# The Most Important Formula in Hydronics

Written on: July 14, 2020 by George Carey

In our world of providing comfort and energy efficiency to our customers, there are certain formulas that are used on a regular basis. The most important one, when talking about a hydronic heating system, is GPM (gallons per minute). Heat is distributed from the boiler room out to where the people are via water. How much water determines the flow rate; the term we use is called GPM. An accurate heat loss reading in a building is very important to establish the design load conditions. Once the load is established, we can calculate the necessary flow rate.

GPM = Heat Load/ 500 ^T

GPM is the flow rate in gallons of water per minute. The heat load is expressed as BTU/H (British Thermal Units per hour), 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 the 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 by 60 minutes (one hour).
The complete calculation is:

GPM = BTU/H
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, you would think that to calculate the correct flow rate, the formula should be based upon more appropriate water temperatures for each type of system—for instance, based on things such as the specific heat of the water, the density changes that occur as the water changes in temperature and the water volume changes when it gets hotter or as it cools down. As you can see from the following example, the differences are so minimal that the standard formula works fine for all of our heating and cooling applications. In hydronic heating systems, the heat is distributed through water.

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, one GPM will convey 10,000 BTU/H (500 x 20) referenced to 60°F water. What happens to the heat conveyance of one GPM @ 20°F ^T when the circulated water has an average temperature of 200°F? Water at 200°F has a density of 8.04 lbs/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 one GPM at 20°^T will then be:

8.04 x 60 x 1.003 x 20 = 9,677 BTU/H

Under pressure
The net effect is not significant, but there is another factor that needs to be considered for a complete evaluation. As water temperature rises, water becomes less viscous, and therefore the 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 a typical small hydronic system.

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 BTU/H

As you can see with regard to heat conveyance, the simple “round number” approach will result in design flows very close to the “temperature-corrected” flows, providing that the results from the “round number” approach isn’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.
The right circulator
GPM plays a major role in ensuring that your heating system performs as expected. You need the right sized circulator to be able to move the heat from the boiler and deliver it out to where the people live. In selecting the proper circulator, not only do you need to know the correct GPM, you also need to know the required pressure drop to circulate the necessary GPM.
As water flows through the pipes and radiation, it “rubs” against the pipe wall causing frictional resistance. This resistance can affect the performance of the heating system by reducing the desired flow rate from circulating, thus reducing the heating capacity of the system. By knowing what this resistance will be, you can select a circulator that can overcome the system’s pressure drop.
Typically, in today’s systems, we use “feet of head” to describe the amount of energy needed so that the required GPM is delivered out to the system. There are pipe sizing charts that have calculated the pressure drop in foot head of energy loss for any flow rate through any size pipe. There are standard piping practices in which the industry references that limit the amount of GPM for a given pipe size. When calculating gallons per minute (GPM), don’t forget about water pressure.

This is based on two reasons:
1. Velocity (how fast the water is moving inside the pipe) can create noise concerns, and in extreme conditions, erosion problems.
2. The required head loss can become so excessive that the required circulator’s head capacity makes for a very “unfriendly” system selection, which can lead to control valve and velocity noise problems (the industry standard is to select a pipe that offers the frictional resistance between 1’–4′ for every 100′ of piping).
For more than 50 years, Bell & Gossett has provided a tool for the hydronics industry called The System Syzer. It is very useful in calculating GPM, the proper pipe size to support the GPM and the corresponding pressure drop and velocity for the calculated GPM.
If you have any questions or comments, e-mail me at gcarey@fiainc.com, call me at FIA 1-800-423-7187 or follow me on Twitter at @Ask_Gcarey. ICM