{kJ}\cdot\text{min}}{\text{Hr}\cdot\text{Liters}\cdot{}^\circ\text{C}} \times \text{LPM} \times \Delta T_M$$

English/Metric Air Change Rate Equation Comparison

$$\text{Air Change Rate per Hour – English} = \frac{AC}{HR} = \frac{\text{CFM} \times 60\,\frac{\text{min}}{\text{h}}}{\text{VOLUME}}$$

$$\text{Air Change Rate per Hour – Metric} = \frac{AC}{HR_M} = \frac{\text{CMM} \times 60\,\frac{\text{min}}{\text{h}}}{\text{VOLUME}_M}$$

English/Metric Temperature and Other Conversions

$$^{o}\textrm{F}=1.8^{o}\textrm{C}+32$$

$$^\circ\mathrm{C} = \frac{^\circ\mathrm{F} - 32}{1.8}$$

Steam and Condensate Equations

A. General

$$\text{LBS.STM./HR} = \frac{\text{BTU/HR}}{H_{FG}} = \frac{\text{BTU/HR}}{960}$$

$$\text{LBS.STM.COND./HR} = \frac{\text{EDR}}{4}$$

$$\text{Equivalent Direct Radiation} = \text{EDR} = \frac{\text{BTU/HR}}{240}$$

$$\text{LBS.STM.COND./HR} = \frac{\text{GPM} \times 500 \times \text{SP.GR.} \times C_w \times \Delta T}{H_{FG}}$$

$$\text{LBS.STM.COND./HR} = \frac{\text{CFM} \times 60 \times D \times C_a \times \Delta T}{H_{FG}}$$

B. Approximating Condensate Loads

$$\text{LBS.STM.COND./HR} = \frac{\text{GPM (WATER)} \times \Delta T}{2}$$

$$\text{LBS.STM.COND./HR} = \frac{\text{GPM (FUEL OIL)} \times \Delta T}{4}$$

$$\text{LBS.STM.COND./HR} = \frac{\text{CFM (AIR)} \times \Delta T}{900}$$

Building Envelope Heating Equation and R-Values/U-Values

$$\text{Heat Flow} = H = U \times A \times \Delta T$$

$$\text{R-Value} = R = \frac{1}{C} = \frac{1}{K} \times \text{Thickness (in.)}$$

$$R = \frac{1}{\sum R}$$

Fan Laws

$$\frac{\text{CFM}_2}{\text{CFM}_1} = \frac{\text{RPM}_2}{\text{RPM}_1}$$

$$\frac{\text{SP}_2}{\text{SP}_1} = \left(\frac{\text{CFM}_2}{\text{CFM}_1}\right)^2 = \left(\frac{\text{RPM}_2}{\text{RPM}_1}\right)^2$$

$$\frac{\text{BHP}_2}{\text{BHP}_1} = \left(\frac{\text{CFM}_2}{\text{CFM}_1}\right)^3 = \left(\frac{\text{RPM}_2}{\text{RPM}_1}\right)^3 = \left(\frac{\text{SP}_2}{\text{SP}_1}\right)^{1.5}$$

$$\text{BHP} = \frac{\text{CFM} \times \text{SP} \times \text{SP.GR.}}{6356 \times \text{FAN}_{\text{EFF}}}$$

$$\text{MHP} = \frac{\text{BHP}}{\text{M/D}_{\text{EFF}}}$$

Pump Laws

$$\frac{\text{GPM}_2}{\text{GPM}_1} = \frac{\text{RPM}_2}{\text{RPM}_1}$$

$$\frac{\text{HD}_2}{\text{HD}_1} = \left(\frac{\text{GPM}_2}{\text{GPM}_1}\right)^2 = \left(\frac{\text{RPM}_2}{\text{RPM}_1}\right)^2$$

$$\frac{\text{BHP}_2}{\text{BHP}_1} = \left(\frac{\text{GPM}_2}{\text{GPM}_1}\right)^3 = \left(\frac{\text{RPM}_2}{\text{RPM}_1}\right)^3 = \left(\frac{\text{HD}_2}{\text{HD}_1}\right)^{1.5}$$

$$\text{BHP} = \frac{\text{GPM} \times \text{HD} \times \text{SP.GR.}}{3960 \times \text{PUMP}_{\text{EFF}}}$$

