Heating System Flow Rates

The volumetric flow rate in a heating system can be expressed as

q = h / (c_p ρ dt)                                           (1)

where

q = volumetric flow rate    (m³/s)

h = heat flow rate  (kJ/s, kW)

c_p = 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/lb_m^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 (lb_m/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

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm