2.3 Psychrometric Processes & Air Mixture Calculations

2.3 Psychrometric Processes & Air Mixture Calculations

[!NOTE] Engineering Applied Psychrometrics: In practical HVAC contracting, psychrometric processes represent the physical changes that air undergoes as it passes through blowers, filters, heating exchangers, cooling coils, humidifiers, and mixing plenums. Thermodynamic calculations establish whether a system meets sensible cooling, latent dehumidification, and outdoor ventilation code mandates. Mastering airflow heat formulas and mixed-air equations is mandatory for passing the Arkansas HVAC/R Contractor License exam.

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The Psychrometric Process Compass

Every environmental conditioning process traces a distinct vector path across the psychrometric chart. Understanding the directional movement across the chart enables rapid visual diagnosis of system behavior.

                             Sensible Humidification
                                       ▲ (Pure Moisture Addition)
                                       │  [Steam Injection]
             Evaporative Cooling       │
           (Adiabatic Saturation)      │       Heating & Humidifying
           ▲                           │                           ▲
            \                          │                          /
             \                         │                         /
              \                        │                        /
   Sensible    \                       │                       /     Sensible
   Cooling      ◄──────────────────────●──────────────────────►     Heating
  (No Dehum)   /                       │                            (No Moisture)
              /                        │                        \
             /                         │                         \
            /                          │                          ▼
           ▼                           │       Chemical Dehumidification
    Cooling & Dehumidifying            │       (Desiccant Drying)
  (Standard AC Coil Process)           ▼
                             Sensible Dehumidification

The Eight Primary Psychrometric Processes

1. Pure Sensible Heating: Path moves horizontally to the right. Dry-bulb temperature increases, enthalpy increases, and relative humidity decreases. Humidity ratio ($W$) and dew-point temperature remain strictly constant because no water is added or removed (e.g., electric resistance duct heater or hot gas reheat).
2. Pure Sensible Cooling: Path moves horizontally to the left. Dry-bulb temperature decreases, enthalpy decreases, and relative humidity increases. Humidity ratio and dew point remain constant because the coil surface temperature is higher than the air's dew point (e.g., chilled water coil operating dry).
3. Pure Humidification (Steam Injection): Path moves vertically straight upward. Moisture is added with negligible sensible heat change. Humidity ratio, dew point, relative humidity, and enthalpy increase while dry-bulb temperature remains unchanged.
4. Pure Dehumidification (Solid Desiccant / Chemical): Path moves vertically straight downward (or down and slightly right). Water vapor is extracted via desiccant adsorption, lowering humidity ratio and dew point.
5. Cooling and Dehumidification (Standard AC Cycle): Path moves diagonally downward and to the left. Air passes across an evaporator coil whose surface temperature is below the entering air's dew point. Dry bulb drops (sensible cooling) and moisture condenses out on fins (latent dehumidification). Both enthalpy and humidity ratio decrease.
6. Heating and Humidification: Path moves diagonally upward and to the right. Winter air conditioning where cold outdoor air is heated by a furnace or heat pump and moisture is introduced via an evaporative or steam humidifier.
7. Cooling and Humidification (Evaporative Cooling / Swamp Cooler): Path moves upward and to the left along a constant wet-bulb / enthalpy line. Water evaporates into the airstream, absorbing its latent heat of vaporization from the sensible heat of the air. Dry-bulb drops while relative humidity and humidity ratio increase, but total enthalpy ($h$) remains constant (adiabatic process).
8. Heating and Dehumidification: Typically occurs in industrial desiccant wheel systems where moisture adsorption releases latent heat of condensation, warming the discharged dry airstream.

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Mathematical Derivations of the Standard HVAC Airflow Formulas

On the licensing examination, three fundamental heat transfer equations are applied to calculate equipment capacity and airflow rates: Sensible Heat ($Q_s$), Latent Heat ($Q_l$), and Total Heat ($Q_t$). These equations are derived directly from standard air density ($0.075\text{ lb/ft}^3$) and specific heat ($0.24\text{ BTU}/[\text{lb}\cdot^\circ\text{F}]$).

