Cooling-Water Demand: Estimating Flow from Heat Load and Temperature Rise

Estimating cooling-water demand is a recurring task in building services, data-center, and industrial design. The required flow follows from a heat balance: water removes heat at a rate set by its mass flow rate, its heat capacity, and how much its temperature is allowed to increase between entering and leaving the load. Any two of the three quantities — cooling load, flow rate, or temperature rise — fix the third. This article explains the relationship, works through examples in US customary and metric units, and describes the follow-on checks that turn a flow estimate into a workable design.

The Governing Relationship

When water absorbs heat without boiling, the heat removed per unit time equals the product of mass flow rate, specific heat capacity, and temperature rise — written q = ṁ c_p ΔT. The cooling load q is expressed in BTU/hr or kilowatts (kW); the specific heat of water is about 1 BTU per lb·°F (roughly 4.19 kJ per kg·°C); and ΔT is the temperature rise across the load, conventionally the return temperature minus the supply temperature. One ton of refrigeration equals 12,000 BTU/hr, so a 120,000 BTU/hr load is a 10-ton load.

US customary units make the arithmetic convenient. A gallon of water weighs about 8.34 lb, so a flow of 1 GPM moves roughly 500 lb of water each hour; multiplied by the specific heat of about 1 BTU/(lb·°F), each GPM absorbs about 500 BTU/hr for every °F of rise. The resulting shortcut is BTU/hr = 500 × GPM × ΔT, rearranged as GPM = BTU/hr ÷ (500 × ΔT). Chilled-water flow guidance for data centers describes 500 as a fluid factor combining density and specific heat, to be replaced with a different factor for other fluids. In metric form the equivalent is L/s = kW ÷ (4.19 × ΔT in °C). Dividing the flow result by the load gives a flow intensity in L/s per kW (or GPM per ton of refrigeration), which liquid-cooling flow-rate calculators normalize to classify a design as too low, marginal, recommended, high, or too high in flow intensity.

Worked Examples

Three examples show the formula in practice; the second and third are hypothetical illustrations.

• Chilled-water load. A circuit serving 120,000 BTU/hr (10 tons) with a designed 10 °F rise needs 120,000 ÷ (500 × 10) = 24 GPM — equivalently 2.4 GPM per ton.
• Metric process load. For a 100 kW load allowed a 5 °C rise, flow is 100 ÷ (4.19 × 5) ≈ 4.8 L/s (about 76 GPM), an intensity of 0.048 L/s per kW — within the 0.035–0.053 L/s per kW band quoted as practical for many chilled-water loops.
• Condenser loop. Suppose a 400-ton water-cooled chiller rejects condenser heat — the refrigeration load plus compressor power — at 15,000 BTU/hr per ton across a 10 °F range. Flow is 15,000 ÷ (500 × 10) = 3 GPM per ton, or 1,200 GPM (about 4,540 L/min), 25 percent more than the 960 GPM needed on the chilled-water side for the same 400 tons at the same rise, because compressor heat joins the load on the condenser side.

Choosing the Temperature Rise

ΔT is a design lever. A larger rise lets each gallon carry more heat, so less circulation — and smaller pipe and pump power — is required; a smaller rise forces more flow because each gallon carries less heat. The rise cannot be chosen freely, however: the load must still receive water cold enough to do its job, and the resulting warm return must be acceptable to the upstream plant, whether a chiller evaporator or a cooling tower. For plain-water chilled systems, a commonly cited design band is 0.035–0.053 L/s per kW, converted to roughly 1.95–2.95 GPM per ton, consistent with water rises of about 8–12 °F. One consistency check is mandatory regardless of the value chosen: ΔT must be positive, with return warmer than supply; an input in which the return equals or falls below the supply describes no cooling rise and is rejected by chilled-water calculators.

From Flow to Pipe Size

Flow alone does not complete a design: the same gallons must move through a chosen pipe at a sensible velocity. Chilled-water guidance pairs the flow estimate with the shortcut V = 0.4085 × GPM ÷ d², where V is velocity in ft/s and d is the internal pipe diameter in inches. Velocity drives pressure drop and pump head, and excessively high values add erosion and noise risk, so a diameter that passes the flow check may still fail a velocity check. For the 24 GPM example above:

Halving the diameter roughly quadruples the velocity, because d appears squared in the denominator — which is why a modest upsizing relieves velocity quickly.

