Heating System Flow Rates
Calculate flow rates in heating systems.
The volumetric flow rate in a heating system can be expressed as
q = h / (cp ρ dt) (1)
where
q = volumetric flow rate (m3/s)
h = heat flow rate (kJ/s, kW)
cp = specific heat (kJ/kg oC)
ρ = density (kg/m3)
dt = temperature difference (oC)
This generic 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 60 oF flow rate can be expressed as
q = h (7.48 gal/ft3) / ((1 Btu/lbm oF) (62.34 lb/ft3) (60 min/h) dt)
= h / (500 dt) (2)
where
q = water flow rate (gal/min)
h = heat flow rate (Btu/h)
ρ = density (lb/ft3)
dt = temperature difference (oF)
For more exact volumetric flow rates 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)
= h / (1.2 dt) (3)
where
m = mass flow (lbm/h)
Volumetric Water Flow Rate in SI-Units
Volumetric water flow in a heating system can be expressed with SI-units as
q = h / ((4.2 kJ/kg oC) (1000 kg/m3) dt)
= h / (4200 dt) (4)
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 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 kJ/kg oC) dt)
= h / (4.2 dt) (5)
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 20 oC .
The volumetric flow can be calculated as:
q = (230 kW) / ((4.2 kJ/kg oC) (1000 kg/m3) (20 oC))
= 2.7 10 -3 m3/s
The mass flow can be expressed as:
m = (230 kW) / ((4.2 kJ/kg oC) (20 oC))
= 2.7 kg/s
Example - Heating Water with Electricity
10 liters of water is heated from 10 oC to 100 oC in 30 minutes . The heat flow rate can be calculated as
h = (4.2 kJ/kg oC) (1000 kg/m3) (10 liter) (1/1000 m3/liter) ((100 oC) - (10 oC)) / ((30 min) (60 s/min))
= 2.1 kJ/s (kW)
The 24V DC electric current required for the heating can be calculated as
I = (2.1 kW) (1000 W/kW) / (24 V)
= 87.5 Amps
