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# Heating System Flow Rates

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

## Related Topics

### • Heating Systems

Design of heating systems - capacities and design of boilers, pipelines, heat exchangers, expansion systems and more.

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