# Relative humidity

This is defined as the ratio of the partial pressure of the water vapour in moist air at a given temperature, t, to the partial pressure of saturated water vapour in air at the same temperature, t.

Namely

 (2.16) This is illustrated in Figure 2.7 which shows the pressure-volume changes for steam alone. Ps at a given temperature ^ pss at the same temperature T

Volume

Fig. 2.7 Relative humidity is the ratio pjpb for a constant absolute temperature T, shown on a

Pressure-volume diagram for steam.

That is to say, accepting Dalton’s law, the water vapour content of moist air is considered separately from the dry air content. The line WXYZ is an isotherm for a value of absolute temperature denoted by T. If moist air at a relative humidity of less than 100 per cent contains steam with a partial pressure of pw and a temperature T, it is represented by the point W in the superheated zone. Saturated steam at the same temperature and having a partial pressure px is represented by the point X. The relative humidity, by equation (2.16), is given by

(|> = — X 100

Px

EXAMPLE 2.6

Calculate the relative humidity of moist air at a dry-bulb temperature of 20°C and a moisture content of 0.007 34 kg per kg dry air for a barometric pressure of (a) 101.325 kPa and (b) 95 kPa.

Answer

(a) From equation (2.13)

_ 10U25 X 000734 Ps~ (0.622 + 0.00734) — L1818kPa

From equation (2.10), or from steam tables, or from CIBSE psychrometric tables at 20°C saturated,

Pss = 2.337 kPa

Then, by equation (2.16)

<|> = x 100 = 50.57%

(b) Similarly

95 x0.00734 1inoni„

Ps (0.622 + 0.007 34)

Pss is unchanged because it is independent of barometric pressure and depends only on temperature, which remains at 20°C. Hence

<|> = x 100 = 47.41%

Compare with the answers to Example 2.5.

Posted in Engineering Fifth Edition