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Home / HVAC Engineering Formulas & Equations Reference
Thermodynamic Equations & Physics

HVAC/R Engineering Formulas & Solvers

Comprehensive thermodynamic equations, heat transfer relations, psychrometrics, and hydronic formulas reference compiled for field engineers, energy auditors, and plant managers in Pune.

Instant Equation Engine

Sensible & Latent Heat Load Equation Solver

Solve Q_s = 1.08 ร— CFM ร— ฮ”T and compute airflow tonnage directly.

Sensible Capacity (Q_s)
25,920 BTU/hr
Equivalent Sized Tonnage
2.16 TR
Metric KW Equivalent
7.60 kW

Master Equations Directory

Air Dynamics ๐Ÿ“ Metric

Sensible Heat Formula (Air)

Q_s = 1.08 ร— CFM ร— ฮ”T
Units: BTU/hr (CFM in cubic ft/min, ฮ”T in ยฐF)

Calculates heat required to raise or lower dry air temperature without moisture phase change.

Field Example: At 400 CFM/ton with a 20ยฐF split: Q_s = 1.08 ร— 400 ร— 20 = 8,640 BTU/hr.
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Air Dynamics ๐Ÿ“ Metric

Latent Heat Formula (Moisture)

Q_l = 4,840 ร— CFM ร— ฮ”W
Units: BTU/hr (ฮ”W in lb water vapor per lb dry air)

Calculates heat absorbed or released when water vapor condenses on the evaporator coil.

Field Example: Moisture removal across coil with 0.003 lb/lb humidity change: Q_l = 4840 ร— 400 ร— 0.003 = 5,808 BTU/hr.
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Air Dynamics ๐Ÿ“ Metric

Total Enthalpy Heat Transfer

Q_total = 4.5 ร— CFM ร— ฮ”h
Units: BTU/hr (ฮ”h in BTU/lb dry air)

Total sensible plus latent cooling capacity based on entering and leaving air enthalpy.

Field Example: CFM = 1,200 (3-Ton unit), ฮ”h = 6.8 BTU/lb: Q = 4.5 ร— 1200 ร— 6.8 = 36,720 BTU/hr (~3.06 TR).
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Hydronics & Water Chillers ๐Ÿ“ Metric

Chilled Water Heat Transfer

Q = 500 ร— GPM ร— ฮ”T
Units: BTU/hr (GPM in gal/min, ฮ”T in ยฐF)

Standard hydronic formula for chilled water and cooling tower loop heat rejection.

Field Example: 100 TR chiller operating with 10ยฐF delta-T: GPM = (100 ร— 12,000) / (500 ร— 10) = 240 GPM.
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Hydronics & Water Chillers ๐Ÿ“ Metric

Hydronic Flow Rate Rule of Thumb

GPM = (Tons TR ร— 24) / ฮ”T
Units: GPM (Typically 2.4 GPM/ton for 10ยฐF ฮ”T)

Quick sizing equation for primary and secondary chilled water circulating pumps.

Field Example: 50 TR chiller requires: (50 ร— 24) / 10 = 120 GPM.
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Air Distribution ๐Ÿ“ Metric

Duct Air Velocity

Velocity (FPM) = CFM / Area (sq.ft)
Units: Feet Per Minute (FPM)

Determines duct air speed. Recommended: 700-900 FPM for residential main ducts; 1000-1500 FPM for commercial.

Field Example: 1,200 CFM through a 16"x12" duct (1.33 sq.ft): V = 1200 / 1.33 = 902 FPM.
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Air Distribution ๐Ÿ“ Metric

Fan Law 1 (Airflow vs RPM)

CFMโ‚‚ = CFMโ‚ ร— (RPMโ‚‚ / RPMโ‚)
Units: Direct proportional airflow scaling

Airflow volume varies directly with fan speed ratio.

Field Example: Speeding fan up from 900 to 1,000 RPM increases 1,800 CFM to 2,000 CFM.
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Air Distribution ๐Ÿ“ Metric

Fan Law 3 (Power Consumption vs RPM)

BHPโ‚‚ = BHPโ‚ ร— (RPMโ‚‚ / RPMโ‚)ยณ
Units: Cubic horsepower demand increase

Motor horsepower increases with the cube of speed! A 20% speed boost requires 73% more electrical power.

Field Example: 1.5 HP motor at 1,000 RPM takes: 1.5 ร— (1200/1000)ยณ = 2.59 HP at 1,200 RPM.
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Refrigeration Diagnostics ๐Ÿ“ Metric

Suction Line Superheat

Superheat = T_suction_temp - T_evap_saturation
Units: ยฐF or ยฐC temperature difference

Indicates TXV metering valve operation. Target: 8ยฐF to 14ยฐF at compressor service valve.

Field Example: R-32 at 118 PSI sat temp = 40ยฐF. Measured line pipe temp = 52ยฐF. Superheat = 52 - 40 = 12ยฐF (Normal).
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Refrigeration Diagnostics ๐Ÿ“ Metric

Liquid Line Subcooling

Subcooling = T_cond_saturation - T_liquid_temp
Units: ยฐF or ยฐC temperature difference

Indicates refrigerant charge amount. Target: 10ยฐF to 15ยฐF on TXV systems.

Field Example: R-410A at 380 PSI sat temp = 112ยฐF. Measured liquid copper line = 98ยฐF. Subcooling = 112 - 98 = 14ยฐF (Correct charge).
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Refrigeration Diagnostics ๐Ÿ“ Metric

Compression Ratio (CR)

CR = (P_discharge + 14.7) / (P_suction + 14.7)
Units: Absolute pressure ratio

Ratio of head pressure to suction pressure. High ratios (> 4.5) overheat compressor oil and cause valve failure.

Field Example: Discharge 350 PSI, Suction 120 PSI: CR = (350 + 14.7) / (120 + 14.7) = 364.7 / 134.7 = 2.71 (Optimal).
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Energy Efficiency ๐Ÿ“ Metric

Coefficient of Performance to EER

EER = COP ร— 3.41214
Units: BTU/Watt-hr per COP unit

Direct conversion between thermodynamic COP and laboratory rating EER.

Field Example: Chiller COP of 5.20 corresponds to EER = 5.20 ร— 3.412 = 17.74 EER.
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Energy Efficiency ๐Ÿ“ Metric

Chiller Specific Consumption (IKW/TR)

IKW/TR = 3.517 / COP
Units: kW input per Ton of Refrigeration

Primary energy metric for central water-cooled and air-cooled chillers in India. Target: < 0.65 for water-cooled.

Field Example: Chiller COP of 5.5: IKW/TR = 3.517 / 5.5 = 0.639 kW/TR (High Efficiency).
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Heat Rejection ๐Ÿ“ Metric

Cooling Tower Approach

Approach = T_water_leaving - T_ambient_wet_bulb
Units: ยฐF or ยฐC temperature approach

Measures cooling tower heat rejection efficiency. Typical good performance is within 3ยฐC to 5ยฐC of wet bulb.

Field Example: Ambient wet bulb 25ยฐC, cold water leaving tower 29ยฐC: Approach = 29 - 25 = 4ยฐC (Normal).
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