$$\text{MHP} = \frac{\text{BHP}}{\text{M/D}_{\text{EFF}}}$$

$$\text{VH} = \frac{V^2}{2g}$$

$$\text{HD} = \frac{P \times 2.31}{\text{SP.GR.}}$$

Pump Net Positive Suction Head (NPSH) Calculations

$$\text{NPSH}_{\text{AVAIL}} > \text{NPSH}_{\text{REQ'D}}$$

NPSHAVAIL	= HA ± HS – HF – HVP
NPSHAVAIL	= net positive suction available at pump (feet)
NPSHREQ'D	= net positive suction required at pump (feet)
HA	= pressure at liquid surface (feet – 34 feet for water at atmospheric pressure)
HS	= height of liquid surface above (+) or below (–) pump (feet)
HF	= friction loss between pump and source (feet)
HVP	= absolute pressure of water vapor at liquid temperature (feet – ASHRAE Fundamentals)
Note: Calculations may also be performed in psig, provided that all values are in psig.

Mixed Air Temperature

$$T_{MA} = \left(T_{ROOM} \times \frac{\text{CFM}_{RA}}{\text{CFM}_{SA}}\right) + \left(T_{OA} \times \frac{\text{CFM}_{OA}}{\text{CFM}_{SA}}\right)$$

$$T_{MA} = \left(T_{RA} \times \frac{\text{CFM}_{RA}}{\text{CFM}_{SA}}\right) + \left(T_{OA} \times \frac{\text{CFM}_{OA}}{\text{CFM}_{SA}}\right)$$

Psychrometric Equations

$$W = 0.622 \,\frac{P_w}{P - P_w}$$

$$\text{RH} \cong \frac{W_{\text{ACTUAL}}}{W_{\text{SAT}}} \times 100\%$$

$$\text{RH} = \frac{P_w}{P_{\text{SAT}}} \times 100\%$$

$$H_s = m \times c_p \times \Delta T$$

$$H_L = L_v \times m \times \Delta W$$

$$H_T = m \times \Delta h$$

$$W = \frac{(2501 - 2.381\,T_{WB})\,(W_{SAT\,WB}) - (T_{DB} - T_{WB})}{(2501 + 1.805\,T_{DB} - 4.186\,T_{WB})}$$

$$W = \frac{(1093 - 0.556\,T_{WB})\,(W_{SAT\,WB}) - 0.240\,(T_{DB} - T_{WB})}{(1093 + 0.444\,T_{DB} - T_{WB})}$$

Ductwork Equations

$$TP = SP + VP$$

$$VP = \left(\frac{V}{4005}\right)^2 = \frac{V^2}{(4005)^2}$$

$$V = \frac{Q}{A} = \frac{Q \times 144}{W \times H}$$

$$D_{EQ} = \frac{1.3 \times (A \times B)^{0.625}}{(A + B)^{0.25}}$$

Equations for Flat Oval Ductwork

 

 

$$FS = \text{MAJOR} - \text{MINOR}$$

$$A = \frac{(FS \times \text{MINOR}) + \frac{\pi \times \text{MINOR}^2}{4}}{144}$$

$$P = \frac{(\pi \times \text{MINOR}) + (2 \times FS)}{12}$$

$$D_{EQ} = \frac{1.55 \times A^{0.625}}{P^{0.25}}$$

Steel Pipe Equations

Steam and Steam Condensate Pipe Sizing Equations

A. Steam Pipe Sizing Equations

$$\Delta P = \frac{0.01306 \times W^2 \left(1 + \frac{3.6}{ID}\right)}{3600 \times D \times ID^5}$$

$$W = 60 \times \sqrt{\frac{\Delta P \times D \times ID^5}{0.01306 \times \left(1 + \frac{3.6}{ID}\right)}}$$

$$W = 0.41667 \times V \times A_{\text{INCHES}} \times D = 60 \times V \times A_{\text{FEET}} \times D$$

$$V = \frac{2.4 \times W}{A_{\text{INCHES}} \times D} = \frac{W}{60 \times A_{\text{FEET}} \times D}$$