Derivation of the Sensible Heat Formula ($Q_s = 1.08 \times \text{CFM} \times \Delta T$)

Sensible heat transfer is defined as:

$Q_s = \dot{m}_{\text{air}} \times c_p \times \Delta T$

To convert volumetric airflow in Cubic Feet per Minute (CFM) to mass airflow rate in pounds of dry air per hour ($\dot{m}_{\text{air}}$):

$\dot{m}_{\text{air}} = \text{CFM} \left(\frac{\text{ft}^3}{\text{min}}\right) \times 60 \left(\frac{\text{min}}{\text{hr}}\right) \times 0.075 \left(\frac{\text{lb}_{\text{da}}}{\text{ft}^3}\right) = 4.5 \times \text{CFM} \left(\frac{\text{lb}_{\text{da}}}{\text{hr}}\right)$

Substituting this mass flow rate into the sensible equation along with the specific heat of standard dry air ($c_p = 0.24\text{ BTU}/[\text{lb}\cdot^\circ\text{F}]$):

$Q_s = (4.5 \times \text{CFM}) \times 0.24 \times \Delta T = (4.5 \times 0.24) \times \text{CFM} \times \Delta T$

$Q_s = 1.08 \times \text{CFM} \times \Delta T$

Where:

• $Q_s$ = Sensible heat capacity (BTU/hr)
• $\text{CFM}$ = Volumetric airflow rate (Cubic Feet per Minute)
• $\Delta T$ = Temperature difference between entering and leaving air ($T_{\text{entering}} - T_{\text{leaving}}$ in °F)
• $\mathbf{1.08}$ = Standard air sensible constant ($60\text{ min/hr} \times 0.075\text{ lb/ft}^3 \times 0.24\text{ BTU}/[\text{lb}\cdot^\circ\text{F}]$)

Derivation of the Total Heat Formula ($Q_t = 4.5 \times \text{CFM} \times \Delta h$)

Total heat transferred across a coil accounts for both sensible temperature drop and latent condensation, calculated directly from entering and leaving specific enthalpies ($h_1$ and $h_2$):

$Q_t = \dot{m}_{\text{air}} \times \Delta h = (4.5 \times \text{CFM}) \times (h_{\text{entering}} - h_{\text{leaving}})$

$Q_t = 4.5 \times \text{CFM} \times \Delta h$

Where:

• $Q_t$ = Total cooling capacity (BTU/hr)
• $\Delta h$ = Enthalpy difference ($h_1 - h_2$ in $\text{BTU/lb}_{\text{da}}$)
• $\mathbf{4.5}$ = Standard air mass flow constant ($60\text{ min/hr} \times 0.075\text{ lb/ft}^3$)

Derivation of the Latent Heat Formula ($Q_l = 4,840 \times \text{CFM} \times \Delta W_{\text{lb}}$ or $0.68 \times \text{CFM} \times \Delta W_{\text{grains}}$)

Latent heat transfer is the heat removed during moisture condensation:

$Q_l = \dot{m}_{\text{air}} \times h_{fg} \times \Delta W$

Where $h_{fg}$ is the latent heat of vaporization of water vapor at coil condensing temperatures (~$50^\circ\text{F}$), which equals approximately $1,075.8\text{ BTU/lb}$.

1. Using Humidity Ratio in Pounds of Moisture per Pound of Dry Air ($\Delta W_{\text{lb}}$): $Q_l = (4.5 \times \text{CFM}) \times 1,075.8 \times \Delta W_{\text{lb}} = \mathbf{4,840 \times \text{CFM} \times \Delta W_{\text{lb}}}$
2. Using Humidity Ratio in Grains of Moisture per Pound of Dry Air ($\Delta W_{\text{grains}}$): Because $1\text{ lb of water} = 7,000\text{ grains}$: $\text{Constant} = \frac{4,840}{7,000} = 0.691 \approx \mathbf{0.68}$ $Q_l = 0.68 \times \text{CFM} \times \Delta W_{\text{grains}}$

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Air Mixture Mechanics: Mixed Air Equations

In commercial HVAC systems, fresh outdoor ventilation air is introduced through an economizer or outside air damper and blended with recirculated return air in the mixing plenum before entering the cooling or heating coil. The resulting mixture condition is a direct mass-weighted average of the two converging airstreams.

