# HYPSOMETRY LEVELLING

Hypsometry in surveying |

The hypsometry deals with temperature at which water boils varies with the atmospheric pressure. A liquid boils when its pressure is equal to the atmospheric pressure. The boiling point of vapour water is lowered at higher altitudes since the atmospheric pressure decreases there. the hypsometry levelling used to determine the Altitude of stations.

A hypsometer essentially consists of a sensitive thermometer graduated to 0.2 F or 0.1° C. The thermometer is held upright in a special vessel in such a way that its bulb is a little above the surface of water contained in a small boiler. A spirit lamp is used to heat the water. Knowing the boiling temperature of water, the atmospheric pressure can be found either from the chart or can be calculated from the following approximate formula:

#### Pressure in inches of mercury 29.92 ± 0.586 T₁,

where T₁ = the difference of boiling point from 212 F

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Having known the atmospheric pressure at the point, elevation can be calculated by using the barometric formula given in the previous article. However, the following formula may also be used to calculate the elevation of the point above datum:

#### E₁=T₁ (521 +0.75 T₁)

Similarly, E₂, at the higher station can also be calculated. The difference in elevation between two points is given by

#### E=(E₁-E₂) α

#### where α = air temperature correction=(1+((t₁+t₂-64)/900))

where t₁ = air temperature at lower station

t₂ = air temperature at the higher station.

Water boils at 212 F (100° C) at sea level at atmospheric pressure of 29.921 inches of mercury. A difference of 0.1° F in the reading of the thermometer corresponds to a difference of elevation of about 50 ft. The method is therefore extremely rough.

### Example problem

#### Determine the difference in elevation of two stations A and B from the following observations :

Boiling point at lower station = 210.9 F ; Air temperature = 61 F

Boiling point at upper station = 206.5 F ; Air temperature = 57 F

### Solution

Height of lower point above mean sea level is given by

E = T₁ (521 +0.75 T₁); where T₁ = 212 - 210.9 = 1.1°

E₁ = 1.1 (521 +0.75 x 1.1) = 574 feet.

Similarly, height of upper point above mean sea level is given by

E₂ = T₂ (521 +0.75 T2); where T₂ = 212° -206.5° = 5.5°

E₂ = 5.5 (521 +0.75 x 5.5)= 2888 ft.

Air temperature correction

= α = (1+((t₁+t₂-64)/900)) = (1+((61+57-64)/900)) = 1.06 :.

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