B. Steam Condensate Pipe Sizing Equations

$$FS = \frac{H_{S(SS)} - H_{S(CR)}}{H_{L(CR)}} \times 100$$

$$W_{CR} = \frac{FS}{100} \times W$$

Air Conditioning Condensate

$$\text{GPM}_{AC\,COND} = \frac{\text{CFM} \times \Delta W_{\text{LB}}}{SpV \times 8.33}$$

$$\text{GPM}_{AC\,COND} = \frac{\text{CFM} \times \Delta W_{\text{GR}}}{SpV \times 8.33 \times 7000}$$

Humidification

$$\text{GRAINS}_{\text{REQ'D}} = \left(\frac{W_{\text{GR}}}{SpV}\right)_{\text{ROOM AIR}} - \left(\frac{W_{\text{GR}}}{SpV}\right)_{\text{SUPPLY AIR}}$$

$$\text{POUNDS}_{\text{REQ'D}} = \left(\frac{W_{\text{LB}}}{SpV}\right)_{\text{ROOM AIR}} - \left(\frac{W_{\text{LB}}}{SpV}\right)_{\text{SUPPLY AIR}}$$

$$\text{LBS.STM./HR} = \frac{\text{CFM} \times \text{GRAINS}_{\text{REQ'D}} \times 60}{7000} = \text{CFM} \times \text{POUNDS}_{\text{REQ'D}} \times 60$$

Humidifier Sensible Heat Gain

$$H_s = (0.244 \times Q \times \Delta T) + (L \times 380)$$

Expansion Tanks

$$\text{CLOSED } V_T = V_s \times \frac{\left[\left(\frac{v_2}{v_1}\right) - 1\right] - 3\alpha \Delta T}{\left(\frac{P_A}{P_1} - \frac{P_A}{P_2}\right)}$$

$$\text{OPEN } V_T = 2 \left\{ V_s \left[ \left(\frac{v_2}{v_1}\right) - 1 \right] - 3\alpha \Delta T \right\}$$

$$\text{DIAPHRAGM } V_T = V_s\times \frac{\left[ \left(\frac{v_2}{v_1}\right) - 1 \right] - 3\alpha \Delta T}{1 - \left(\frac{P_1}{P_2}\right)}$$

Air Balance Equations

Efficiencies

$$\text{COP} = \frac{\text{BTU OUTPUT}}{\text{BTU INPUT}} = \frac{\text{EER}}{3.413}$$

$$\text{EER} = \frac{\text{BTU OUTPUT}}{\text{WATTS INPUT}} = \text{COP} \times 3.413$$

$$\text{kW/TON} = \frac{12{,}000\ \text{BTU/HR TON}}{\text{COP} \times 3{,}517\ \text{BTU/HR kW}}$$

$$\text{Turndown Ratio} = \text{Maximum Firing Rate} : \text{Minimum Firing Rate}$$

$$\text{OVERALL THERMAL EFF.} = \frac{\text{GROSS BTU OUTPUT}}{\text{GROSS BTU INPUT}} \times 100\%$$

$$\text{COMBUSTION EFF.} = \frac{\text{BTU INPUT} - \text{BTU STACK LOSS}}{\text{BTU INPUT}} \times 100\%$$

$$\text{Overall Thermal Efficiency Range} = 75\% - 90\%$$

$$\text{Combustion Efficiency Range} = 85\% - 95\%$$

Cooling Towers and Heat Exchangers

$$\text{APPROACH}_{\text{CT'S}} = \text{LWT} - \text{AWB}$$

$$\text{APPROACH}_{\text{HE'S}} = \text{EWT}_{HS} - \text{LWT}_{CS}$$

$$\text{RANGE} = \text{EWT} - \text{LWT}$$

Cooling Tower/Evaporative Cooler Blowdown Equations

$$C = \frac{E + D + B}{D + B}$$

$$B = \frac{E - \left[(C - 1) \times D\right]}{C - 1}$$

Electricity

A. General

B. Single-Phase Power

$$\text{kW}_{1\phi} = \frac{V \times A \times PF}{1000}$$

$$\text{kVA}_{1\phi} = \frac{V \times A}{1000}$$

$$\text{BHP}_{1\phi} = \frac{V \times A \times PF \times \text{DEVICE}_{\text{EFF}}}{746}$$

