Worked problem

Sensible Cooling Capacity from Airflow and Temperature Difference

Use Q = 1.08 × CFM × ΔT to find the sensible cooling delivered by 2,000 CFM of air at a 20 °F temperature drop, and convert it to tons.

Mechanical, HVAC & Fluids · Last reviewed

Given

An air handler delivers 2,000 CFM of supply air to a room. The supply air is 20 °F colder than the room air. Standard air at sea level.

Find

The sensible cooling capacity in Btu/h and in tons of refrigeration.

Solution

Q(sensible, Btu/h) = 1.08 × CFM × ΔT(°F)
  1. Q = 1.08 × 2,000 × 20 = 43,200 Btu/h.
  2. One ton of refrigeration is 12,000 Btu/h, so 43,200 ÷ 12,000 = 3.6 tons.

Answer

43,200 Btu/h sensible | 3.6 tons

Where the 1.08 comes from

It is the air density (about 0.075 lb/ft³) times the specific heat (about 0.24 Btu/lb·°F) times 60 minutes per hour: 0.075 × 0.24 × 60 = 1.08. It holds for standard air near sea level. At altitude or high temperature the density changes and so does the factor.

Common mistakes

  • Using the sensible formula for total load. Moisture removal (latent load) is not included in 1.08 × CFM × ΔT.
  • Using the supply-to-return difference instead of the supply-to-room difference.
  • Using the sea-level factor at high altitude without correcting for density.

Try a variation: find the airflow

  1. A room has a sensible cooling load of 60,000 Btu/h and the supply air is 18 °F colder than the room.
  2. CFM = 60,000 ÷ (1.08 × 18) = 3,086 CFM.
  3. At 5,000 ft the air is about 83% as dense, so the factor drops to 1.08 × 0.832 = 0.90. The airflow needed rises to 60,000 ÷ (0.90 × 18) = 3,710 CFM, about 20% more.

Sanity check

Pure sensible cooling at a 20 °F split needs 12,000 ÷ (1.08 × 20) = 556 CFM per ton. Comfort systems are usually quoted at about 350 to 400 CFM per ton of total capacity, because roughly a quarter of the capacity removes moisture rather than temperature.

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Questions

How do I include latent cooling?

The latent load uses 0.68 × CFM × Δgrains of moisture per pound of dry air (Btu/h, standard air), or an enthalpy calculation. Total capacity is sensible plus latent.

How do I find the airflow I need?

Rearrange: CFM = Q ÷ (1.08 × ΔT). A 43,200 Btu/h sensible load at ΔT = 20 °F needs 2,000 CFM.

Why is the factor 1.08 and not 1?

It combines the density of air, its specific heat and the 60 minutes in an hour. See the explanation above for how it is built.

How does altitude change the calculation?

Thinner air carries less heat per cubic foot, so the factor is lower and more airflow is needed for the same capacity. Correct it with the density ratio at the site elevation.

What is the difference between sensible, latent and total cooling?

Sensible cooling lowers the air temperature. Latent cooling removes moisture. Total cooling is the sum of the two and is what the equipment capacity rating describes.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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