Differential pressure due to difference in density between hot and cold water is the circulating force in a self circulating heating system
A self circulation heating system operates by a force created by a density difference between the hot and cold fluid.
The head available forcing circulation through a radiator in a gravity system is proportional to the elevation - he - of the radiator or heating element above the boiler, and the temperature difference between the flow and return pipes.
The head available for circulation can be expressed as:
hl = hr (ρr - ρf) / [(ρr + ρf) / 2] (1)
hl = head available for circulation (m, ft)
hr = height of radiator or heating element above boiler (m, ft)
ρf = density of water in flow (hot) pipe (lb/ft3, kg/m3)
ρr = density of water in return (cold) pipe (lb/ft3, kg/m3)
The thermal expansion of water is 4.2% from 4 oC to 100 oC.
Converting Head to Pressure
Head can be converted to pressure units by the expression:
p = hl ρ g (2)
p = pressure (Pa, N/m2) - Other units?
ρ = density (kg/m3). Using hot or cold density have very little impact on this calculation.
g = gravitation 9.81 (m/s2)
Circulating Pressure - Flow and Return Temperature
The forcing pressures in self circulation system with operating temperatures between 50 to 95oC are indicated in the diagram and table below.
|Circulating Pressure in Pa (N/m2) per m circulating elevation - he|
|Flow Temperature (oC)|