$$\text{MHP}_{1\phi} = \frac{\text{BHP}_{1\phi}}{\text{M/D}_{\text{EFF}}}$$

C. Three-Phase Power

$$\text{kW}_{3\phi} = \frac{\sqrt{3} \times V \times A \times PF}{1000}$$

$$\text{kVA}_{3\phi} = \frac{\sqrt{3} \times V \times A}{1000}$$

$$\text{BHP}_{3\phi} = \frac{\sqrt{3} \times V \times A \times PF \times \text{DEVICE}_{\text{EFF}}}{746}$$

$$\text{MHP}_{3\phi} = \frac{\text{BHP}_{3\phi}}{\text{M/D}_{\text{EFF}}}$$

Moisture Condensation on Glass

$$T_{\text{GLASS}} = T_{\text{ROOM}} - \left[\frac{R_{IA}}{R_{\text{GLASS}}} \times (T_{\text{ROOM}} - T_{OA})\right]$$

$$T_{\text{GLASS}} = T_{\text{ROOM}} - \left[\frac{U_{\text{GLASS}}}{U_{IA}} \times (T_{\text{ROOM}} - T_{OA})\right]$$

$$\text{If } T_{\text{GLASS}} < DP_{\text{ROOM}}, \text{ condensation occurs}$$

Calculating Heating Loads for Loading Docks, Heavily Used Vestibules and Similar Spaces

• Find volume of space to be heated (cu.ft.).
• Determine acceptable warm-up time for space (min.).
• Divide volume by time (CFM).
• Determine inside and outside design temperatures—assume inside space temperature has dropped to the outside design temperature because doors have been open for an extended period of time.
• Use sensible heat equation to determine heating requirement using CFM and inside and outside design temperatures determined earlier in this Part.

Ventilation of Mechanical Rooms with Refrigeration Equipment

A.    For a more detailed description of ventilation requirements for mechanical rooms with refrigeration equipment, see ASHRAE Standard 15 and Part 8.

      B.    Completely Enclosed Equipment Rooms

C.    Partially Enclosed Equipment Rooms

Pipe Expansion Equations

A. L-Bends

 

 

B. Z-Bends

 

C. U-Bends or Expansion Loops

 

Relief Valve Vent Line Maximum Length

$$L = \frac{9 \times P_1^2 \times D^5}{C^2} = \frac{9 \times P_2^2 \times D^5}{16 \times C^2}$$

Relief Valve Sizing

A. Liquid System Relief Valves—Spring-Style Relief Valves

$$A = \frac{\text{GPM} \times \sqrt{G}}{28.14 \times K_B \times K_V \times \sqrt{\Delta P}}$$

B. Liquid System Relief Valves—Pilot-Operated Relief Valves

$$A = \frac{\text{GPM} \times \sqrt{G}}{36.81 \times K_V \times \sqrt{\Delta P}}$$

C. Steam System Relief Valves

$$A = \frac{W}{51.5 \times K \times P \times K_{SH} \times K_N \times K_B}$$

D. Gas and Vapor System Relief Valves—lbs./h

$$A = \frac{W \times \sqrt{TZ}}{C \times K \times P \times K_B \times \sqrt{M}}$$

E. Gas and Vapor System Relief Valves—SCFM

$$A = \frac{\text{SCFM} \times \sqrt{TGZ}}{1.175 \times C \times K \times P \times K_B}$$

F. Relief Valve Equation Definitions

1. A	= Minimum required effective relief valve discharge area (sq.in.)
2. GPM	= Required relieving capacity at flow conditions (gal./min.)
3. W	= Required relieving capacity at flow conditions (lbs./h)
4. SCFM	= Required relieving capacity at flow conditions (standard cu.ft./min.)
5. G	= Specific gravity of liquid, gas, or vapor at flow conditions Water = 1.0 for most HVAC applications Air = 1.0
6. C	= Coefficient determined from expression of ratio of specific heats C = 315 if value is unknown
7. K	= Effective coefficient of discharge K = 0.975
8. KB	= Capacity correction factor due to back pressure KB = 1.0 for atmospheric discharge systems
9. KV	= Flow correction factor due to viscosity KV = 0.9 to 1.0 for most HVAC applications with water
10. KN	= Capacity correction factor for dry saturated steam at set pressures above 1500 psia and up to 3200 psia KN = 1.0 for most HVAC applications
11. KSH	= Capacity correction factor due to the degree of superheat KSH = 1.0 for saturated steam
12. Z	= Compressibility factor Z = 1.0 if value is unknown
13. P	= Relieving pressure (psia) P = Set pressure (psig) + over pressure (10% psig) + atmospheric pressure (14.7 psia)
14. ΔP	= Differential pressure (psig) ΔP = Set pressure (psig) + over pressure (10% psig) – back pressure (psig)
15. T	= Absolute temperature (°R = °F + 460)
16. M	= Molecular weight of the gas or vapor

