Wet-bulb temperatures

The wet-bulb temperature is the steady-state temperature reached by a small amount of liquid evaporating into a large amount of unsaturated gas-vapor mixture. Under properly controlled conditions it can be used to measure the humidity of the mixture. For this purpose a thermometer whose bulb has been covered with a wick kept wet with the liquid is immersed in a rapidly moving stream of the gas mixture. 

The temperature indicated by this thermometer will ultimately reach a value lower than the dry-bulb temperature of the gas if the latter is unsaturated. From a knowledge of this value the humidity is calculated. 

Consider a drop of liquid immersed in a rapidly moving stream of unsaturated gas-vapor mixture. If the liquid is initially at a temperature higher than the gas dew point, the vapor pressure of the liquid will be higher at the drop surface than the partial pressure of the vapor in the gas, and the liquid will evaporate and diffuse into the gas. The latent heat required for the evaporation will at first be supplied at the expense of the sensible heat of the liquid drop, which will then cool down. As soon as the liquid temperature drops below the dry-bulb temperature of the gas, heat will flow from the gas to the liquid, at an increasing rate as the temperature difference becomes larger. Eventually the rate of heat transfer from the gas to the liquid will equal the rate of heat required for the evaporation, and the temperature of the liquid will remain constant at some low value, the wet-bulb temperature Tw. The mechanism of the wet-bulb process is essentially the same as that governing the adiabatic saturation process, except that in the wet-bulb process the humidity of the rapidly moving gas is assumed to remain constant. 

Since both heat and mass transfer occur simultaneously during the wet-bulb process, equation (2-77) applies with qt = 0 since no heat passes through the gas-liquid interface. Given that NB = 0, equation (2-76) reduces to 

The approximation on the right-hand side of equation (8-11) is usually satisfactory since ordinarily the rate of mass transfer is small. Further, 

The wet-bulb temperature, denoted w.b., or is measured by placing a common mercury thermometer, with a water-moistened wick covered bulb, into a fast moving stream of ambient air (e.g., using a sling thermometer). Evaporation of water from the wick cools the bulb, and the amount of cooling is proportional to the evaporation rate, which in turn is inversely proportional to the amount of water in the air. 

Regardless of the type of cooling tower, the same criteria is used to gauge performance the approach of the cooled water temperature compared to the air wet bulb temperature. 

Water is not significantly cooled by exchanging sensible heat with cold air. Most of the cooling results from the humidification of the air. If you live in the Central Valley of California, your home is likely cooled with a swamp cooler, rather than with a freon compressor. The water partially evaporates as it mixes with the dry air. The latent heat of evaporation of water is 1000 Btu/lb. If 2 percent of the water evaporates by contact with the cold air, the water loses 20 Btu/lb. The specific heat of water is one Btu/lb per 1°F. Thus, the water will be cooled by 20°F by evaporation. 

It s my mother s mushroom soup story again, from the first chapter. Converting the sensible heat content of the water into latent heat of evaporation of the water. But for the air to carry away the evolved water vapor, it has to be below its dew-point temperature. 

To gauge how efficiently a cooling tower is working requires two temperatures  

To get the wet bulb temperature, turn on your TV. Switch to the weather channel. Read the current dew-point temperature, which is the same as the wet bulb temperature. 

Water is not significantly cooled by exchanging sensible heat with cold air. Most of the cooling results from the humidification of the air. If you live in the Central Valley of California, your home is likely 

When a stream of unsaturated gas is passed over the surface of a liquid, the huiiiidity of the gas is increased due to evaporation of the liquid. The temperature of the liquid falls below that of the gas and heat is transferred from the gas to the liquid. A equilibrium the rate of heat transfer from the gas just balances that required to vaporise the liquid and the liquid is said to be at the wet-bulb temperature. The rate at which this temperature reached depends on the initial temperatures and the rate of flow of gas past tfe liquid surface. With a small area of contact between the gas and the liquid and a high gas iiowrate, the temperature and the humidity of the gas stream remain virtually unchaDged. The rate of transfer of heat from the gas to the liquid can be written as  

The liquid evaporating into the gas is transferred by diffusion from e interface to the gas stream as a result of a concentration difference (cq - c), where cq is the coneentration of the vapour at the surface (mass per unit volume) and c is the concenUation in the gas stream. The rate of evaporation is then given by  

Both h and /id are dependent on the equivalent gas film thickness, and thus any decrease in the thickness, as a result of increasing the gas velocity for example, increases both h and ho. At normal temperatures, (h/ho) is virtually independent of the gas velocity provided this is greater than about 5 m/s. Under these conditions, heat transfer by convection from the gas stream is large compared with that from the surroundings by radiation and conduction. 

