CHAPTER
7
Humidity (Y) is the measure of the water content of the air. The absolute humidity, sometimes called the humidity ratio, is the mass of water vapour per unit mass of dry air and the units are therefore kg kg^{1}, and this will be subsequently termed just the humidity. Air is said to be saturated with water vapour at a given temperature and pressure if its humidity is a maximum under these conditions. If further water is added to saturated air, it must appear as liquid water in the form of a mist or droplets. Under conditions of saturation, the partial pressure of the water vapour in the air is equal to the saturation vapour pressure of water at that temperature. 
The
total pressure of a gaseous mixture, such as air and water vapour, is
made up from the sum of the pressures of its constituents, which are called
the partial pressures. Each partial pressure arises from the molecular
concentration of the constituent and the pressure exerted is that which
corresponds to the number of moles present and the total volume of the
system. The partial pressures are added to obtain the total pressure.
The relative humidity (RH) is defined as the ratio of the partial pressure of the water vapour in the air (p) to the partial pressure of saturated water vapour at the same temperature (p_{s}). Therefore:
and is often expressed as a percentage = 100 p/p_{s}
From steam tables,
the saturation pressure of water vapour at 60°C is 19.9 kPa. If such air were cooled, then when the percentage relative humidity reached 100% the air would be saturated and this would occur at that temperature at which p = p_{}_{s} = 4.8 kPa. Interpolating from the steam tables, or reading from the water vapour pressure/temperature graph, this occurs at a temperature of 32°C and this temperature is called the dew point of the air at this particular moisture content. If cooled below the dew point, the air can no longer retain this quantity of water as vapour and so water must condense out as droplets or a fog, and the water remaining as vapour in the air will be that corresponding to saturation at the temperature reached. The humidity Y can therefore be related to the partial pressure p_{w} of the water vapour in air by the equation:
where P is the total pressure. In circumstances where p_{w} is small compared with P, and this is approximately the case in air/water systems at room temperatures, Y » 18p_{w}^{}/29P. Corresponding to the specific heat, c_{p}, of gases, is the humid heat, c_{s} of moist air. It is used in the same way as a specific heat, the enthalpy change being the mass of dry air multiplied by the temperature difference and by the humid heat. The units are J kg^{1} °C^{1} and the numerical values can be read off a psychrometric chart. It differs from specific heat at constant pressure in that it is based only on the mass of the dry air. The specific heat of the water it contains is effectively incorporated into the humid heat which therefore is numerically a little larger than the specific heat to allow for this. A useful concept in psychrometry is the wetbulb temperature, as compared with the ordinary temperature, which is called the drybulb temperature. The wetbulb temperature is the temperature reached by a water surface, such as that registered by a thermometer bulb surrounded by a wet wick, when exposed to air passing over it. The wick and therefore the thermometer bulb decreases in temperature below the drybulb temperature until the rate of heat transfer from the warmer air to the wick is just equal to the rate of heat transfer needed to provide for the evaporation of water from the wick into the air stream. Equating these two rates of heat transfer gives
where a and s denote actual and saturation temperatures and humidities; h_{c} is the heattransfer coefficient and k'_{g} the mass transfer coefficient from the air to the wick surface; l is the latent heat of evaporation of water. As the relative humidity of the air decreases, so the difference between the wetbulb and drybulb temperatures, called the wetbulb depression, increases and a line connecting wetbulb temperature and relative humidity can be plotted on a suitable chart. When the air is saturated, the wetbulb temperature and the drybulb temperature are identical. Therefore if (T_{a}– T_{s}) is plotted against (Y_{s}– Y_{a}) remembering that the point (T_{s}, Y_{s}) must correspond to a dewpoint condition, we then have a wetbulb straight line on a temperature/humidity chart sloping down from the point (T_{s}, Y_{s}) with a slope of:
A further important concept is that of the adiabatic saturation condition. This is the situation reached by a stream of water, in contact with the humid air, and where the temperature of the air and the humidity follow down a line called the adiabatic saturation line. Both ultimately reach a temperature at which the heat lost by the humid air on cooling is equal to the heat of evaporation of the water leaving the stream of water by evaporation. Under this condition with no heat exchange to the surroundings, the total enthalpy change (kJ kg^{1 dry air)}
where
c_{s} is the humid heat of the air.
This has a useful practical consequence. The wet bulb line and the adiabatic saturation line coincide when the Lewis number = 1. It is now time to examine the chart we have spoken about. It is called a psychrometric chart. In the preceding discussion, we have been considering a chart of humidity against temperature, and such a chart is given in skeleton form on Fig. 7.3 and more fully in Appendix 9, (a) Normal Temperatures and (b) High Temperatures.
running down into the unsaturated region of the chart (that “below” the saturation line). This is the wet bulb or adiabatic cooling line and a net of such lines is shown. Any constant temperature line running between the saturation curve and the zero humidity axis can be divided evenly into fractional humidities which will correspond to fractional relative humidities [for example, a 0.50 ratio of humidities will correspond to a 50% RH because of eqn. (7.4) if P » p_{w}]. This discussion is somewhat oversimplified and close inspection of the chart shows that the axes are not exactly rectangular and that the lines of constant drybulb temperature are not exactly parallel. The reasons are beyond the scope of the present discussion but can be found in appropriate texts such as Keey (1978). The chart also contains other information whose use will emerge as familiarity grows. This chart can be used as the basis of many calculations. It can be used to calculate relative humidities and other properties.