G. Relief Valve Sizing Notes

• When multiple relief valves are used, one valve shall be set at or below the maximum allowable working pressure, and the remaining valves may be set up to 5 percent over the maximum allowable working pressure.
• When sizing multiple relief valves, the total area required is calculated on an over pressure of 16 percent or 4 psi, whichever is greater.
• For superheated steam, the following correction factor values may be used:

• Gas and vapor properties

Gas or Vapor	Molecular Weight	Ratio of Specific Heats	Coefficient C	Specific Gravity
Acetylene	26.04	1.25	342	0.899
Air	28.97	1.40	356	1.000
Ammonia (R-717)	17.03	1.30	347	0.588
Argon	39.94	1.66	377	1.379
Benzene	78.11	1.12	329	2.696
N-Butane	58.12	1.18	335	2.006
Iso-Butane	58.12	1.19	336	2.006
Carbon Dioxide	44.01	1.29	346	1.519
Carbon Disulphide	76.13	1.21	338	2.628
Carbon Monoxide	28.01	1.40	356	0.967
Chlorine	70.90	1.35	352	2.447
Cyclohexane	84.16	1.08	325	2.905
Ethane	30.07	1.19	336	1.038
Ethyl Alcohol	46.07	1.13	330	1.590
Ethyl Chloride	64.52	1.19	336	2.227
Ethylene	28.03	1.24	341	0.968
Helium	4.02	1.66	377	0.139
N-Heptane	100.20	1.05	321	3.459
Hexane	86.17	1.06	322	2.974
Hydrochloric Acid	36.47	1.41	357	1.259
Hydrogen	2.02	1.41	357	0.070
Hydrogen Chloride	36.47	1.41	357	1.259
Hydrogen Sulphide	34.08	1.32	349	1.176
Methane	16.04	1.31	348	0.554
Methyl Alcohol	32.04	1.20	337	1.106
Methyl Butane	72.15	1.08	325	2.491
Methyl Chloride	50.49	1.20	337	1.743
Natural Gas	19.00	1.27	344	0.656
Nitric Oxide	30.00	1.40	356	1.036
Nitrogen	28.02	1.40	356	0.967
Nitrous Oxide	44.02	1.31	348	1.520
N-Octane	114.22	1.05	321	3.943
Oxygen	32.00	1.40	356	1.105
N-Pentane	72.15	1.08	325	2.491
Iso-Pentane	72.15	1.08	325	2.491
Propane	44.09	1.13	330	1.522
R-11	137.37	1.14	331	4.742
R-12	120.92	1.14	331	4.174
R-22	86.48	1.18	335	2.985
R-114	170.93	1.09	326	5.900
R-123	152.93	1.10	327	5.279
R-134a	102.03	1.20	337	3.522
Sulfur Dioxide	64.04	1.27	344	2.211
Toluene	92.13	1.09	326	3.180

Motor Drive Formulas

$$DFP \times RPM_{FP} = DMP \times RPM_{MP}$$

$$BL = \left[(DFP + DMP) \times 1.5708\right] + (2 \times L)$$

Domestic Water Heater Sizing

$$H_{\text{OUTPUT}} = \text{GPH} \times 8.34\,\frac{\text{LBS}}{\text{GAL}} \times \Delta T \times 1.0$$

$$H_{\text{INPUT}} = \frac{\text{GPH} \times 8.34\,\frac{\text{LBS}}{\text{GAL}} \times \Delta T}{\% \text{EFFICIENCY}}$$

