Humidity

C LIMATE AND A TMOSPHERIC T HERMODYNAMICS

3.8 Humidity

Water vapor is a very important component of air. It is capable of transforming from gas to liquid (condensation) to solid (freezing), and from solid to liquid (melting) to gas (evaporation). It is responsible for the formation of clouds and precipitation. Water vapor is also capable of transforming directly into solid ice crystals (deposition) and from ice directly back to vapor (sublimation). The formation of clouds starts from particles called condensation nuclei. These small particles are present due to pollutants such as sulphur, salt, gas, smoke, and smog. These particles attract water droplets to form agglomerates that later expand to form clouds. You may employ isoplats (lines of constant acid precipitation) and isoflors (lines of constant areas of comparable biological diversity) to investigate the effect of human population and related pollutants on precipitation occurrence, duration, and intensity. Depending on the method of formation of these droplets, different temperature levels can be identified that are categorized into three main groups known as dew-point, dry-bulb, and wet-bulb temperatures.

There are two properties associated with humidity: relative humidity and humidity ratio, also known as moisture content, are associated with mole and mass fractions, respectively [75,76]. Relative humidity is the

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ratio of the mole fraction of water vapor in moist air to the mole fraction of water in the saturated case at a constant temperature and is expressed as a percentage. It may also be expressed as the ratio of the vapor partial pressure to that of the equilibrium state at a constant temperature. At low temperatures, vapor partial pressure increases, resulting in less humidity in the air compared to that of high temperature cases. Fully saturated moist air is another way of expressing the relative humidity as 100 percent.

Humidity ratio, on the other hand, is the ratio of the mass of the water vapor to that of the dry air. You may come across the term mixing ratio, especially in thermodynamic diagrams, which is another term for humidity ratio. Using the dry-bulb and wet-bulb temperatures and a psychrometric chart, you can obtain the value of the humidity ratio for the relative humidity of 100 percent. Humidity is measured by a hygrometer.

Both excess and insufficient humidity can lead to undesirable effects for human and mechanical systems, especially in the aviation industry. For humans, lack of humidity may aggravate allergies and promote respiratory problems, dryness of nasal passages and bleeding as a result, and dry skin. High humidity may result in serious health issues, as the body may not be able to accomplish the heat dissipation required to moderate its temperature. The heat index and humidex are factors that combine the effects of temperature as well as humidity on the atmosphere cooling effect. A relative humidity of 50 to 60 percent may be recommended as a comfortable range for human beings.

When flying at high altitudes, temperature is low and therefore there is a low humidity content, which decreases even further with heating the cabin air. The cabin air relative humidity may drop to 10 percent or less, and this may lead to health risks for passengers and the crew. If your skin feels dry during the winter months, you may use a humidifier at your leisure;

however, when flying thousands of feet above the MSL, the humidity that is generated by a supply of water to the system does not seem that practical for the extra weight it introduces, which may or may not be supported by the aircraft weight balance limitations. If, on the other hand, the captain decides to fly at a lower altitude or through the clouds, the increased level of humidity may result in water condensation on the skin of the buoyant object in contact with its surroundings or internal systems, which may be the cause of worry in close to sub-freezing temperatures for the systems—

either internal or external—if not specifically designed for these operating conditions. Carburetor heat is a method to reduce the negative effects of cold humid air flowing into the piston engine of an aircraft. For this

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reason, the dew-point temperature is provided with weather reports so that the spread can be evaluated, especially when making cross-country flight plans. Dry air is better at keeping an aircraft buoyant due to the lift forces it produces and higher flight efficiency compared to that of moist warm air.

This is the reason for including weather conditions in the flight calculations related to the runway length required for takeoff and landing as well as ascent, descent, and cruise performance. Higher humidity combined with high temperatures requires longer takeoff and landing distances. Dry air in general is better able to hold moisture than the moist air.

A number of empirical relationships have been developed in which the saturation vapor pressure (e_s) may be obtained using absolute pressure along with the dry-bulb temperature (T). There are a number of assumptions associated with each formula: for example, the temperature must be between -80 °C (112 °F) and 50 °C (122 °F). Given their empirical nature, each formula poses its own complexity that is a function of the contamination level as well as the applicable temperature range. Equations (40) and (41) are among the most common empirical relations to estimate saturation vapor pressure in kPa versus the temperature in degrees Celsius [77,78,79]. Equation (42) presents Relative Humidity (RH) as the ratio of the partial vapor pressure (e) to saturation partial vapor pressure (e_s) at temperature T. These relations are also known as Arden Buck equations and are considered accurate for temperatures between -80 °C (112 °F) and 50 °C (122 °F).

( ) 0.61121exp 18.678 0 C

234.5 257.14

s

T T

e T T

T

  

 

        (40)

( ) 0.61115exp 23.036 0 C

333.7 279.82

s

T T

e T T

T

  

 

        (41)

 

s  RH e T

e T (42)

3.8.1 Mixing Ratio

Mixing ratio is the ratio of the mass of the mixed components to the total mass—equation (43)—where w₁ is the weight fraction for component 1 with mass (m₁) and w₂ is the weight fraction for component 2 with mass (m₂), with (r_m) the ratio of the component masses (r_m  m₂ /m₁). In weather applications where one deals with vapor and dry air, the mixing ratio (or humidity ratio) may be defined as the mass of the wet component (m_v) to that of the dry component (m_d  m  m_v)—equation (44)—where mis the total mass.

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1 2

1

m m

w w r

w r

 

 (43)

v d

w m

m (44)