Circulating Force in Gravity Heating Systems

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 the force created by the density difference between the hot and cold fluid.

Gravity Head

The head available forcing circulation through a radiator in a gravity system is proportional to the elevation - h_e - 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:

h_l = h_r ( ρ_r - ρ_f ) / [( ρ_r + ρ_f ) / 2] (1)

where

h_l = head available for circulation (m, ft)

h_r = height of radiator or heating element above boiler (m, ft)

ρ_f = density of water in flow (hot) pipe (lb/ft³, kg/m³)

ρ_r = 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 = h_l ρ g (2)

where

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 95^oC are indicated in the diagram and table below.

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