4.3 Psychrometric Properties, Air Processes & Chart Navigation

Psychrometric Properties, Air Processes & Chart Navigation

Core Principle: Psychrometrics is the study of the thermodynamic properties of moist air (a mixture of dry air and water vapor) and the effects of atmospheric conditions on human thermal comfort and materials. In HVAC design and diagnostics, knowing any two independent psychrometric properties allows a technician or engineer to locate the precise state point on the psychrometric chart and determine all remaining five properties.

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The Seven Fundamental Psychrometric Properties

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|                    THE 7 FUNDAMENTAL PSYCHROMETRIC PROPERTIES                     |
+-----------------------------------------------------------------------------------+
|  1. Dry-Bulb Temperature (DB):  Sensible air temp | Bottom axis, vertical lines   |
|  2. Wet-Bulb Temperature (WB):  Evaporative cooling | Saturation line, diagonals   |
|  3. Dew Point Temperature (DP): Condensation temp | Saturation line, horizontals  |
|  4. Relative Humidity (RH):     Vapor pressure % | Curved lines (0% to 100%)      |
|  5. Humidity Ratio (W):         Grains or lbs moisture / lb dry air | Right axis  |
|  6. Specific Volume (v):        Cubic feet / lb dry air | Steep diagonal lines     |
|  7. Enthalpy (h):               Total heat content (BTU/lb dry air) | Outer scale |
+-----------------------------------------------------------------------------------+

1. Dry-Bulb Temperature ($DB / T_{\text{db}}$)

• Definition: The sensible temperature of air measured by a standard thermometer shielded from direct solar radiation and moisture.
• Chart Representation: Located on the horizontal baseline axis at the bottom of the chart. Lines of constant dry-bulb extend vertically straight upward.

2. Wet-Bulb Temperature ($WB / T_{\text{wb}}$)

• Definition: The dynamic equilibrium temperature reached by a water-wetted thermometer wick exposed to rapid air movement ($> 900\text{ FPM}$). Reflects the evaporative cooling capacity of the surrounding air.
• Chart Representation: Read along the curved saturation curve (100% RH line) on the upper left. Lines of constant wet-bulb extend diagonally downward to the right.
• Diagnostic Rule: In unsaturated air, wet-bulb is always lower than dry-bulb due to evaporative cooling ($WB < DB$). At 100% saturation, $DB = WB = DP$.

3. Dew Point Temperature ($DP / T_{\text{dp}}$)

• Definition: The temperature to which air must be cooled at constant pressure and constant moisture content to reach 100% saturation, at which point water vapor begins to condense into liquid water.
• Chart Representation: Read along the saturation curve. From any state point, move horizontally to the left to the 100% saturation curve to read dew point temperature.
• HVAC Significance: Any surface (cooling coil, uninsulated ductwork, basement wall) whose temperature is below the surrounding air's dew point will form surface condensation.

4. Relative Humidity ($RH / \phi$)

• Definition: The ratio of the actual partial vapor pressure of water ($p_v$) to the saturation water vapor pressure ($p_{\text{ws}}$) at the same dry-bulb temperature, expressed as a percentage:

$RH = \left( \frac{p_v}{p_{\text{ws}}} \right)_{T_{\text{db}}} \times 100\%$

• Chart Representation: Represented by curvilinear lines arching from the lower-left to the upper-right. The outermost curve represents 100% RH (Saturation Line). Human comfort guidelines (ASHRAE Standard 55) recommend maintaining indoor relative humidity between $30%$ and $60%$ (ideally $45%$ to $50%$) to inhibit mold proliferation and dust mite growth.

5. Humidity Ratio ($W$ / Specific Humidity)

• Definition: The actual mass of water vapor present per unit mass of dry air, expressed as pounds of moisture per pound of dry air ($\text{lb}w/\text{lb}{da}$) or grains of moisture per pound of dry air ($\text{grains/lb}$):

$1\text{ pound of water} = 7,000\text{ grains of moisture}$

• Chart Representation: Located on the vertical axis on the far right side of the chart. Lines of constant humidity ratio run horizontally across the chart.

