Calculating Flow Rates in Heating Systems

Basic flow rate calculations in heating systems

The volumetric flow rate in a heating system can be expressed by the basic equation:

q = h / ( c_p ρ dt ) (1)

where

q = volumetric flow rate

h = heat flow rate

c_p = specific heat capacity

ρ = density

dt = temperature difference

The basic 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) (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 Rate in Imperial Units

Water mass flow can be expressed as:

m = h / ((1.2 Btu/lbm.^oF) dt) (2c)

where

m = mass flow (lbm/h)

Volumetric Water Flow Rate in SI-Units

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.

Water Mass Flow Rate in SI-units

Mass flow of water can be expressed as:

m = h / ((4.2 kg.^oC) dt) (3b)

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 expressed as:

q = (230 kW) / ((4.2 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

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