Worked problem

Chilled-Water Flow Rate from Load and Delta-T

Use GPM = 24 × tons ÷ ΔT to find the chilled-water flow for a 120-ton load at a 10 °F temperature rise.

Mechanical, HVAC & Fluids · Last reviewed

Given

A chilled-water coil load of 120 tons. The water enters the coils at 44 °F and leaves at 54 °F (ΔT = 10 °F). Water.

Find

The required chilled-water flow in gallons per minute.

Solution

Q(Btu/h) = 500 × GPM × ΔT(°F)
  1. Convert the load: 120 tons × 12,000 Btu/h per ton = 1,440,000 Btu/h.
  2. GPM = Q ÷ (500 × ΔT) = 1,440,000 ÷ (500 × 10) = 288 GPM.
  3. Shortcut: GPM per ton = 24 ÷ ΔT = 2.4 GPM/ton at a 10 °F rise. 120 × 2.4 = 288 GPM.

Answer

288 GPM (2.4 GPM per ton)

Common mistakes

  • Applying the 500 factor to a glycol mixture. Glycol has a different density and specific heat, so the factor is lower.
  • Mixing tons and Btu/h.
  • Using a flow that was sized for a larger ΔT than the plant actually delivers. A low ΔT at part load is a common cause of poor chilled-water plant efficiency.

Try a variation: a larger temperature rise

  1. With a 14 °F rise, flow per ton = 24 ÷ 14 = 1.71 GPM per ton.
  2. For 120 tons the flow is 120 × 1.71 = 206 GPM, down from 288 GPM at a 10 °F rise.
  3. With a poor 6 °F rise the flow per ton is 4.0 GPM, so 120 tons needs 480 GPM, which costs more pump energy and larger pipe.

A low temperature rise at part load is common and is called low delta-T syndrome. It makes a plant run more pumps and chillers than the load needs.

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Questions

Where does 500 come from?

About 8.33 lb per gallon of water × 1 Btu/lb·°F × 60 min/h = 500 Btu/h per GPM per °F.

What happens at a larger ΔT?

The flow falls in proportion. A 16 °F rise needs only 1.5 GPM per ton, which cuts pump energy, but the coils must be selected for it.

What is low delta-T syndrome?

A condition where the chilled-water return temperature is lower than designed, so the plant moves a lot of water for little heat. Causes include control valves that bypass water, dirty coils and poor control of the loop.

How does glycol change the calculation?

Glycol mixtures have a lower specific heat and a different density, so the factor 500 becomes smaller and more flow is needed for the same load. Use the fluid properties for the actual mixture.

How do I size the pipe for the flow?

Choose a pipe size so that velocity and friction loss per 100 ft stay within the project criteria, then check the pump head. The pump sizing problem in this section shows the head calculation.

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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