Cooling Coil in an AHU: Capacity and Dehumidification Calculation

The cooling coil in an air handling unit (AHU) cools the supply air below its dew point — condensing out the excess moisture and draining it away as condensate. The total cooling capacity is the sum of the sensible and latent heat: $Q_{total} = 4.5 \cdot \dot{V} \cdot (h_1 - h_2)$, where $h_1$ and $h_2$ are the air enthalpies before and after the coil.

The principle of cooling with dehumidification

The air enters the coil at temperature $t_1$ and relative humidity $\varphi_1$. The coil cools it through the dew point ($t_d$) to the outlet temperature $t_2$:

1. Sensible cooling — a drop in temperature with no change in humidity, until the air reaches its dew point
2. Latent cooling (dehumidification) — below the dew point the water vapor condenses, and the humidity ratio $W$ falls
3. Outlet state — the air leaves the coil saturated ($\varphi_2 \approx 95\text{–}100\%$) or is subsequently reheated to the required temperature

The principle of cooling without dehumidification

If the outlet temperature $t_2$ stays above the dew-point temperature, no condensation occurs — the air is merely cooled.

1. Sensible cooling — a drop in temperature with no change in humidity, until the air reaches its dew point
2. Outlet state — the air leaves the coil more saturated than at the inlet

Calculating the cooling capacity

Total cooling capacity

$$Q_{total} = 4.5 \cdot \dot{V} \cdot (h_1 - h_2) \quad \text{[Btu/h]}$$

with $\dot{V}$ in CFM and enthalpies in Btu/lb. The constant 4.5 is 60 min/h × 0.075 lb/ft³ — recompute it at altitude.

The sensible component

$$Q_s = 1.08 \cdot \dot{V} \cdot (t_1 - t_2) \quad \text{[Btu/h]}$$

The latent component (dehumidification)

$$Q_{lat} = Q_{total} - Q_s \quad \text{[Btu/h]}$$

Condensate flow

$$\dot{m}_{cond} = 4.5 \cdot \dot{V} \cdot (W_1 - W_2) \quad \text{[lb/h]}$$

Divide by 8.34 lb/gal for gallons per hour — the number that sizes the drain pan and trap.

A worked example

Given: an AHU at 1,800 CFM, coil inlet: $t_1$ = 90°F, $φ_1$ = 55%, outlet: $t_2$ = 57°F, $φ_2$ = 95%.

Psychrometric values:

• Air density at inlet: $\rho \approx 0.0714\ \text{lb/ft}^3$
• $h_1$ (90°F, φ 55%): $\approx \mathbf{40.08}\ \textbf{Btu/lb}$
• $h_2$ (57°F, φ 95%): $\approx \mathbf{23.93}\ \textbf{Btu/lb}$
• $W_1 \approx 117.5\ \text{gr/lb}$, $W_2 \approx 66.1\ \text{gr/lb}$

Results:

• Total capacity: $Q_{total} = 4.5 \cdot 1800 \cdot 16.15 = \mathbf{130{,}800}\ \textbf{Btu/h}$ (10.9 tons)
• Sensible capacity: $Q_s = 1.08 \cdot 1800 \cdot (90 - 57) = \mathbf{64{,}150}\ \textbf{Btu/h}$
• Latent capacity: $Q_{lat} = 130{,}800 - 64{,}150 = \mathbf{66{,}650}\ \textbf{Btu/h}$
• Condensate: $4.5 \cdot 1800 \cdot 0.00735 = \mathbf{59.5}\ \textbf{lb/h}$ — about 7.1 gal/h

Sensible heat ratio (SHR)

The SHR (Sensible Heat Ratio) gives the share of the total cooling capacity that is sensible cooling:

$$\text{SHR} = \frac{Q_s}{Q_{total}} = \frac{64{,}150}{130{,}800} = \mathbf{0.49}$$

Typical values:

• Offices: SHR = 0.75–0.85 (low internal latent-heat production)
• Restaurants, natatoriums: SHR = 0.45–0.65
• Hot, humid climates: SHR = 0.50–0.65

An SHR this far below the office range is the signature of a hot, humid design day — over half the coil duty is going into moisture removal, not temperature.

The temperature after the coil (bypass factor)

A real coil never cools all the air exactly to the surface temperature of the exchanger. The bypass factor (BF) = the fraction of air that passes through the coil without contact:

$$t_2 = t_{\text{ADP}} + \text{BF} \cdot (t_1 - t_{\text{ADP}})$$

where $t_{\text{ADP}}$ is the apparatus dew point temperature — the effective surface temperature of the exchanger.

The BF for a finned exchanger is typically 0.05–0.15. On the psychrometric chart, the outlet-air state lies on the line connecting the state $t_1$, $\varphi_1$ with the saturation curve — the distance corresponds to the BF.

Cooling on the psychrometric chart

On the chart:

1. Plot the inlet air state (point 1)
2. Draw the coil process line down and to the left toward the saturation curve — point 2’ is the ideal outlet at the ADP (BF = 0)
3. The actual outlet (point 2) lies on the segment 1–2’ at a distance BF from the saturation curve

You can also work the construction through by hand — a blank chart to print draws the saturation curve at 0.5 mm, so it is easy to aim at with a ruler. PsychroView performs this calculation automatically once you enter the inlet state and the outlet temperature or enthalpy.

Frequently asked questions

How do I find the cooling capacity I need? The cooling capacity is set by the room’s heat gains (sun, people, lighting, equipment) plus the heat brought in by ventilation. For a standard office, reckon on roughly 19–32 Btu/h per square foot of total cooling capacity — the familiar 375 to 630 square feet per ton.

Why is the coil outlet saturated air? The coil cools the air below its dew point — moisture condenses and the air approaches saturation. Downstream of the coil the air is typically φ = 90–100% and relatively cold (54–61°F), which is why a reheat coil is usually placed after it.

What is a chilled-water coil and a DX coil? Chilled-water coil (CW) — cold water (typically 43/54°F supply/return) from a central cooling source (a chiller) flows through the tubes. DX coil (direct expansion) — refrigerant evaporates in the coil directly from a compressor unit.