The Wet-Bulb Temperature

We start by examining the events that occur when a flowing gas comes in contact with a liquid surface. From personal experience, you are aware that this process results in a drop in the temperature of the liquid, often referred to as evaporative cooling. The chill we experience when wind blows over our perspiring bodies is one manifestation of fiiis effect. 

Assume that both the water and the air are initially at the same temperature. During the first stage of evaporation, the energy required for the process (i.e., the latent heat AH ) will come from the liquid, which consequently experiences a drop in temperature. That decline, once it is trigger, will cause a corresponding amount of heat transfer to take place from the air to the water. At this intermediate stage, the latent heat of vaporization is provided both by the liquid and by heat transfer from the warmer gas. 

The relation between T Y, and the system parameters is established by equahng the rate of heat transfer from air to water to the rate of evaporation (i.e., the rate at which moisture is transferred from the water surface to the air). Thus, 

Temperature and humidity distribution around a water drop exposed to a flowing airslream. 

We note from Equation 9.1b that the humidity of the air Yji, can, in principle, be established from measured values of T b, T, and Y b, the latter being obtained from the relation 

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Thus, a measurement of the wet-bulb temperature, and the temperature T, allows the molal humidity, Y, to be calculated because is known. 

For the air—water system, Lewis recognized that Cf = hg/ ky based on empirical evidence. Thus, the adiabatic saturation equation is identical to the wet-bulb temperature line. In general, again based on empirical evidence (21),... 

It is important to have the most accurate measurement of exhaust temperature attainable. Note that Fig. 8-55 shows the sensor inserted into the diyer upstream of the rotating seal, because leakage there could cause the temperature in the exhaust duc t to read low—even lower than the wet-bulb temperature, an impossibility without leakage of either heat or outside air. 

HumidiRcation Chambers The air-cooled heat exchanger is provided with humidification chambers in which the air is cooled to a close approach to the wet-bulb temperature before entering the finned-tube bundle of the heat exchanger. 

Evaporative Cooling The process fluid can be cooled by using evaporative cooling with the sink temperature approaching the wet-bulb temperature. 

Approach temperature. The approach temperature, which is the difference between the process-fluid outlet temperature and the design dry-bulb air temperature, has a practical minimum of 8 to 14°C (15 to 25°F). When a lower process-fluid outlet teiTperature is required, an air-humidification chamber can be providea to reduce the inlet air temperature toward the wet-bulb temperature. A 5.6°C (10°F) approach is feasible. Since typical summer wet-bulb design temperatures in the United States are 8.3°C (15°F) lower than diy-bulb temperatures, the outlet process-fliiid temperature can be 3°C (5°F) below the dry-bulb temperature. 

Experimentally it has been shown that for air-water systems the value of Tj /Zc c, the psychrometric ratio, is approximately equal to 1. Under these conditions the wet-bulb temperatures and adiabatic-saturation temperatures are substantially equal and can be used interchangeably. The difference between adiabatic-saturation temperature and wet-bulb temperature increases with increasing humidity, but this effect is unimportant for most engineering calculations. An empirical formula for wet-bulb temperature determination of moist air at atmospheric pressure is presented by Liley [Jnt. J. of Mechanical Engineering Education, vol. 21, No. 2 (1993)]. 

Example 1 Compare Wet-Bulb and Adiabatic-Saturation Temperatures For tne air-water system at atmospheric pressure, the measured values of dry-bulh and wet-hulh temperatures are 85 and 72 F respectively. Determine the absolute humidity and compare the wet-bulb temperature and adiabatic-saturation temperature. Assume that h /k is given by Eq. (12-4). 

Values of andt, are given by the saturation curve of the psychrometric chart, such as Fig. 12-2. By trial and error, = 72.1 F, or the adiabatic-saturation temperature is 0.1 F higher than the wet-bulb temperature. 

Example 2 Determination of Moist Air Properties Find the properties of moist air when the dry-bulb temperature is 80 F and the wet-bulb temperature is 67 F. 

Solution. Figure 12-8 shows the path on a psychrometric chart. The leaving dry-bulb temperature is obtained directly from Fig. 12-2 as 72.2 F. Since the spray water enters at the wet-bulb temperature of 70 F and there is no heat added to or removed from it, this is by definition an adiabatic process and there will be no change in wet-bulb temperature. The only change in enthalpy is that from the heat content of the makeup water. This can be demonstrated as follows ... 

Theoretical possible heat removal per pound of air circulated in a cooling tower depends on the temperature and moisture content of air. An indication of the moisture content of the air is its wet-bulb temperature. Ideally, then, the wet-bulb temperature is the lowest theoretical temperature to which the water can be cooled. Practically, the cold-water temperature approaches but does not equal the air wet-bulb temperature in a coohng tower this is so because it is impossible to contact all the water with fresh air as the water drops through the wetted fill surface to the basin. The magnitude of approach to the wet-bulb temperature is dependent on tower design. Important factors are air-to-water contact time, amount of fill surface, and breakup of water into droplets. In actual practice, cooling towers are seldom designed for approaches closer than 2.8°C (5°F). 

