There are the 3 commonly used hydronic formulas;
     Delta-T=Q/(500*F) (Calculates Delt-T through boiler or system)
     f=Q/(500*Delta-T) (Calculates flow in boiler or piping)
     Q=500*Delta-T (Calculates BTUs removed or inputted)
     Where;
     Q=BTU's
     f=Flow Rate in GPM
     Delta-T=Temperature change in water
     500 - Constant physical properties of water

Let's look at an example to determine boiler flow in a cast iron boiler.
     Boiler DOE output = 150,000 btu's
     Delta-T=14

  Using the formula to determine flow is f=Q/(500*Delta-T)
     F=150,000/(500*14)
     F=150,000/7000
     F=21.4 gpm

The boiler flow rate should be a maximum of 15 gpm (Input divided by 10,000 = 20°F Delta-T). The flow rate is over 21 gpm.

Here is the problem.
Residential cast iron boilers, the industry usually tries to keep the flow rate between a 20°F and 40°F delta-T. To do this, the flow rate must be kept within a range for the boiler. Determining the flow rate is simple. Find the DOE input of the boiler. Let's use the above boiler of 150,000 BTU. A 20f delta-T can be determined by dividing the DOE output by 10,000. In our example, 150,000/10,000 = 15 gpm. To get the flow at a 40F delta-T, divide the 20F in half. A 20f to 40f Delta-T for a 150,000 BTU DOE output boiler, the flow rate should be between 7.5 and 15 gpm.
Generally speaking, a flow rate below 7.5 gpm in this example would cause the boiler to short-cycle, lowering the boiler efficiency. If the flow rate exceeds 15 gpm, the boiler will struggle to achieve the desired water temperature. This can cause the building to take much longer to reach the thermostat setpoint, and possibly condense for a longer time during operation.
There are variables to consider when changing a boiler or installing a new system. These consist of the following.