# 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

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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/ft^{3}, kg/m^{3})

ρ_{r}= density of water in return (cold) pipe (lb/ft^{3}, kg/m^{3})

The thermal expansion of water is *4.2%* from* 4 ^{o}C to 100 ^{o}C*.

### 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/m^{2}) - Other units?

ρ= density (kg/m^{3}). Using hot or cold density have very little impact on this calculation.

g= gravitation 9.81 (m/s^{2})

### Circulating Pressure - Flow and Return Temperature

The forcing pressures in self circulation system with operating temperatures between *50 to 95 ^{o}C* are indicated in the diagram and table below.

Circulating Pressure in Pa (N/m circulating elevation - ^{2}) per mh_{e} | ||||||
---|---|---|---|---|---|---|

Return Temperature(^{o}C) | Flow Temperature (^{o}C) | |||||

40 | 50 | 60 | 70 | 80 | 90 | |

90 | 0 | |||||

80 | 0 | 64 | ||||

70 | 0 | 59 | 123 | |||

60 | 0 | 54 | 113 | 177 | ||

50 | 0 | 48 | 101 | 161 | 225 | |

40 | 0 | 41 | 89 | 143 | 203 | 267 |

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