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