6.5 Ventilation Loads & Sensible / Latent / Total Cooling Load Synthesis

6.5 Ventilation Loads & Sensible / Latent / Total Cooling Load Synthesis

The final phase of load calculations synthesizes all individual load components—envelope transmission, fenestration conduction, solar radiation, lighting, occupants, plug loads, and outdoor ventilation air—into a unified psychrometric system analysis. Correctly synthesizing these loads allows the mechanical engineer to determine required supply airflow ($\text{CFM}{\text{supply}}$), establish the supply air temperature ($T{\text{supply}}$) and apparatus dew point (ADP), evaluate mixed air properties ($T_{\text{mix}}, W_{\text{mix}}, h_{\text{mix}}$), and size central cooling and heating coils in Tons of Refrigeration (TR) or MBH.

---

1. ASHRAE Standard 62.1 Ventilation Rate Procedure (VRP)

Outdoor air must be continuously introduced to occupied spaces to dilute bioeffluents, volatile organic compounds (VOCs), and off-gassing from building materials.

+-----------------------------------------------------------------------------------------+
| ASHRAE 62.1 VENTILATION RATE PROCEDURE (VRP) FLOWCHART                                  |
+-----------------------------------------------------------------------------------------+
| 1. Breathing Zone Outdoor Airflow:    V_bz = (R_p * P_z) + (R_a * A_z)                  |
|                                                |                                        |
| 2. Zone Outdoor Airflow:              V_oz = V_bz / E_z                                 |
|                                                |                                        |
| 3. Multi-Zone System Efficiency:      E_v = 1 + X_s - Z_p  (or tabular lookup)          |
|                                                |                                        |
| 4. Total System Outdoor Air Intake:   V_ot = V_ou / E_v                                 |
+-----------------------------------------------------------------------------------------+

1. Breathing Zone Outdoor Airflow ($V_{bz}$)

$V_{bz} = R_p \cdot P_z + R_a \cdot A_z$

Where:

• $R_p = \text{Outdoor airflow rate per person } (\text{CFM/person, typically } 5\text{ to }10\text{ CFM/person})$
• $P_z = \text{Design zone population (occupants)}$
• $R_a = \text{Outdoor airflow rate per unit area } (\text{CFM/ft}^2\text{, typically } 0.06\text{ to }0.12\text{ CFM/ft}^2)$
• $A_z = \text{Zone floor area } (\text{ft}^2)$

2. Zone Outdoor Airflow ($V_{oz}$)

$V_{oz} = \frac{V_{bz}}{E_z}$

Where $E_z$ is the Zone Air Distribution Effectiveness:

• $E_z = 1.0$: Ceiling supply of cool air; or floor supply of warm air ($T_{\text{supply}} < T_{\text{room}} + 15^\circ\text{F}$).
• $E_z = 0.8$: Ceiling supply of warm air with ceiling return ($T_{\text{supply}} > T_{\text{room}}$), due to thermal stratification and short-circuiting.

---

2. Ventilation Load Allocation: Coil Load vs. Space Load

A critical distinction on the PE Mechanical exam is the physical location where outdoor air enters the building:

• Outdoor Air Introduced at Central AHU (Ventilation): Outdoor air mixes with return air in the mixing plenum before passing across the central cooling/heating coil. This air is conditioned before entering the room. Therefore, ventilation outdoor air is a central coil load, NOT a direct space load.
• Uncontrolled Infiltration Across Envelope: Outdoor air leaks directly into the room through cracks and doors without conditioning. Therefore, infiltration is a direct space sensible and latent load.

+-----------------------------------------------------------------------------------------+
| SPACE LOAD VS. CENTRAL COIL LOAD MATRIX                                                 |
+-----------------------------------------------------------------------------------------+
| LOAD COMPONENT                         | IMPOSES LOAD ON SPACE? | IMPOSES LOAD ON COIL? |
| -------------------------------------- | ---------------------- | --------------------- |
| Envelope Conduction (Walls/Roofs)      | YES (Sensible)         | YES (Sensible)        |
| Window Solar Radiation (SHGC)          | YES (Sensible)         | YES (Sensible)        |
| Lighting (Room Fraction)               | YES (Sensible)         | YES (Sensible)        |
| Lighting (Plenum Fraction)             | NO                     | YES (Sensible)        |
| People (Occupants)                     | YES (Sensible+Latent)  | YES (Sensible+Latent) |
| Equipment & Plug Loads                 | YES (Sensible)         | YES (Sensible)        |
| Envelope Infiltration                  | YES (Sensible+Latent)  | YES (Sensible+Latent) |
| Central Ventilation Outdoor Air        | NO                     | YES (Sensible+Latent) |
| Supply Fan Motor Heat                  | NO                     | YES (Sensible)        |
| Return Air Duct Heat Gain              | NO                     | YES (Sensible)        |
+-----------------------------------------------------------------------------------------+

---

3. Sensible Heat Ratios & Supply Airflow Sizing

Psychrometric load synthesis establishes the operating state points connecting room conditions, mixed air conditions, and coil leaving conditions.

