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Engineering ToolBox > Calculating Flow Rates in Heating Systems
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
ρ = density
dt = temperature difference
The basic equation can be modified for the actual units - SI or imperial - and the liquids in use.
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 can be expressed as:
m = h / ((1.2 Btu/lbm.oF) dt) (2c)
where
m = mass flow (lbm/h)
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.
Mass flow of water can be expressed as:
m = h / ((4.2 kg.oC) dt) (3b)
where
m = mass flow rate (kg/s)
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