Circulating Force in a Gravity Heating System

Differential pressure due to difference in density between hot and cold water is the circulating force in a self circulating heating system

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 bythe 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 can be taken from the table below:

Circulating Pressure in Pa (N/m²) per m circulating elevation - h_e
Return Temperature ^oC	Flow Temperature ^oC
Return Temperature ^oC	95	90	85	80	75	70	65	60
50	257	223	190	159	129	101	74	39
55	232	200	168	136	106	97	50	24
60	209	176	143	112	82	53	26
65	183	150	117	87	56	27
70	156	123	90	59	28
75	127	94	61	30
80	98	64	31
85	66	32

Gravity Heating Systems Design

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