The wet-bulb temperature depends only on the temperature and the humidity of the gas and values normally quoted are determined for comparatively high gas velocities, such that the condition of the gas does not ehaaige appreciably as a result of being brought into contaci with the liquid and the ratio (fe/ho) has reached a constant value. For the air-water system, the ratio (h/hoPA) about 1.0 kJ/kg K and varies from 1.5 to 2.0 kJ/kg K for organic liquids. 

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Wet-bulb Temperature. The equiUbrium temperature which air attains if adiabaticaHy saturated by water from a condensed phase. 

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),... 

Hours in kiln Dry-bulb temperature, °C Wet-bulb temperature, °C Relative humidity, %... 

In Figure 2 the lines, volume, m /kg dry air, indicate humid volume, which includes the volume of 1.0 kg of dry gas plus the volume of vapor it carries. Enthalpy at saturation data are accurate only at the saturation temperature and humidity however, for air—water vapor mixtures, the diagonal wet bulb temperature lines are approximately the same as constant-enthalpy adiabatic cooling lines. The latter are based on the relationship ... 

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. 

If the feed flows countercurrent to the air, as is the case when drying granulated sugar, exhaust temperature does not respond to variations in product moisture. For these diyers, product moisture can better be regulated by controlhng its temperature at the point of discharge. Conveyor-type diyers are usually divided into a number of zones, each separately heated with recirculation of air which raises its wet-bulb temperature. Only the last two zones may require indexing of exhaust-air temperature as a function of AT... 

Trim Coolers Conventional air-cooled heat exchangers can cool the process fluid to within 8.3°C (15°F) of the design dry-biilb temperature. When a lower process outlet temperature is required, a trim cooler is installed in series with the air-cooled heat exchanger. The water-cooled trim cooler can be designed for a 5.6 to 11.1°C (10 to 20°F) approach to the wet-biilb temperature (which in the United States is about 8.3°C (15°F) less than the diy-bulb temperature). In arid areas the difference between diy- and wet-bulb temperatures is much greater. 

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. 

Wet-bulb temperature is the dynamic equilibrium temperature attained by a water surface when the rate of heat transfer to the surface by convection equals the rate of mass transfer away from the surface. At equilibrium, if neghgible change in the dry-bulb temperature is assumed, a heat balance on the surface is... 

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. 

Example 3 Air Heating Air is heated by a steam coil from 30 F dry-bulb temperature and 80 percent relative humidity to 75 F dry-bulb temperature. Find the relative humidity, wet-bulb temperature, and dew point of the heated air. Determine the quantity of heat added per pound of dry air. 

Relative humidity = 15 percent Wet-bulb temperature = 51.5 F Dew point = 25.2 F... 

Example 4 Evaporative Cooling Air at 95 F dry-bulb temperature and 70 F wet-bulb temperature contacts a water spray, where its relative humidity is increased to 90 percent. The spray water is recirculated makeup water enters at 70 F. Determine exit dry-bulb temperature, wet-bulb temperature, change in enthalpy of the air, and quantity of moisture added per pound of dry air. 

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 ... 

Example 5 Cooling and Dehumidification Find the cooling load per pound of dry air resulting from infiltration of room air at 80 F dry-bulb temperature and 67 F wet-bulb temperature into a cooler maintained at. 30 F dry-bulb and 28 F wet-bulb temperature, where moisture freezes on the coil, which is maintained at 20 F. 

Example 6 Cooling Tower Determine water consumption and amount of heat dissipated per 1000 ftVmin of entering air at 90 F drydsulb temperature and 70 F wet-bulb temperature when the air leaves saturated at 110 F and the makeup water is at 75 F. 

AH = moisture-content correction of air saturated at wet-bulb temperature when barometric pressure differs from standard barometer, gr/lb dry air NOTE To obtain AH reduce value of AH by 1 percent where t — t, = 24 F and correct proportionally when t — is not 24 F h = enthalpy of moist air, Btu/lb dry air... 

Example At a barometric pressure of 25.92 with 220 F dry-bulb and 100 F wet-bulb temperatures, determine H, h, andi . Ap = —4, and from table AH = 50.4. From note. 

Since the Schmidt number, Prandtl number, latent heat of vaporization, and humid heat are all essentially independent of pressure, the adiabatic-saturation-temperature and wet-bulb-temperature hues will be substantially equal at pressures different from atmospheric. 

Example 8 Determination of Air Properties For a barometric pressure of 25.92 inHg (Ap = —4), a dry-bulb temperature of 90 F, and a wet-bulb temperature of 70 F determine the following absolute humidity, enthalpy, dew point, relative humidity, and specific volume. 

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