6. Specific Volume ($v$)

• Definition: The volume occupied by one pound of dry air plus its associated water vapor, expressed in cubic feet per pound of dry air ($\text{ft}^3/\text{lb}_{da}$).
• Chart Representation: Represented by steep diagonal lines sloping upward to the left (typically ranging from $13.0\text{ to }15.0\text{ ft}^3/\text{lb}$).
• Standard Air Density ($\rho_{\text{std}}$): At standard sea-level barometric conditions ($29.92\text{ in. Hg}$, $70^\circ\text{F}$ dry-bulb, standard density), specific volume is $v = 13.33\text{ ft}^3/\text{lb}$, yielding standard air density:

$\rho_{\text{std}} = \frac{1}{v_{\text{std}}} = \frac{1}{13.333\text{ ft}^3/\text{lb}} = \mathbf{0.075\text{ lbs/ft}^3}$

7. Enthalpy ($h$)

• Definition: The total thermal energy content of the moist air mixture per unit mass of dry air, including the sensible heat of air and vapor plus the latent heat of the water vapor, expressed in $\text{BTU per pound of dry air}$ ($\text{BTU/lb}_{da}$).
• Chart Representation: Read on the external diagonal scale on the upper left periphery of the chart, running roughly parallel to lines of constant wet-bulb.

$\text{Total Air Enthalpy } (h) \approx 0.240 \cdot T_{\text{db}} + W_{\text{lbs}} \cdot (1,061 + 0.444 \cdot T_{\text{db}}) \quad (\text{BTU/lb})$

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Fundamental HVAC Airflow & Heat Transfer Equations

All HVAC air-side load calculations, psychrometric balancing, and capacity verifications rely on three standard equations derived from air density ($\rho = 0.075\text{ lbs/ft}^3$) and specific heat ($c_p = 0.240\text{ BTU}/(\text{lb}\cdot^\circ\text{F})$):

1. The Sensible Air Heat Equation

$q_s = 1.08 \times \text{CFM} \times \Delta T_{\text{db}} \quad (\text{BTU/hr})$

Mathematical Derivation: $q_s = \dot{m} \times c_p \times \Delta T = (\text{CFM} \times 60\text{ min/hr} \times 0.075\text{ lbs/ft}^3) \times 0.240\text{ BTU}/(\text{lb}\cdot^\circ\text{F}) \times \Delta T$ $60 \times 0.075 \times 0.240 = \mathbf{1.08}$

2. The Latent Air Heat Equation

$q_l = 0.68 \times \text{CFM} \times \Delta W_{\text{grains}} \quad (\text{BTU/hr})$

$q_l = 4,840 \times \text{CFM} \times \Delta W_{\text{lbs}} \quad (\text{BTU/hr})$

Mathematical Derivation: $q_l = (\text{CFM} \times 60 \times 0.075) \times \frac{1,061\text{ BTU/lb (latent heat)}}{7,000\text{ grains/lb}} \times \Delta W_{\text{grains}}$ $\frac{60 \times 0.075 \times 1,061}{7,000} = \mathbf{0.682} \approx \mathbf{0.68}$

3. The Total Air Heat Equation (Enthalpy Method)

$q_t = 4.5 \times \text{CFM} \times \Delta h \quad (\text{BTU/hr})$

Mathematical Derivation: $q_t = \dot{m} \times \Delta h = (\text{CFM} \times 60\text{ min/hr} \times 0.075\text{ lbs/ft}^3) \times \Delta h$ $60 \times 0.075 = \mathbf{4.5}$

4. Sensible Heat Ratio ($SHR$)

The Sensible Heat Ratio defines the proportion of total cooling load that is sensible (temperature reduction) versus latent (moisture dehumidification):

$\text{SHR} = \frac{q_s}{q_t} = \frac{q_s}{q_s + q_l}$

• Typical Residential Load in NC: Sensible Heat Ratio typically ranges from $0.70\text{ to }0.80$ (70% sensible cooling, 30% latent dehumidification).
• High Latent Loads: In humid coastal North Carolina climates with high ventilation rates, the SHR may drop to $0.60\text{ to }0.65$, requiring lower airflow rates ($325\text{ to }350\text{ CFM/ton}$) to drop coil surface temperature below the dew point for enhanced dehumidification.

