Simple Snow Part 2

Wet Bulb Temperature - What is its origin and meaning?

Yaroslav Stanchak (Revised 2/26/09)

Atmospheric air has the capability of absorbing moisture (water vapor) from its surroundings by a process called evaporation. Evaporation can be simply described as water changing state from a liquid to a gas. This common phenomena is linked to our everyday lives in an almost unnoticeable fashion and yet, it is part of the worldwide engine that in combination with the sun's heat, produces our daily weather patterns. The evaporative process of water is such that the change of state from liquid water to water vapor requires the addition of heat energy in order for it to occur. At a normal air pressure of 14.7 psi (sea level) and at a given temperature air can absorb moisture up to a certain point - this point is called the saturation point in thermodynamic technical jargon. At this saturation point the relative humidity (RH) equals 100% and no additional moisture can be absorbed. It is interesting to point out that as the ambient air temperature rises, the moisture absorption capacity of the air increases, that is a given volume of air can hold more water vapor as the air temperature rises. As the surrounding air temperature falls the moisture capacity decreases and the surplus moisture will condense out. Two important points!

In very simple terms, the relative humidity value is a measure describing the amount of moisture absorption capacity in the surrounding ambient air for a given air temperature. Mentioned above is the simple fact that for evaporation to occur the addition of heat energy is required.

Evaporative coolers have been used effectively for perhaps a couple of thousand years and it is only in the recent times that the scientific eye been able to describe the process in terms that are more mathematical. Necessity forced the development of methods to accurately describe the evaporative cooling process for applications requiring refrigeration and cooling. One very simple method for describing the evaporative cooling effect is the "sling psychrometer" device, which consists of a "dry bulb" and "wet bulb" thermometer mounted together on a simple frame. The "wet bulb" thermometer has a clean thin wetted cloth or wick covering the thermometer bulb. The frame has a handle that allows it to be "whirled" rapidly through the air and after a suitable time the readings of both thermometers are recorded. Usually both thermometers will have different values with the exception of the saturation point at 100% RH. The wet bulb thermometer is normally cooler due to evaporation. This temperature differential is called the "wet bulb depression". The lower the relative humidity, the greater the temperature difference between the two thermometers. At 100% RH the temperature difference between both thermometers will be zero. Utilizing semi-empirical equations, developed by W.H. Carrier around 1900, the necessary cooling calculations could then be made from this information. An outgrowth of these calculations is the "psychrometric chart", which was used for rapid calculation of relative humidity and other variables. In snowmaking, a type of psychrometric chart is used for wet bulb calculations by utilizing relative humidity and dry bulb temperature. So how does all this affect and impact the snowmaking process? The key phrase here is heat energy!

In thermodynamic terms, by definition, the amount of released heat energy required to change the state of one pound of water from a liquid to a solid (ice) is 144 BTU. A BTU (British Thermal Unit) is defined as the amount of energy required to raise one pound of water 1 degree F from 59.5F to 60.5F. Of more interest to snowmaking is the fact that for water to change from a liquid to a vapor requires the addition of 1,076 BTU/lb. of heat energy. Therefore, the evaporative cooling affect is approximately seven and a half times greater than the heat energy needed to freeze one pound of water - a very significant advantage to the snowmaking process, particularly in the marginal temperature ranges. The theoretical limit to the evaporative weight loss is thusly less than 12% of the water volume to be cooled. This limit does not necessarily hold true under real world snowmaking conditions. For an extreme example of the heat energy magnitude from evaporative cooling consider the following, a snowmaking system utilizes 1,000 gpm (8340 lbs. per minute) of water at an ambient dry bulb temperature of 32F under low humidity conditions. In order to freeze this volume of water 1,059,200 BTU/min of heat energy are required to be removed and this can be theoretically provided by 984.4 lbs/min of evaporated water volume. The heat energy due to evaporation is equivalent to 24,958 horsepower, or in more understandable terms, 18.6 megawatts of electrical demand. This extreme example illustrates that without evaporation marginal temperature snowmaking would be impractical from a cost and energy perspective. The impact and magnitude of evaporative cooling is greatest at the marginal snowmaking temperatures and rapidly diminishes as the temperature falls below 20F. Under increasing relative humidity conditions the cooling effect is steadily diminished to a zero value at 100% RH. Methods that are more modern utilize complex equations for the wet bulb calculation, which are normally executed by a computer. One little known, but interesting item, related to the wet bulb calculation, is the impact of altitude on the wet bulb temperature for a given snowmaking dry bulb temperature and humidity. Normally altitude is neglected in the wet bulb calculation for the majority of snowmaking applications, however altitudes over 5,000 ft have a significant impact on the calculated wet bulb value. In effect, at the higher elevations atmospheric air will absorb more moisture per pound of air resulting in a lower wet bulb temperature for a given temperature and humidity condition. This impact is noticeable over the range of normal snowmaking temperature conditions. For the above example of 20F, the evaporative cooling effect is approximately 10 % greater at 5,000 feet of elevation than at sea level - greater altitudes further amplify this effect.

The above information was distilled from a number of resources. The Internet contains a wealth of information on this subject, see:

http://www.the-snowman.com/wetbulb2.html (downloadable wet bulb calculator)

http://www.thermalinc.com/math/wetbulbcalc.htm (wet bulb calculator, altitude impact)

http://joseph-bartlo.net/articles/070297.htm (wet bulb equations)

http://www.its.caltech.edu/~atomic/snowcrystals/ice/ice.htm (ice crystal information)

http://www.dfrc.nasa.gov/DTRS/1977/PDF/H-937.pdf (comprehensive equations)