mechanical engineering

The volumetric flow rate in a heating system can be expressed by the basic equation:

q = h / ( cp ρ dt ) (1)
where
q = volumetric flow rate
h = heat flow rate
cp = specific heat capacity
ρ = density
dt = temperature difference

The basic equation can be modified for the actual units - SI or imperial - and the liquids in use.
Volumetric Water Flow Rate in Imperial Units
For water with temperature 60oF flow rate can be expressed as:
q = h (7.48 gal/ft3) / ((1 Btu/lbm.oF) (62.34 lb/ft3) (60 min/h) dt) (2)
or
q = h / (500 dt) (2b)
where
q = water flow rate (gal/min)
h = heat flow rate (Btu/h)
dt = temperature difference (oF)

For more exact volumetric flow rates for hot water the properties of hot water should be used.
Water Mass Flow Rate in Imperial Units
Water mass flow can be expressed as:
m = h / ((1.2 Btu/lbm.oF) dt) (2c)
where
m = mass flow (lbm/h)

Volumetric Water Flow Rate in SI-Units
For a water heating system the volumetric flow can be expressed in SI-units as:
q = h / ((4.2 kg.oC) (1000 kg/m3) dt) (3)
where
q = water flow rate (m3/s)
h = heat flow rate (kW or kJ/s)
dt = temperature difference (oC)

For more exact volumetric flow rates for hot water the properties of hot water should be used.
Water Mass Flow Rate in SI-units
Mass flow of water can be expressed as:
m = h / ((4.2 kg.oC) dt) (3b)
where
m = mass flow rate (kg/s)

Example - Flow Rate in a Heating System
A water circulating heating systems delivers 230 kW with a temperature difference of 20oC.
The volumetric flow can be expressed as:
q = (230 kW) / ((4.2 kg.oC) (1000 kg/m3) (20oC))
= 2.7 10-3 m3/s
The mass flow can be expressed as:
m = (230 kW) / ((4.2 kJ/kg.oC) (20oC))
= 2.7 kg/s