+-----------------------------------------------------------------------------------------+
| PSYCHROMETRIC LOAD PROCESS LINES (RSHR VS. GSHR)                                        |
+-----------------------------------------------------------------------------------------+
| Humidity Ratio (W)                                                                      |
|   ^                                                                                     |
|   |                     (O) Outdoor Air State                                           |
|   |                      .                                                              |
|   |                     .                                                               |
|   |                    (M) Mixed Air State                                              |
|   |                   /  .                                                              |
|   |                  /    .                                                             |
|   |                 /      .                                                            |
|   |                /        (R) Room Air State (75°F, 50% RH)                           |
|   |               /        .                                                            |
|   |              /       . <--- Room Sensible Heat Ratio (RSHR) Slope                   |
|   |             /      .                                                                |
|   |            (S) Supply Air State (55°F DB)                                           |
|   |           .                                                                         |
|   |         (ADP) Apparatus Dew Point                                                   |
|   +--------------------------------------------------------------------> Dry Bulb (T)   |
+-----------------------------------------------------------------------------------------+

1. Room Sensible Heat Ratio (RSHR)

The slope of the state line between supply air ($S$) and room air ($R$) is governed by the space loads:

$\text{RSHR} = \frac{q_{\text{space, sensible}}}{q_{\text{space, sensible}} + q_{\text{space, latent}}} = \frac{q_{ss}}{q_{st}}$

2. Grand Sensible Heat Ratio (GSHR)

The slope of the state line across the cooling coil between mixed air ($M$) and leaving supply air ($S$) includes both room loads and ventilation outdoor air loads:

$\text{GSHR} = \frac{q_{\text{total, sensible}}}{q_{\text{total, sensible}} + q_{\text{total, latent}}} = \frac{q_{ss} + q_{oa,s}}{q_{st} + q_{oa,t}}$

3. Supply Airflow ($\text{CFM}_{\text{supply}}$) Determination

Supply airflow is determined strictly by the room sensible heat load ($q_{ss}$) and design supply-to-room temperature difference (typically $\Delta T = 75^\circ\text{F} - 55^\circ\text{F} = 20^\circ\text{F}$):

$\text{CFM}_{\text{supply}} = \frac{q_{\text{space, sensible}}}{1.08 \times (T_{\text{room}} - T_{\text{supply}})}$

---

4. Mixed Air Psychrometric State Evaluation

When outdoor air and return air mix in the AHU plenum, the mixed air state ($M$) represents a mass-weighted average:

+-----------------------------------------------------------------------------------------+
| MIXED AIR PSYCHROMETRIC EQUATIONS                                                       |
+-----------------------------------------------------------------------------------------+
| Mixed Dry-Bulb:    T_mix = (CFM_oa * T_oa + CFM_ra * T_ra) / CFM_supply                 |
| Mixed Humidity:    W_mix = (CFM_oa * W_oa + CFM_ra * W_ra) / CFM_supply                 |
| Mixed Enthalpy:    h_mix = (CFM_oa * h_oa + CFM_ra * h_ra) / CFM_supply                 |
+-----------------------------------------------------------------------------------------+

Letting the outdoor air fraction be $X_{oa} = \frac{\text{CFM}{oa}}{\text{CFM}{\text{supply}}}$:

$T_{\text{mix}} = X_{oa} \cdot T_{oa} + (1 - X_{oa}) \cdot T_{ra}$

$W_{\text{mix}} = X_{oa} \cdot W_{oa} + (1 - X_{oa}) \cdot W_{ra}$

$h_{\text{mix}} = X_{oa} \cdot h_{oa} + (1 - X_{oa}) \cdot h_{ra}$

---

5. Total Cooling Coil Capacity & Tonnage Calculations

Once mixed air and leaving coil states are established, central coil capacity is calculated using the three standard moist air equations:

1. Coil Sensible Capacity ($q_{\text{coil, sensible}}$)

$q_{\text{coil, sensible}} = 1.08 \times \text{CFM}_{\text{supply}} \times (T_{\text{mix}} - T_{\text{leaving}})$