Outdoor Air (OA): CFM_oa, T_oa, W_oa, h_oa
───────────────►\ 
                 \──────► Mixed Air (MA): CFM_total, T_ma, W_ma, h_ma ───► [Cooling Coil]
                 / 
───────────────►/ 
Return Air (RA):  CFM_ra, T_ra, W_ra, h_ra

Mixed Air Temperature Formula

$T_{\text{ma}} = \frac{(\text{CFM}_{\text{ra}} \times T_{\text{ra}}) + (\text{CFM}_{\text{oa}} \times T_{\text{oa}})}{\text{CFM}_{\text{total}}}$

Where:

• $\text{CFM}{\text{total}} = \text{CFM}{\text{ra}} + \text{CFM}_{\text{oa}}$
• $T_{\text{ma}}$ = Mixed air dry-bulb temperature (°F)
• $T_{\text{ra}}$ = Return air dry-bulb temperature (°F)
• $T_{\text{oa}}$ = Outdoor air dry-bulb temperature (°F)

Alternatively, expressing outdoor air as a percentage fraction ($X_{\text{oa}} = \text{CFM}{\text{oa}} / \text{CFM}{\text{total}}$):

$T_{\text{ma}} = T_{\text{ra}} + [X_{\text{oa}} \times (T_{\text{oa}} - T_{\text{ra}})]$

Mixed Air Humidity Ratio and Enthalpy

Identical mass-weighted equations govern humidity ratio and enthalpy:

$W_{\text{ma}} = \frac{(\text{CFM}_{\text{ra}} \times W_{\text{ra}}) + (\text{CFM}_{\text{oa}} \times W_{\text{oa}})}{\text{CFM}_{\text{total}}} \quad \text{and} \quad h_{\text{ma}} = \frac{(\text{CFM}_{\text{ra}} \times h_{\text{ra}}) + (\text{CFM}_{\text{oa}} \times h_{\text{oa}})}{\text{CFM}_{\text{total}}}$

Calculating Outdoor Air Percentage from Temperature Readings

A common field diagnostic and exam requirement is calculating the actual percentage of outside air entering an air handler when CFM values are unknown:

$\%\text{OA} = \frac{T_{\text{ma}} - T_{\text{ra}}}{T_{\text{oa}} - T_{\text{ra}}} \times 100\%$

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Coil Apparatus Dew Point (ADP) and Bypass Factor (BF)

When moist air passes through a finned cooling coil, not all air molecules make direct physical contact with the cold copper tubes or aluminum fins. A portion of the air passes through the center of the fin openings untouched.

• Apparatus Dew Point (ADP): The theoretical effective surface temperature of the cooling coil. On the psychrometric chart, if the process line connecting entering air to leaving air is extended straight to the 100% saturation curve, the point of intersection is the Apparatus Dew Point (ADP).
• Coil Bypass Factor (BF): The fraction of total entering air that completely bypasses the coil surface without conditioning. Residential coils typically have a bypass factor of 0.10 to 0.20 (10% to 20% bypass); commercial coils with 6 to 8 rows of fins achieve bypass factors of 0.03 to 0.08 (3% to 8% bypass).
• Contact Factor (CF): The fraction of air that makes direct contact with the coil: $\text{CF} = 1 - \text{BF}$.

The leaving air dry-bulb temperature is calculated from the ADP and Bypass Factor:

$T_{\text{leaving}} = T_{\text{adp}} + [\text{BF} \times (T_{\text{entering}} - T_{\text{adp}})]$

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Step-by-Step Worked Engineering Calculations

Calculation 1: Complete Air Handler Capacity & SHR Determination

Problem: A commercial packaged rooftop unit delivers $4,000\text{ CFM}$ of supply air. Air enters the cooling coil at $80^\circ\text{F DB}$ and $67^\circ\text{F WB}$ ($h_1 = 31.62\text{ BTU/lb}$, $W_1 = 78\text{ gr/lb}$). Air leaves the cooling coil at $55^\circ\text{F DB}$ and $54^\circ\text{F WB}$ ($h_2 = 22.60\text{ BTU/lb}$, $W_2 = 60\text{ gr/lb}$). Calculate: (a) Sensible cooling capacity ($Q_s$), (b) Latent cooling capacity ($Q_l$), (c) Total cooling capacity ($Q_t$), (d) System tonnage, and (e) Sensible Heat Ratio (SHR).