Enthalpy data are given on the basis of kilojoules per kilogram of diy air. Entbalpy-at-saturation data are accurate only at the saturation temperature and humidity. Enthalpy deviation curves permit enthalpy corrections for humidities less than saturation and show how the wet-bulb-temperature hues do not precisely coincide with constant-enthalpy, adiabatic cooling hnes. 

The wet-bulb-temperature lines represent also the adiabatic-saturation hnes for air and water vapor only. These are based on the relationship... 

For air-water-vapor mixtures, it so happens that h /k = C, approximately, although there is no theoretical reason for this. Hence, since the ratio — H )/(f , — t) equals h /k /X, which represents the slope of the wet-bulb-temperature lines, it is also equal to C, /X, the slope of the adiabatic-saturation lines as shown previously. 

Humidity charts for other solvent vapors may be prepared in an analogous manner. There is one important difference involved, however, in that the wet-bulb temperature differs considerably from the adiabatic-saturation temperatures for vapors other than water. 

Figures 12-37 to 12-39 show humidity charts for carbon tetrachloride, oenzene, and toluene. The lines on these charts have been calculated in the manner outlined for air-water vapor except for the wet-bulb-temperature lines. The determination of these hnes depends on data for the psychrometric ratio /j Z/c, as indicated by Eq. (12-22). For the charts shown, the wet-bulb-temperature hnes are based on the following equation ...

If heat is transferred solely by convection and in the absence of other heat effects, the surface temperature approaches the wet-bulb temperature. However, when heat is transferred by radiation, convection, or a combination of these and convection, the temperature at the saturated surface is between the wet-bulb temperature and the boiling point of water. Under these conditions, the rate of heat transfer is increased and a higher drying rate results. 

When heat is transferred to a wet sohd by convection to hot surfaces and heat transfer by convection is negligible, the solids approach the boiling-point temperature rather than the wet-bulb temperature. This method of heat transfer is utilized in indirect diyers (see classification... 

When the hquid is water and the drying gas is air, is the wet-bulb temperature. 

Determination of the Temperature of the Evaporating Surface in Direct-Heat Tray Dryers When radiation and conduction are negligible, the temperature of the evaporating surface approaches the wet-bulb temperature and is readily obtained from the humidity and diy-bulb temperature. Frequently, however, radiation and conduction cause the temperature of the evaporating surface to exceed the wet-bulb temperature. When this occurs, the true surface temperature must be estimated. 

The temperature driving force for drying is the difference between the drying-gas outlet temperature and, in the case of pure water, the gas wet-bulb temperature. In the case of a solution, the adiabatic saturation temperature of the pure saturated solution is employed rather than the wet-bulb temperature. 

The wet bulb temperatures shown will be exceeded not more than 5% of the total hours during June to September inclusive, of a normal summer. 

This equation is good if the air temperature is 50°F or above, the cooling tower s approach to the wet bulb temperature is 5°F or above, and Hog is within a range of about 0.1 to 8. 

For cooling tow ers, one specifies the required cold water temperature and heat duty. Usually, the 95% summer hours maximum w et bulb temperature for the area is the starting point. To this, an allowance is added for recirculation by raising the wet bulb temperature (say, 1-3°F). After the design air wet bulb inlet temperature is set, the cold w ater approach temperature difference to this W et bulb temperature is specified (often, 10°F). 

For example, if 12° is the wet bulb temperature not exceeded for 95% of the summer hours for the area, a conservative design air w et bulb inlet temperature would be 75°F. Then, for a 10°F approach, the design cold water temperature would be 85°F. 

P v Saturation pressure of water at the wet-bulb temperature. mmHg RH Relative humidity, %... 

A comparison of wet and dry bulb readings allows the relative humidity to be determined from a psychrometric chart. The wet bulb temperature is always lower than the dry bulb value except when the air is already saturated with water - 100% relative humidity. This is when the wet and dry bulb temperatures are the same. Tlie air will no longer accept water and the lack of evaporation does not allow the wetted bulb to reject heat into the air by evaporation. This situation would be... 

The size of the eooling tower, the flow rate and the wet bulb temperature determine the inlet and outlet water temperatures- but not the differenee between them. Inereased eooling tower performanee ean be aehieved by adding surfaee area or by boosting the efm. 

Ambient Wet-Bulb Temperature The temperature in degrees Fahrenheit to which air can be cooled, making it adiabatic to saturation by the addition of water vapor, in practical terms, the wet-bulb temperature is the temperature indicated by a thermometer, the bulb of which is kept moist by a wick and over which air is circulated. 

Approach or Approach to the Wet-BuJb The difference in temperature (°F) of the cold water leaving the tower and the wet-bulb temperature of the ambient air. 

Wet-Bulb Temperature The temperature of saturated air. The lower the wet-bulb temperature, the more exchange of heat a cooling tower can do. A tower cannot cool the water to a temperature below the wet-bulb temperature of the entering air. 

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