2. Coil Latent Capacity ($q_{\text{coil, latent}}$)

$q_{\text{coil, latent}} = 4840 \times \text{CFM}_{\text{supply}} \times (W_{\text{mix}} - W_{\text{leaving}})$

3. Total Coil Capacity ($q_{\text{coil, total}}$)

$q_{\text{coil, total}} = 4.5 \times \text{CFM}_{\text{supply}} \times (h_{\text{mix}} - h_{\text{leaving}})$

$\text{Coil Tonnage (TR)} = \frac{q_{\text{coil, total}}\text{ (Btu/hr)}}{12,000\text{ Btu/(hr}\cdot\text{Ton)}}$

Fan Heat Gain & Duct Parasitic Corrections

• Supply Fan Temperature Rise (Draw-Through Fan): The fan is located downstream of the cooling coil. Motor and impeller mechanical dissipation heat the supply air before it reaches the zone: $\Delta T_{\text{fan}} = \frac{\Delta P_{\text{total}}\text{ (in. w.g.)}}{6356 \times \eta_{\text{fan}} \times \eta_{\text{motor}}} \times 2545 \times \frac{1}{1.08} \approx \frac{\Delta P_{\text{total}}}{2.7 \times \eta_{\text{total}}}$ Typically, $\Delta T_{\text{fan}} = 1.0^\circ\text{F}\text{ to }2.5^\circ\text{F}$. To deliver $55^\circ\text{F}$ air to the room, the coil must leave at $T_{\text{coil, leaving}} = 55 - \Delta T_{\text{fan}} = 53^\circ\text{F}$.
• Duct Heat Gain: Conditioned supply air traveling through unconditioned ceiling plenums absorbs $1.0^\circ\text{F}\text{ to }2.0^\circ\text{F}$ of sensible heat.

---

6. NCEES Reference Handbook Navigation Tactics

• ASHRAE 62.1 Equations: Search "Ventilation Rate Procedure" or "Breathing Zone" in Section 7 (HVAC & Refrigeration Applications) to find $V_{bz} = R_p P_z + R_a A_z$ and $E_z$ tables.
• Psychrometric Equations: Search "Sensible Heat Ratio" or "RSHR" in Section 6 (Psychrometrics) to find formulas for RSHR, GSHR, mixed air equations, and shortcut constants ($1.08, 4840, 4.5$).
• Fan Temperature Rise: Search "Fan Heat Gain" to find the exact mechanical energy temperature rise equation.

---

7. Master Worked Computational Example

Comprehensive Building Cooling Load & Psychrometric Synthesis

A single-zone commercial office building ($12,000\text{ ft}^2$, $14\text{ ft}$ floor-to-floor) in Charlotte, NC has the following design parameters:

• Indoor Design Conditions: $75^\circ\text{F}$ DB, $50%\text{ RH}$ ($W_r = 0.00925\text{ lb}w/\text{lb}{da}$, $h_r = 28.14\text{ Btu/lb}$).
• Outdoor Design Conditions (0.4%): $95^\circ\text{F}$ DB, $75^\circ\text{F}$ MCWB ($W_o = 0.01410\text{ lb}w/\text{lb}{da}$, $h_o = 38.60\text{ Btu/lb}$).
• Occupancy: 100 people ($q_s = 250\text{ Btu/hr}$, $q_l = 200\text{ Btu/hr}$ per person).
• ASHRAE 62.1 Ventilation Rates: $R_p = 5\text{ CFM/person}$, $R_a = 0.06\text{ CFM/ft}^2$, $E_z = 1.0$.
• Lighting & Plug Loads: Lighting = $1.0\text{ W/ft}^2$ (all entering room space); Plug Loads = $0.75\text{ W/ft}^2$.
• Building Envelope & Glazing Transmission: Net space envelope conduction + solar heat gain = $78,000\text{ Btu/hr}$ (100% sensible).
• Infiltration: $0.15\text{ ACH}$ (unconditioned direct space infiltration).
• Supply Air Conditions: Air leaves cooling coil at $53.0^\circ\text{F}$ DB saturated ($W_{\text{coil}} = 0.00850\text{ lb}w/\text{lb}{da}$, $h_{\text{coil}} = 22.00\text{ Btu/lb}$). Supply fan adds $2.0^\circ\text{F}$ of draw-through heat, delivering air to the space at $T_{\text{supply}} = 55.0^\circ\text{F}$ DB.

Calculate: (1) Required ventilation airflow, (2) Space sensible and latent loads, (3) Required supply airflow, (4) Mixed air psychrometric properties, (5) Total cooling coil capacity and chiller tonnage.