Step 1: Calculate Sensible Heat ($Q_s = 1.08 \times \text{CFM} \times \Delta T$) $\Delta T = 80^\circ\text{F} - 55^\circ\text{F} = 25^\circ\text{F}$ $Q_s = 1.08 \times 4,000\text{ CFM} \times 25^\circ\text{F} = 108,000\text{ BTU/hr}$

Step 2: Calculate Latent Heat ($Q_l = 0.68 \times \text{CFM} \times \Delta W_{\text{gr}}$) $\Delta W = 78\text{ gr/lb} - 60\text{ gr/lb} = 18\text{ gr/lb}$ $Q_l = 0.68 \times 4,000\text{ CFM} \times 18\text{ gr/lb} = 48,960\text{ BTU/hr}$

Step 3: Calculate Total Heat ($Q_t = 4.5 \times \text{CFM} \times \Delta h$) $\Delta h = 31.62 - 22.60 = 9.02\text{ BTU/lb}$ $Q_t = 4.5 \times 4,000\text{ CFM} \times 9.02\text{ BTU/lb} = 162,360\text{ BTU/hr}$

(Cross-check: $Q_s + Q_l = 108,000 + 48,960 = 156,960\text{ BTU/hr}$, aligning within 3% due to standard rounding of the 0.68 latent constant.)

Step 4: Calculate System Tonnage $\text{Tons} = \frac{162,360\text{ BTU/hr}}{12,000\text{ BTU/ton}} = \mathbf{13.53\text{ Tons}}$

Step 5: Calculate Sensible Heat Ratio (SHR) $\text{SHR} = \frac{Q_s}{Q_t} = \frac{108,000}{162,360} = \mathbf{0.665}$

Result: The unit produces 108,000 BTU/hr sensible, 48,960 BTU/hr latent, 13.5 tons total capacity, and operates at an SHR of 0.67, providing strong latent dehumidification ideal for humid Arkansas weather.

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Calculation 2: Commercial Economizer Mixed Air Temperature

Problem: A commercial air handling unit in Little Rock draws $3,000\text{ CFM}$ of return air at $74^\circ\text{F DB}$ and blends it with $1,000\text{ CFM}$ of hot outdoor ventilation air at $94^\circ\text{F DB}$. Calculate the resulting mixed air dry-bulb temperature entering the filter rack.

Step 1: Calculate total system airflow $\text{CFM}_{\text{total}} = 3,000 + 1,000 = 4,000\text{ CFM}$

Step 2: Apply the mixed air temperature formula $T_{\text{ma}} = \frac{(3,000\text{ CFM} \times 74^\circ\text{F}) + (1,000\text{ CFM} \times 94^\circ\text{F})}{4,000\text{ CFM}}$ $T_{\text{ma}} = \frac{222,000 + 94,000}{4,000} = \frac{316,000}{4,000} = \mathbf{79.0^\circ\text{F}}$

Result: The air mixture enters the cooling coil at 79.0°F DB.

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Calculation 3: Verifying Outside Air Ventilation Percentage

Problem: An HVAC contractor tests an air handling unit during a ventilation compliance audit. The field technician measures the following temperatures: Return air = 72°F, Outdoor air = 32°F (winter conditions), and Mixed air plenum = 62°F. What percentage of the total airflow is outdoor ventilation air?

$\%\text{OA} = \frac{T_{\text{ma}} - T_{\text{ra}}}{T_{\text{oa}} - T_{\text{ra}}} \times 100\% = \frac{62 - 72}{32 - 72} \times 100\% = \frac{-10}{-40} \times 100\% = \mathbf{25\%}$

Result: Outdoor ventilation air constitutes 25% of the total supply airflow.

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Exam Traps & Common Field Pitfalls

[!WARNING] Exam Trap 1: Misapplying Wet-Bulb in Mixed Air Equations: Never calculate mixed air wet-bulb temperature by taking a linear weighted average of entering wet-bulb temperatures! Wet-bulb lines are non-linear. To find mixed wet-bulb accurately, calculate mixed enthalpy ($h_{\text{ma}}$) and mixed humidity ratio ($W_{\text{ma}}$), plot that intersection point on the chart, and read the wet bulb.

Exam Trap 2: Constant Inconsistency (0.68 vs. 4,840): Do not plug grains into the 4,840 latent formula or pounds into the 0.68 formula! Using 70 grains in $4,840 \times \text{CFM} \times \Delta W$ creates a massive mathematical error ($7,000\times$ too large). Remember: 0.68 pairs with grains; 4,840 pairs with pounds.

Exam Trap 3: Thermal Stratification in Mixed Plenums: When cold winter outdoor air enters a mixing box, it tends to sink to the bottom while warm return air rides along the top without mixing. If this stratified cold air hits a hydronic hot water coil, it can freeze the lower coil tubes and trip the low-limit freezestat, even if the "average" mixed air temperature is 50°F. Modern commercial designs require mechanical air blenders or baffles.