Circulating Flow versus Makeup Water

Cooling-water demand has two distinct senses. Circulating flow is the volume moved through the pipes each minute; consumptive demand is the fresh water a system must replace. Historically, systems drew a continuous stream from utility supplies or natural water bodies and discharged it heated to a sewer or waterway, but as the ASHRAE Handbook chapter on cooling towers recounts, purchased water became prohibitively expensive and thermal discharge ecologically unacceptable, so recirculation through cooling towers became the norm. In a tower, evaporation removes heat and cools the water toward the ambient wet-bulb temperature; the resulting cold-water temperature is characterized by the tower approach. That lets evaporative towers produce colder water than dry air-cooled exchangers, which per ASHRAE can economically cool water only to within about 20 °F of the ambient dry-bulb temperature. Tower water balances therefore track evaporation, drift (small droplets entrained in the air stream), and blowdown — the deliberate bleed that limits dissolved-solids concentration, expressed as cycles of concentration — and sum the three into makeup-water demand and annual cost, as in a cooling-tower flow and makeup calculator. The evaporation share can be estimated from the heat balance itself: at a 10 °F range, each GPM carries about 5,000 BTU/hr, enough at a latent heat near 1,000 BTU/lb to evaporate roughly 5 lb of water per hour — about 1 percent of the circulating flow, before blowdown and drift add to it.

Assumptions and Limits

The flow formula rests on assumptions worth stating:

• Steady conditions. The balance assumes constant load and flow; real loads fluctuate, and diversity among parallel equipment means design flow may be less than the sum of individual branch flows.
• Water properties. The fluid factor of 500 applies to plain water at ordinary temperatures and varies only modestly with temperature. Glycol solutions carry less heat per gallon because of lower specific heat, so the same load demands more flow until the factor is corrected.
• Sensible heat only. The relationship covers warming of liquid water, not boiling or condensation; duty involving phase change needs a latent-heat treatment.
• Necessary, not sufficient. Adequate circulation must be matched by adequate heat-exchange surface; the right flow alone does not guarantee heat removal.
• Sign convention. ΔT is return minus supply; an inverted or non-positive rise makes the calculation meaningless.

Common Mistakes

• Interchanging tons and BTU/hr without the 12,000 BTU/hr conversion, so a 10-ton load is misread as 10,000 BTU/hr.
• Sizing condenser water from refrigeration tonnage alone, forgetting compressor heat — the reason tower tools ask for heat rejection in BTU/hr per ton rather than assuming the bare refrigeration rate.
• Sizing pipe by flow alone and skipping the velocity check, leaving high pressure drop or erosion risk.
• Treating higher flow as harmless: excessive flow intensity wastes pumping energy, while very low intensity leaves marginally cooled loads — both extremes are flagged in calculator classifications.

A Practical Checklist

1. Fix the load. Express it in one unit system, converting tons at 12,000 BTU/hr each.
2. Allow for rejection duty. For condenser water, add compressor heat through a heat-rejection-per-ton allowance instead of the bare refrigeration load.
3. Choose the rise. Select a ΔT that both the load and the upstream plant can deliver.
4. Compute flow. Apply GPM = BTU/hr ÷ (500 × ΔT), or L/s = kW ÷ (4.19 × ΔT), using a corrected fluid factor for non-water coolants.
5. Sanity-check intensity. Compare the result against roughly 0.035–0.053 L/s per kW (about 1.95–2.95 GPM per ton) for typical chilled-water service.
6. Check velocity. Apply V = 0.4085 × GPM ÷ d² and resize the pipe if velocity is too high.
7. Estimate makeup. For evaporative heat rejection, sum evaporation, drift, and blowdown, and weigh higher cycles of concentration against water-treatment cost.

Combined, the heat balance and these checks turn a bare number — so many GPM or liters per second — into a circulation rate sized for the load, a pipe sized for the flow, and a realistic account of the fresh water the system will consume.