Solution Step-by-Step:

Step 1: Calculate Outdoor Ventilation Airflow (ASHRAE 62.1)

$V_{bz} = (5\text{ CFM/person} \times 100) + (0.06\text{ CFM/ft}^2 \times 12,000\text{ ft}^2) = 500 + 720 = 1,220\text{ CFM}$ $V_{oa} = \frac{1,220}{1.0} = 1,220\text{ CFM}$

Step 2: Calculate Infiltration Load Entering Space

$\text{Volume } = 12,000\text{ ft}^2 \times 14\text{ ft} = 168,000\text{ ft}^3$ $\text{CFM}_{\text{inf}} = \frac{0.15 \times 168,000}{60} = 420\text{ CFM}$ $q_{s,\text{inf}} = 1.08 \times 420 \times (95 - 75) = 1.08 \times 420 \times 20 = 9,072\text{ Btu/hr}$ $q_{l,\text{inf}} = 4840 \times 420 \times (0.01410 - 0.00925) = 4840 \times 420 \times 0.00485 = 9,859\text{ Btu/hr}$

Step 3: Calculate Internal Heat Gains Entering Space

• Occupants: $q_{s,\text{occ}} = 100 \times 250 = 25,000\text{ Btu/hr}$; $q_{l,\text{occ}} = 100 \times 200 = 20,000\text{ Btu/hr}$
• Lighting: $q_{\text{light}} = 12,000\text{ ft}^2 \times 1.0\text{ W/ft}^2 \times 3.412 = 40,944\text{ Btu/hr}$
• Plug Loads: $q_{\text{plug}} = 12,000\text{ ft}^2 \times 0.75\text{ W/ft}^2 \times 3.412 = 30,708\text{ Btu/hr}$

Step 4: Sum Total Space Loads & Determine Supply Airflow ($\text{CFM}_{\text{supply}}$)

$q_{\text{space, sensible}} = 78,000\text{ (envelope)} + 9,072\text{ (inf)} + 25,000\text{ (occ)} + 40,944\text{ (light)} + 30,708\text{ (plug)} = 183,724\text{ Btu/hr}$ $q_{\text{space, latent}} = 9,859\text{ (inf)} + 20,000\text{ (occ)} = 29,859\text{ Btu/hr}$ $q_{\text{space, total}} = 183,724 + 29,859 = 213,583\text{ Btu/hr}$ $\text{RSHR} = \frac{183,724}{213,583} = 0.860$ $\text{CFM}_{\text{supply}} = \frac{q_{\text{space, sensible}}}{1.08 \times (T_{\text{room}} - T_{\text{supply}})} = \frac{183,724}{1.08 \times (75 - 55)} = \frac{183,724}{21.6} = 8,506\text{ CFM}$

Step 5: Evaluate Mixed Air State at AHU Intake

$\text{Outdoor Air Fraction } X_{oa} = \frac{1,220\text{ CFM}}{8,506\text{ CFM}} = 0.1434\text{ (14.34\%)}$ $\text{Return Airflow } \text{CFM}_{ra} = 8,506 - 1,220 = 7,286\text{ CFM}$ $T_{\text{mix}} = (0.1434 \times 95) + (1 - 0.1434) \times 75 = 13.62 + 64.25 = 77.87^\circ\text{F}$ $W_{\text{mix}} = (0.1434 \times 0.01410) + (1 - 0.1434) \times 0.00925 = 0.002022 + 0.007924 = 0.009946\text{ lb}_w/\text{lb}_{da}$ $h_{\text{mix}} = (0.1434 \times 38.60) + (1 - 0.1434) \times 28.14 = 5.535 + 24.105 = 29.64\text{ Btu/lb}$

Step 6: Sizing Central Cooling Coil Capacity & Tonnage

$q_{\text{coil, sensible}} = 1.08 \times 8,506 \times (77.87 - 53.0) = 1.08 \times 8,506 \times 24.87 = 228,468\text{ Btu/hr}$ $q_{\text{coil, latent}} = 4840 \times 8,506 \times (0.009946 - 0.00850) = 4840 \times 8,506 \times 0.001446 = 59,531\text{ Btu/hr}$ $q_{\text{coil, total}} = 4.5 \times 8,506 \times (29.64 - 22.00) = 4.5 \times 8,506 \times 7.64 = 292,442\text{ Btu/hr}$ $\text{Total Coil Tonnage} = \frac{292,442\text{ Btu/hr}}{12,000\text{ Btu/(hr}\cdot\text{Ton)}} = 24.37\text{ Tons}$

(Notice that the central coil capacity of 24.37 Tons exceeds the net space load of 17.80 Tons by 6.57 Tons due to the ventilation outdoor air load and fan heat gain!)