5. Moisture Removal Rate & Condensate Generation

$\text{Condensate Mass Rate} = \frac{q_l}{1,061\text{ BTU/lb}} = \frac{0.68 \times \text{CFM} \times \Delta W_{\text{grains}}}{1,061} \quad (\text{lbs/hr})$

$\text{Condensate Volume Rate (Gallons/Hour)} = \frac{\text{Condensate (lbs/hr)}}{8.34\text{ lbs/gal}}$

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Psychrometric Air Processes & Chart Navigation

Air conditioning processes represent directional vector movements across the psychrometric chart:

Psychrometric Process Vector Map

              HUMIDIFYING (Up: +W)
                       ^
                       |
 EVAPORATIVE COOLING   |   HEATING & HUMIDIFYING
 (Up-Left: -DB, +W, =h)|   (Up-Right: +DB, +W, +h)
         \             |             /
          \            |            /
           \           |           /
SENSIBLE    <----------+---------->  SENSIBLE
COOLING                |             HEATING
(Left: -DB, =W, =DP)   |             (Right: +DB, =W, =DP)
           /           |           \
          /            |            \
         /             |             \
  COOLING &            |    CHEMICAL DEHUMIDIFICATION
  DEHUMIDIFYING        |    (Down-Right: +DB, -W)
  (Down-Left: -DB, -W) v
             DEHUMIDIFYING (Down: -W)

Analysis of Standard Psychrometric Processes

Coil Bypass Factor ($BF$) & Apparatus Dew Point ($ADP$)

When air passes through a cooling coil, not all air molecules make physical contact with the cold coil fins:

• Apparatus Dew Point ($ADP$): The effective surface temperature of the cooling coil tubes and fins.
• Contact Factor ($CF$): The percentage of air that physically contacts the coil surface and is cooled to the $ADP$.
• Bypass Factor ($BF$): The percentage of air that passes through the coil fins without contacting the surface, remaining unconditioned: $BF = 1 - CF = \frac{T_{\text{leaving air}} - T_{\text{ADP}}}{T_{\text{entering air}} - T_{\text{ADP}}}$ Modern residential multi-row coils typically achieve a Bypass Factor of $0.05\text{ to }0.15$ ($85%\text{ to }95%$ Contact Factor).

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Adiabatic Mixing of Two Airstreams

When two air streams mix adiabatically (without external heat addition or loss), the resulting mixed air condition lies on the straight line connecting the two initial state points on the psychrometric chart, positioned inversely proportional to their mass flow rates:

$T_{\text{db, mix}} = \frac{(\text{CFM}_1 \times T_{\text{db, 1}}) + (\text{CFM}_2 \times T_{\text{db, 2}})}{\text{CFM}_{\text{total}}}$

$W_{\text{mix}} = \frac{(\text{CFM}_1 \times W_1) + (\text{CFM}_2 \times W_2)}{\text{CFM}_{\text{total}}}$

$h_{\text{mix}} = \frac{(\text{CFM}_1 \times h_1) + (\text{CFM}_2 \times h_2)}{\text{CFM}_{\text{total}}}$

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Step-by-Step Worked Technical Examples

Example 1: Adiabatic Air Mixing Calculation

Problem: A commercial rooftop air handler operates with $2,000\text{ CFM}$ total supply airflow. The system mixes $1,600\text{ CFM}$ of Return Air (80%) at $75^\circ\text{F}$ DB and $63^\circ\text{F}$ WB ($h_{\text{RA}} = 28.5\text{ BTU/lb}$, $W_{\text{RA}} = 65.0\text{ grains/lb}$) with $400\text{ CFM}$ of Outdoor Ventilation Air (20%) at $95^\circ\text{F}$ DB and $78^\circ\text{F}$ WB ($h_{\text{OA}} = 41.5\text{ BTU/lb}$, $W_{\text{OA}} = 118.0\text{ grains/lb}$).

