11.3 Mixed Air, Ventilation, and Infiltration Calculations

11.3 Mixed Air, Ventilation, and Infiltration Calculations

"Calculating mixed air problems for infiltration and ventilation" appears on both the General Studies and System Performance sheets. It is the calculation that connects the psychrometric chart (Sections 11.1 and 11.2) to real equipment selection, because almost no air handler recirculates 100% of its return air, and no building is airtight.

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1. The Mixing Equation

When two airstreams combine, the result is a weighted average by mass. Since specific volume varies only slightly across normal conditions, weighting by volume (CFM) is accurate enough for field work.

$$T_{\text{mixed}} = \left(\frac{\text{CFM}_{\text{OA}}}{\text{CFM}_{\text{total}}} \times T_{\text{OA}}\right) + \left(\frac{\text{CFM}_{\text{RA}}}{\text{CFM}_{\text{total}}} \times T_{\text{RA}}\right)$$

The same weighting applies to humidity ratio (grains) and enthalpy. It does not apply to relative humidity, which is a ratio rather than a quantity — averaging two RH values is a common and wrong shortcut.

Worked example — commercial rooftop, summer. A unit moves 8,000 CFM total with 2,000 CFM of outdoor air (25% OA). Outdoor air is 95°F DB / 78°F WB (about 120 grains/lb, 41.5 BTU/lb); return air is 75°F DB / 63°F WB (65 grains/lb, 28.6 BTU/lb).

$$T_{\text{mixed}} = (0.25 \times 95) + (0.75 \times 75) = 23.75 + 56.25 = 80.0^\circ\text{F DB}$$ $$W_{\text{mixed}} = (0.25 \times 120) + (0.75 \times 65) = 30 + 48.75 = 78.75\text{ grains/lb}$$ $$h_{\text{mixed}} = (0.25 \times 41.5) + (0.75 \times 28.6) = 10.4 + 21.5 = 31.9\text{ BTU/lb}$$

Plot 80°F DB and 78.75 grains: the mixed-air wet bulb reads about 67°F. That 80°F/67°F condition — not the 75°F/63°F return air — is what actually enters the cooling coil, and it is what the coil must be selected for.

The graphical solution

On the chart, the mixed-air point always lies on the straight line connecting the outdoor and return points, and its position along that line is set by the outdoor-air fraction — measured from the return point toward the outdoor point. At 25% OA the mixed point sits one-quarter of the way from return toward outdoor. Sketching this is faster than the arithmetic and is exactly the "plot any two points and evaluate the data" skill the task list requires.

Winter mixed air and the freeze-stat

The same math in January exposes a real hazard. With 10°F outdoor air, 72°F return, and 25% OA:

$$T_{\text{mixed}} = (0.25 \times 10) + (0.75 \times 72) = 2.5 + 54 = 56.5^\circ\text{F}$$

Comfortable. But if the outdoor-air damper sticks open at 50%:

$$T_{\text{mixed}} = (0.50 \times 10) + (0.50 \times 72) = 41^\circ\text{F}$$

That air is approaching the point where a hydronic preheat or chilled-water coil will freeze and split. This is why every commercial mixed-air system carries a low-limit (freeze-stat) — typically a capillary sensing element serpentined across the coil face, tripping near 35–38°F, responding to the coldest one-foot segment of its capillary rather than an average.

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2. Ventilation Load

Outdoor air brought in deliberately must be conditioned, and its load is calculated on outdoor conditions, not mixed conditions.

$$Q_{s,\text{vent}} = 1.08 \times \text{CFM}_{\text{OA}} \times (T_{\text{OA}} - T_{\text{room}})$$ $$Q_{l,\text{vent}} = 0.68 \times \text{CFM}_{\text{OA}} \times (W_{\text{OA}} - W_{\text{room}})$$

Worked example. 2,000 CFM of 95°F/120-grain outdoor air conditioned to a 75°F/65-grain room:

$$Q_s = 1.08 \times 2{,}000 \times 20 = 43{,}200\text{ BTU/hr}$$ $$Q_l = 0.68 \times 2{,}000 \times 55 = 74{,}800\text{ BTU/hr}$$

Total ventilation load: 118,000 BTU/hr — nearly 10 tons, of which 63% is latent. In humid climates the moisture in outdoor air is usually a larger burden than its temperature, which is the entire argument for dedicated outdoor air systems and energy recovery.

How much outdoor air? ASHRAE 62.1's Ventilation Rate Procedure sets commercial rates as people-based plus area-based:

$$V_{bz} = (R_p \times P_z) + (R_a \times A_z)$$

An office at $R_p = 5$ CFM/person and $R_a = 0.06$ CFM/ft², with 40 people in 4,000 ft²: $(5 \times 40) + (0.06 \times 4{,}000) = 200 + 240 = 440\text{ CFM}$ to the breathing zone. Residential whole-building ventilation uses the ASHRAE 62.2 formula in Section 1.1.

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3. Infiltration

Infiltration is uncontrolled air leakage driven by stack effect, wind, and mechanical imbalance (Section 10.5).

$$\text{CFM}_{\text{infiltration}} = \frac{\text{Conditioned volume (ft}^3) \times \text{ACH}_{\text{natural}}}{60}$$

Converting a blower door result to a design rate. ACH50 is a test result at 50 Pa; natural infiltration happens at roughly 1–4 Pa. The LBL (Lawrence Berkeley Laboratory) division method converts between them:

$$\text{ACH}_{\text{natural}} \approx \frac{\text{ACH50}}{N}$$

where N is a climate, height, and shielding factor, typically 15 to 20 for a one- or two-story house — around 20 in mild, sheltered locations and nearer 15 in cold, windy, exposed ones.

Worked example. A 22,300 ft³ house tests at 5.65 ACH50 in a moderate climate ($N = 18$):

$$\text{ACH}_{\text{natural}} = 5.65 \div 18 = 0.314$$ $$\text{CFM}_{\text{infiltration}} = \frac{22{,}300 \times 0.314}{60} = \frac{7{,}002}{60} = 117\text{ CFM}$$

At winter design conditions of 15°F outdoors and 70°F indoors:

$$Q_s = 1.08 \times 117 \times 55 = 6{,}950\text{ BTU/hr}$$

That single number is often 15–25% of a house's entire design heating load, and it is why air sealing appears in a heat load calculation as directly as insulation does.

The 0.35 ACH rule of thumb — the old assumption that a house "naturally" changes its air about a third of a time per hour — is a historical average, not a measurement. Modern practice measures with a blower door and calculates, because real houses range from 0.05 to over 1.0 ACH natural.

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4. Energy and Heat Recovery Ventilation

The ventilation-load arithmetic above is the case for recovering energy from the air being exhausted.

An ERV in the 2,000 CFM example above, at 70% sensible and 60% latent effectiveness, would cut the ventilation load from 118,000 BTU/hr to roughly $43{,}200 \times 0.30 + 74{,}800 \times 0.40 = 12{,}960 + 29{,}920 = 42{,}880$ BTU/hr — a saving of about 6 tons of coil capacity.

Balanced airflow is the requirement. An HRV or ERV must move approximately equal supply and exhaust volumes; an imbalance pressurizes or depressurizes the building and reintroduces exactly the uncontrolled infiltration the system exists to replace. Commissioning includes measuring both airstreams and adjusting to within roughly 10% of each other.

Demand-controlled ventilation (Section 12.3) reduces the load a different way: a CO₂ sensor in the space modulates the outdoor-air damper to actual occupancy rather than design occupancy, which in intermittently occupied spaces such as conference rooms, gyms, and auditoriums is the largest single ventilation saving available.