On the humidity chart (Appendix 9a) follow down the wetbulb line for a temperature of 20°C until it meets the drybulb temperature line for 25°C. Examining the location of this point of intersection with reference to the lines of constant relative humidity, it lies between 60% and 70% RH and about 4/10 of the way between them but nearer to the 60% line. Therefore the RH is estimated to be 64%. Similar examination of the enthalpy lines gives an estimated enthalpy of 57 kJ kg^{1}, and from the volume lines a specific volume of 0.862 m^{3} kg^{1}. Once the properties of the air have been determined other calculations can easily be made.
On heating, the air condition moves, at constant absolute humidity as no water vapour is added or subtracted, to the condition at the higher (dry bulb) temperature of 40°C. At this condition, reading from the chart at 40°C and humidity 0.0125 kg kg^{1}, the enthalpy is 73 kJ kg^{1}, specific volume is 0.906 m^{3} kg^{1} and RH 27%.
If the air is used for drying, with the heat for evaporation being supplied by the hot air passing over a wet solid surface, the system behaves like the adiabatic saturation system. It is adiabatic because no heat is obtained from any source external to the air and the wet solid, and the latent heat of evaporation must be obtained by cooling the hot air. Looked at from the viewpoint of the solid, this is a drying process; from the viewpoint of the air it is humidification.
Using the psychrometric chart (hightemperature version, Appendix 9(b) to take in the conditions), the inlet air condition shows the humidity of the drying air to be 0.01 kg kg^{1} and its specific volume to be 0.96 m^{3} kg^{1}. Through the dryer, the condition of the air follows a constant wetbulb line of about 27°C , so at 35°C its condition is a humidity of 0.0207kg kg^{1}.
So each kg, i.e. 0.96 m^{3}, of air passing will remove 0.0107kg water,
If air is cooled, then initially its condition moves along a line of constant humidity, horizontally on a psychrometric chart, until it reaches the saturation curve at its dew point. Further cooling then proceeds down the saturation line to the final temperature, with water condensing to adjust the humidity as the saturation humidity cannot be exceeded.
On
the psychrometric chart, the saturation temperature is 40°C and proceeding
at constant humidity from this, the 45°C line is intersected at a
point indicating: In dryers, it is sometimes useful to reheat the air so as to reduce its relative humidity and thus to give it an additional capacity to evaporate more water from the material being dried. This process can easily be followed on a psychrometric chart.
From the psychrometric chart [normal temperatures, Appendix 9(a)] the humidity of the initial air is 0.0062 kg kg^{1}, specific volume is 0.834 m^{3} kg^{1}, and enthalpy 35 kJ kg^{1}. Proceeding at constant humidity to a temperature of 140°C, the enthalpy is found (high temperature chart) to be 160 kJ kg^{1}. Proceeding along a wetbulb line to an RH of 60% gives the corresponding temperature as 48°C and humidity as 0.045 kg kg^{1}. Reheating to 140°C keeps humidity constant and enthalpy goes to 268 kJ kg^{1}. Thence along a wetbulb line to 60 % RH gives humidity of 0.082 kg kg^{1}.
Exit
temperature of air (from chart) = 60°C.
Assuming that the
air changes are calculated at the conditions in the working space.
Reheat required DH
=
(37  33.5) Methods depend largely upon the concepts that have been presented in the preceding sections, but because they are often needed it seems useful to set them out specifically. Instruments for the measurement of humidity are called hygrometers. Wet and drybulb thermometers. The drybulb temperature is the normal air temperature and the only caution that is needed is that if the thermometer bulb, or element, is exposed to a surface at a substantially higher or lower temperature the possibility of radiation errors should be considered. A simple method to greatly reduce any such error is to interpose a radiation shield, e.g. a metal tube, which stands off from the thermometer bulb 1 cm or so and prevents direct exposure to the radiation source or sink. For the wet bulb thermometer, covering the bulb with a piece of wicking, such as a hollow cotton shoelace of the correct size, and dipping the other end of the wick into water so as to moisten the wet bulb by capillary water flow, is adequate. The necessary aspiration of air past this bulb can be effected by a small fan or by swinging bulb, wick, water bottle and all through the air, as in a sling psychrometer. The maximum difference between the two bulbs gives the wetbulb depression and a psychrometric chart or appropriate tables will then give the relative humidity. Drying > EQUILIBRIUM MOISTURE CONTENT Back to the top 
