George R. Carey, Jr.
Vice President,
Fluid Industrial Associates
gcarey@fiainc.com
twitter: @Ask_GCarey
Boiler Facts
The Most Important
Formula in Hydronics
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.
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.
In hydronic heating systems, the heat is distributed through
water.
16 ICM/July/August 2020