Written on: November 11, 2019 by George Carey
In the business of hydronic heating and cooling, there are certain formulas that are used on a regular basis. An important one deals with a system that uses water as its means to deliver comfort in GPM (gallons per minute). Water is the way in which heat is distributed from the boiler room out to where the people are.
How much water determines the flow rate and GPM. An accurate assessment of heat loss in a building is very important to establish the design load conditions. Once the load is established, then we can calculate the necessary flow rate.
GPM = Heat Load/ 500 ^T
GPM describes the flow rate; the heat load is expressed as BTU/H, which is the heat loss of the building at design conditions. ^T is the temperature difference that occurs from the supply to the return when water is circulated through the radiation. Five hundred is the constant for standard water properties at 60°F and it comes from multiplying the weight of one gallon of water at 60°F which is 8.33 pounds x 60 minutes (1 hour).
The complete calculation is then:
GPM = BTU/hr
8.33lb./gal x 60 min x ^t°F
The formula indicates a water temperature of 60°F. However, since 60°F water is too cool for a hot water heating system and too warm for a chilled water system, to calculate the correct flow rate, the formula should be based upon more appropriate water temperatures for each type of system, such as the specific heat of the water or the density changes that occur with changing water temperature. Also, the volume of the water changes when it gets hotter or as it cools down. As you can see from the example that follows, the differences are so minimal that the standard formula works fine for all of our heating and cooling applications.
An example
The formula we use to determine system flow rate assumes a mass flow rate of 500 lbs per hour for each GPM, which means at a 20°^T, 1 GPM will convey 10,000 BTUH (500 x 20) referenced to 60°F water. What happens to the heat conveyance of 1 GPM at 20°F ^T when the circulated water has an average temperature of 200°F? Water at 200°F has a density of 8.04 lb/gallon instead of 8.33 as at 60°F; however, its specific heat goes up to 1.003 from 1.0 as at 60°F. The heat conveyance for 1 GPM at 20°^T will then be:
8.04 x 60 x 1.003 x 20 = 9677 BTUH
The net effect is not significant, but there is another factor that needs to be considered for a complete evaulation. As water temperature rises, it becomes less viscous, and therefore its pressure drop is reduced. When water is circulated at 200°F, the corresponding pressure drop or “head loss” is about 80% of water at 60°F for typical small hydronic systems. When calculated using a system curve, the flow increases by about 10.5%. Now you can multiply the new heat conveyance just calculated by the percentage of flow increase:
1.105 x 9677 = 10,693 BTUH
As you can see, with regards to heat conveyance, the simple “round number” approach will result in design flows very close to the “temperature corrected” flows, providing the results from the “round number” approach aren’t corrected from the original 60°F base for both the heat conveyance and piping pressure drop. The plus and minus factors very closely offset one another.
This article provides an accurate formula to calculate the
flow rate in gallons per minute (GPM) for hydronic heating
and cooling systems.
Bell & Gossett’s The System Syzer is helpful to determine
gallons per minute (GPM).
