HVAC - Equations,Data,and Rules of Thumb (PDF COPY)

 

HVAC - Equations, Data, and Rules of Thumb

Heating, Ventilation, and Air Conditioning (HVAC) systems are designed based on fundamental principles of thermodynamics, fluid mechanics, and heat transfer. Engineers and technicians use standard equations, empirical data, and industry rules of thumb to size and optimize HVAC systems efficiently.

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1. Key HVAC Equations

1.1 Heat Transfer Equations

1. Sensible Heat Transfer (Air Heating/Cooling)

   $$Q_s = 1.08 \times CFM \times \Delta T$$

   Where:

   • $Q_s$ = Sensible heat (BTU/hr)
   • $CFM$ = Airflow (Cubic Feet per Minute)
   • $\Delta T$ = Temperature difference (°F)

2. Latent Heat Transfer (Moisture Removal/Dehumidification)

   $$Q_l = 0.68 \times CFM \times \Delta W$$

   Where:

   • $Q_l$ = Latent heat (BTU/hr)
   • $\Delta W$ = Change in humidity ratio (grains/lb of dry air)

3. Total Cooling Load

   $$Q_t = 4.5 \times CFM \times \Delta h$$

   Where:

   • $Q_t$ = Total cooling load (BTU/hr)
   • $\Delta h$ = Enthalpy difference (BTU/lb of dry air)

4. Conduction Heat Transfer (Walls, Roofs, etc.)

   $$Q = U \times A \times \Delta T$$

   Where:

   • $U$ = Overall heat transfer coefficient (BTU/hr·ft²·°F)
   • $A$ = Surface area (ft²)

5. Radiant Heat Gain (Sun Load Through Windows)

   $$Q = SHGF \times A \times SC$$

   Where:

   • $SHGF$ = Solar Heat Gain Factor (BTU/hr·ft²)
   • $SC$ = Shading Coefficient

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1.2 Airflow and Duct Sizing Equations

1. Continuity Equation for Airflow

   $$Q = V \times A$$

   Where:

   • $Q$ = Airflow (CFM)
   • $V$ = Air velocity (ft/min)
   • $A$ = Duct cross-sectional area (ft²)

2. Duct Friction Loss (Darcy-Weisbach)

   $$h_f = \frac{f L V^2}{2g D}$$

   Where:

   • $h_f$ = Friction loss (ft)
   • $f$ = Friction factor
   • $L$ = Duct length (ft)
   • $D$ = Duct diameter (ft)

3. Fan Laws

   $$CFM_2 = CFM_1 \times \frac{RPM_2}{RPM_1}$$ $$SP_2 = SP_1 \times \left(\frac{RPM_2}{RPM_1}\right)^2$$ $$BHP_2 = BHP_1 \times \left(\frac{RPM_2}{RPM_1}\right)^3$$

   Where:

   • $SP$ = Static pressure
   • $BHP$ = Fan brake horsepower

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1.3 Psychrometrics (Moist Air Properties)

1. Relative Humidity (%)

   $$RH = \frac{Pw}{Pws} \times 100$$

   Where:

   • $Pw$ = Partial pressure of water vapor
   • $Pws$ = Saturation pressure at the given temperature

2. Dew Point Temperature (°F)

   $$T_d = T - \frac{(100 - RH)}{5}$$

3. Enthalpy of Moist Air

   $$h = 0.24T + W(1061 + 0.444T)$$

   Where:

   • $W$ = Humidity ratio (lb of water/lb of dry air)

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2. Common HVAC Design Data

1. Standard Air Properties

   • Air Density: 0.075 lb/ft³
   • Specific Heat of Air: 0.24 BTU/lb·°F
   • Standard Atmospheric Pressure: 14.7 psi (101.3 kPa)
   • Standard Airflow per Ton of Cooling: 400 CFM/ton

2. Typical Indoor Conditions

   • Comfort Cooling: 75°F, 50% RH
   • Server Room: 68°F, 40% RH
   • Operating Room: 60-65°F, 50-60% RH

3. Ventilation Airflow Rates (ASHRAE 62.1)

   • Office Spaces: 5-20 CFM per person
   • Restaurants: 15-20 CFM per person
   • Hospital Rooms: 25-30 CFM per person

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3. HVAC Rules of Thumb

Cooling Load Estimates

1. Cooling Load (Commercial Buildings):

   • 500-600 sq. ft per ton (for well-insulated buildings)
   • 300-400 sq. ft per ton (for older or poorly insulated buildings)
   • 1 ton = 12,000 BTU/hr

2. Cooling Load (Residential):

   • 1 ton per 400-600 sq. ft in moderate climates
   • 1 ton per 300-400 sq. ft in hot/humid climates

Heating Load Estimates

1. Heating Load (Residential/Commercial):
   • 30-60 BTU/hr per sq. ft (depending on insulation and climate)
   • Average Heating System Sizing:
     • Cold Climate: 40-50 BTU/hr per sq. ft
     • Moderate Climate: 30-40 BTU/hr per sq. ft

Ventilation & Air Exchange

1. Air Changes per Hour (ACH) Guidelines:

   • Offices: 4-6 ACH
   • Restaurants: 8-12 ACH
   • Hospital Operating Rooms: 20-30 ACH

2. Fresh Air Requirements:

   • ASHRAE Standard 62.1 recommends 15-20 CFM per person for most indoor spaces.

Ductwork & Fan Rules of Thumb

1. Duct Velocity Guidelines:

   • Main Supply Ducts: 1,000-1,500 ft/min
   • Branch Ducts: 600-900 ft/min
   • Return Ducts: 500-700 ft/min

2. Fan Selection:

   • 1 CFM requires ~0.25 Watts of fan power
   • Fans lose efficiency if static pressure exceeds 1 in. w.g.

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Conclusion

These equations, data points, and rules of thumb provide a foundational approach for HVAC design and troubleshooting. While these estimates are helpful for quick calculations, detailed load calculations using software like Carrier HAP, Trane TRACE 700, or ASHRAE Handbook methodologies ensure precise system performance.

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HVAC - Equations, Data, and Rules of Thumb