$$\text{GPH} = \frac{H_{\text{INPUT}} \times \% \text{EFFICIENCY}}{\Delta T \times 8.34\,\frac{\text{LBS}}{\text{GAL}}} = \frac{\text{kW} \times 3413\,\frac{\text{BTU}}{\text{kW}}}{\Delta T \times 8.34\,\frac{\text{LBS}}{\text{GAL}}}$$

$$\Delta T = \frac{H_{\text{INPUT}} \times \% \text{EFFICIENCY}}{\text{GPH} \times 8.34\,\frac{\text{LBS}}{\text{GAL}}} = \frac{\text{kW} \times 3413\,\frac{\text{BTU}}{\text{kW}}}{\text{GPH} \times 8.34\,\frac{\text{LBS}}{\text{GAL}}}$$

$$\text{kW} = \frac{\text{GPH} \times 8.34\,\frac{\text{LBS}}{\text{GAL}} \times \Delta T \times 1.0}{3413\,\frac{\text{BTU}}{\text{kW}}}$$

$$\% \text{COLD WATER} = \frac{T_{\text{HOT}} - T_{\text{MIX}}}{T_{\text{HOT}} - T_{\text{COLD}}}$$

$$\% \text{HOT WATER} = \frac{T_{\text{MIX}} - T_{\text{COLD}}}{T_{\text{HOT}} - T_{\text{COLD}}}$$

Domestic Hot Water Recirculation Pump/Supply Sizing

• Determine the approximate total length of all hot water supply and return piping.
• Multiply this total length by 30 Btu/ft. for insulated pipe and 60 Btu/ft. for uninsulated pipe to obtain the approximate heat loss.
• Divide the total heat loss by 10,000 to obtain the total pump capacity in GPM.
• Select a circulating pump to provide the total required GPM and obtain the head created at this flow.
• Multiply the head by 100 and divide by the total length of the longest run of the hot water return piping to determine the allowable friction loss per 100 feet of pipe.
• Determine the required GPM in each circulating loop and size the hot water return pipe based on this GPM and the allowable friction loss as determined earlier.

Swimming Pools

A. Sizing Outdoor Pool Heater

• Determine pool capacity in gallons – obtain from architect if available.

Length × Width × Depth × 7.5 gal./cu.ft. (If depth is not known, assume an average depth of 5.5 feet.)

• Determine heat pick-up time in hours from owner.
• Determine pool water temperature in °F from the owner. If owner does not specify temperature, assume 80°F.
• Determine the average air temperature on the coldest month in which the pool will be used.
• Determine the average wind velocity in miles per hour. For pools less than 900 square feet and where the pool is sheltered by nearby buildings, fences, shrubs, etc., from the prevailing wind, an average wind velocity of less than 3.5 mph may be assumed. The surface heat loss factor of 5.5 Btu/hr.sq.ft. °F in the following equation assumes a wind velocity of 3.5 mph. If a wind velocity of less than 3.5 mph is used, multiply the equation by 0.75; for 5.0 mph, multiply the equation by 1.25; and for 10 mph, multiply the equation by 2.0.
• Pool heater equations:

$$H_{\text{POOLHEATER}} = H_{\text{HEAT-UP}} + H_{\text{SURFACE LOSS}}$$

$$H_{\text{HEAT-UP}} = \frac{\text{GAL} \times 8.34\,\frac{\text{LBS}}{\text{GAL}} \times \Delta T_{\text{WATER}} \times 1.0\,\frac{\text{BTU}}{\text{LBS}\cdot^\circ\text{F}}}{\text{HEAT PICK-UP TIME}}$$

$$H_{\text{SURFACE LOSS}} = 5.5\,\frac{\text{BTU}}{\text{HR}\cdot\text{SQ.FT}\cdot^\circ\text{F}} \times \Delta T_{\text{WATER/AIR}} \times \text{POOL AREA}$$

$$\Delta T_{\text{WATER}} = T_{\text{FINAL}} - T_{\text{INITIAL}}$$

$$T_{\text{FINAL}} = \text{POOL WATER TEMPERATURE}$$

$$T_{\text{INITIAL}} = 50^\circ\text{F}$$

$$\Delta T_{\text{WATER/AIR}} = T_{\text{FINAL}} - T_{\text{AVERAGE AIR}}$$