TAHA Engineering Toolsby TAHA Knowledge Lab

HVAC & Building Services

Chilled & Hot Water Flow Rate Calculator

Water flow rate for a cooling or heating load and ΔT — or the load carried by a known flow.

Inputs

Calculate from
Loop diagram: a chiller on the left and a coil on the right. Supply water flows along the top pipe from chiller to coil at the supply temperature; return water flows back along the bottom pipe at the return temperature. The coil absorbs the load Q.chillercoilsupply water, flow V̇return water (warmer by ΔT)Q (load)
Chilled-water loop: water leaves the chiller at the supply temperature, picks up the load Q in the coil and returns warmer. ΔT = return − supply. For heating, the boiler and coil work the other way round. Diagram not to scale.

Difference between return and supply water temperature, e.g. chilled water 12 °C return and 7 °C supply → ΔT = 5 K. Enter it as a difference.

Water ≈ 4.19 kJ/(kg·K). For glycol mixtures use the manufacturer’s data.

Water ≈ 1000 kg/m³ (998 at 20 °C). Glycol mixtures are denser.

Result

Water flow rate
4.77783
Mass flow
4.77783
Working
ṁ = Q ÷ (cp × ΔT) = 100 ÷ (4.186 × 5) = 4.7778 kg/s V̇ = ṁ ÷ ρ = 4.7778 ÷ 1,000 = 4.7778 L/s

This load needs about 4.77783 L/s of water (4.77783 kg/s).

Educational estimate — check the assumptions below.

About this calculator

In chilled-water and hot-water (hydronic) systems, water carries heat between the chiller or boiler and the coils, fan-coil units or radiators. The flow needed depends on the load and on the temperature difference (ΔT) between the supply and return water: a larger ΔT means less flow, smaller pipes and pumps, but different coil performance. Use this calculator to find the flow for a load, or to check the load a measured flow is carrying.

Formula

Flow for a load

ṁ = Q ÷ (cp × ΔT)    V̇ = ṁ ÷ ρ

Q = load (W), cp = specific heat (J/(kg·K)), ΔT = water temperature difference (K), ṁ = mass flow (kg/s), ρ = density (kg/m³), V̇ = volume flow (m³/s).

For water, the inch-pound rule gpm = Btu/h ÷ (500 × ΔT °F) gives almost the same result (500 = 8.33 lb/gal × 60 min/h × 1 Btu/(lb·°F)). It is often written as gpm = 24 × TR ÷ ΔT.

Load from a flow

Q = ρ × V̇ × cp × ΔT

The heat carried by a measured water flow with a measured temperature difference. Inch-pound form for water: Btu/h = 500 × gpm × ΔT (°F).

Worked example

  • Metric: a 100 kW cooling load with 7 °C supply and 12 °C return (ΔT = 5 K) → ṁ = 100 ÷ (4.186 × 5) = 4.78 kg/s → 4.78 L/s (17.2 m³/h).
  • Inch-pound: 10 TR (120 000 Btu/h) with ΔT = 10 °F → 120 000 ÷ (500 × 10) = 24 gpm (2.4 gpm per ton).
  • Load from flow: 2 L/s of heating water with ΔT = 20 K → Q = 2 × 4.186 × 20 = 167 kW.

Assumptions and limitations

  • Steady flow with constant properties. Water properties change slightly with temperature; the defaults suit chilled and low-temperature hot water.
  • Glycol mixtures have a lower specific heat and higher density than water, so they need more flow for the same load. Enter values from the fluid supplier.
  • Heat gains or losses in the pipework are not included.
  • This gives the flow only. Pipe size, pressure drop and pump selection must be checked separately — see the Pipe Flow calculator for velocity.

References

  • First law of thermodynamics for steady flow: Q = ṁ × cp × ΔT.
  • ASHRAE Handbook — HVAC Systems and Equipment, chapters on hydronic heating and cooling (water-side design).