Calculate: (1) Mixed air dry-bulb temperature ($T_{\text{db, mix}}$), (2) Mixed air humidity ratio ($W_{\text{mix}}$), and (3) Mixed air enthalpy ($h_{\text{mix}}$).

Solution:

1. Mixed Air Dry-Bulb Temperature: $T_{\text{db, mix}} = (0.80 \times 75^\circ\text{F}) + (0.20 \times 95^\circ\text{F}) = 60.0 + 19.0 = \mathbf{79.0^\circ\text{F}}$

2. Mixed Air Humidity Ratio: $W_{\text{mix}} = (0.80 \times 65.0) + (0.20 \times 118.0) = 52.0 + 23.6 = \mathbf{75.6\text{ grains/lb}}$

3. Mixed Air Enthalpy: $h_{\text{mix}} = (0.80 \times 28.5) + (0.20 \times 41.5) = 22.8 + 8.3 = \mathbf{31.1\text{ BTU/lb}}$

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Example 2: Cooling Coil Capacity, SHR & Condensate Rate

Problem: An air conditioning evaporator coil receives $1,600\text{ CFM}$ of entering air at $80.0^\circ\text{F}$ DB and $67.0^\circ\text{F}$ WB ($h_1 = 31.5\text{ BTU/lb}$, $W_1 = 78.0\text{ grains/lb}$). Air leaves the coil at $55.0^\circ\text{F}$ DB and $53.5^\circ\text{F}$ WB ($h_2 = 22.3\text{ BTU/lb}$, $W_2 = 56.0\text{ grains/lb}$).

Calculate: (1) Sensible cooling capacity ($q_s$), (2) Latent cooling capacity ($q_l$), (3) Total cooling capacity ($q_t$), (4) Sensible Heat Ratio ($SHR$), and (5) Hourly condensate removal rate in gallons per hour.

Solution:

1. Sensible Cooling Capacity: $q_s = 1.08 \times \text{CFM} \times (T_{\text{db, in}} - T_{\text{db, out}})$ $q_s = 1.08 \times 1,600\text{ CFM} \times (80.0 - 55.0)^\circ\text{F} = 1.08 \times 1,600 \times 25.0 = \mathbf{43,200\text{ BTU/hr}}$

2. Latent Cooling Capacity: $q_l = 0.68 \times \text{CFM} \times (W_{\text{in}} - W_{\text{out}})$ $q_l = 0.68 \times 1,600\text{ CFM} \times (78.0 - 56.0)\text{ grains/lb} = 0.68 \times 1,600 \times 22.0 = \mathbf{23,936\text{ BTU/hr}}$

3. Total Cooling Capacity (Enthalpy Method): $q_t = 4.5 \times \text{CFM} \times (h_1 - h_2)$ $q_t = 4.5 \times 1,600\text{ CFM} \times (31.5 - 22.3)\text{ BTU/lb} = 4.5 \times 1,600 \times 9.2 = \mathbf{66,240\text{ BTU/hr}} \quad (5.52\text{ Tons})$ (Sum of Sensible + Latent: $43,200 + 23,936 = 67,136\text{ BTU/hr}$; within $1.3%$ of enthalpy method due to standard density constants).

4. Sensible Heat Ratio ($SHR$): $\text{SHR} = \frac{q_s}{q_s + q_l} = \frac{43,200}{43,200 + 23,936} = \frac{43,200}{67,136} = \mathbf{0.643} \quad (64.3\%\text{ Sensible}, 35.7\%\text{ Latent})$

5. Condensate Removal Rate: $\text{Condensate Mass Rate} = \frac{q_l}{1,061\text{ BTU/lb}} = \frac{23,936\text{ BTU/hr}}{1,061\text{ BTU/lb}} = 22.56\text{ lbs/hr}$ $\text{Condensate Volume} = \frac{22.56\text{ lbs/hr}}{8.34\text{ lbs/gal}} = \mathbf{2.70\text{ Gallons/Hour}}$