Psychrometric line

The reader should be familiar with the use of the air-water psychrometric chart (Figure 2.5). If not, the reader should take a look at some of the problems at the end of Chapters 2 and 3. By way of review, the basic chart consists of a humidity(>/)-temperature (dry-bulb) set of coordinates along with additional parameters (curves) of constant relative humidity, constant moist volume (humid volume), adiabatic cooling curves (which are the same as the wet-bulb or psychrometric lines, for water vapor only) and the 100% relative humidity curve, also called the saturated-air curve. If any two values are known, we can determine the air-moisture condition on Figure 2.5 and evaluate all other required parameters. 

PSYCHROMETRIC LINE AND LEWIS RELATION. For a given wet-bulb temperature, Eq. (23.19) can be plotted on the humidity chart as a straight line having a slope of —hylMJCyX and intersecting the 100 percent line at T . This line is called the psychrometric line. When both a psychromctric line, from Eq. (23.19), and an adiabatic-saturation line, from Eq. (23.11), are plotted for the same point on the 100 percent curve, the relation between the lines depends on the relative magnitudes of and hyIMjJCy. 

Equation (23.21) is known as the Lewis relation. When this relation holds, the psychrometric line and the adiabatic-saturation line becomes essentially the same. In Fig. 23.2 for air-water, therefore, the same line may be used for both. 

For other systems separate lines must be used for psychrometric lines. With nearly all mixtures of air and organic vapors the psychrometric lines are steeper than the adiabatic-saturation lines, and the wet-bulb temperature of any mixture other than a saturated one is higher than the adiabatic-saturation temperature. 

Psychometric methods. A very common method of measuring the humidity is to determine simultaneously the wet-bulb and dry-bulb temperatures. From these readings the humidity is found by locating the psychrometric line intersecting the saturation line at the observed wet-bulb temperature and following the psychrometric line to its intersection with the ordinate of the observed diy-bulb temperature. 

Fig. 2. Psychrometric chart. Below 0°C properties and enthalpy deviation lines ate for ice. Courtesy of Carrier Corp. To convert kj to kcal, divide by 4.184.

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 ...

Constant volume lines Lines on a steam or psychrometric chart passing through the state points representing an equal volume of steam or air (dry or wet). 

When two samples of air are brought together the condition of the mixture may be arrived at arithmetically by adding the heat flow of each and dividing by the total mass flow and similarly for the moisture flow. Alternatively, plot the condition of each onto a psychrometric chart. The mixed condition lies on a straight line between the two in a position proportional to the two quantities. 

Where the pan is in the air stream the condition downstream of the pan has increased moisture content (kg/kg) found from the airflow and moisture input. On a psychrometric chart, this will lie on a line of sensible-to-total heat ratio of 0.3. Thus, the psychrometric plot shows a steep rise in moisture content with a small rise in dry bulb temperature. The latter is a disadvantage when cooling is... 

Water is injected into the air stream in a fine mist by pumped jets or spinning disc. For practical purposes, the psychrometric plot follows a wet bulb line. The air provides the latent heat of evaporation, resulting in a fall in dry bulb temperature. If water were to be supplied at up to 100°C the humidified condition would be at a correspondingly higher total heat of 420 kJ per kg water supplied. 

If the temperature of the water is not controlled it will come to the wet bulb temperature of the air passing through. Ignoring pump heat, the process is adiabatic. The psychrometric plot follows a wet bulb line. 

On this chart, the wet bulb temperatures appear as diagonal lines, coinciding with the dry bulb at the saturation line. If measurements are taken with the two thermometers of the sling psychrometer, the condition can be plotted on the psychrometric chart by taking the intersection of the dry bulb temperature, as read on the vertical line, with the wet bulb temperature, read down the diagonal wet bulb line. 

A further property which is shown on the psychrometric chart is the specific volume of the mixture, measured in cubic metres per kilogram. This appears as a series of diagonal lines, at intervals of 0.01 ml... 

A further complication arises with the application to temperate conditions of room air-conditioners which have heen designed primarily for tropical markets. These units typically work with a sensible/total heat ratio of 0.7. Plotting this process line on the psychrometric chart (see Figure 35.3) shows that the ADP will he about 9°C. 

Calculations involving to systems where the Lewis relation is not applicable are very much more complicated because the adiabatic saturation temperature and the wet-bulb temperature do not coincide. Thus the significance of the adiabatic cooling lines on the psychrometric chart is very much restricted. They no longer represent the changes which take place in a gas as it is humidified by contact with liquid initially at the adiabatic saturation temperature of the gas, but simply give the compositions of all gases with the same adiabatic saturation temperature. 

Derive" the equations for saturated volume, humid heat and the adiabatic cooling lines for the psychrometric chart. 

The interaction between the plume and atmospheric air is represented on the psychrometric chart in Figure 6.12. The saturation line (100% relative humidity) is the focus for saturation of air at various temperatures. At points above this line, the air is supersaturated and a plume is visible. 

When this relation holds, the psychrometric curve for a system can be approximated by the adiabatic saturation line. 

A discussion of the theory of the relationship between he and kg may be found in the psychrometry part of this section. Because both theoretical and experimental values of hjk pply only to dilute gas mixtures, the wet-bulb lines at high concentrations nave been omitted. For a discussion of the precautions to be taken in making psychrometric determinations of solvent vapors at low solvent wet-bulb temperatures in the presence of water vapor, see the paper by Sherwood and Comings [TYans. Am. Inst. Chem. Eng., 28,88 (1932)]. 

The humid volume is the volume occupied by 1 kg of dry air plus the water vapor that accompanies it. Lines of constant humid volume on the psychrometric chart are steep and have negative slopes. On Figure 8.4-1, humid volume lines are shown corresponding to 0.75, 0.80,0.85, and 0.90 m /kg dry air. 

The humid air conditions that correspond to a given wet-bulb temperature fall on a straight line on the psychrometric chart, called a constant wet-bulb temperature line. The constant wet-bulb temperature lines for air-water at 1 atm appear on Rgures 8.4-1 and 8.4-2 as lines with negative slopes extending beyond the saturation curve that are less steep than the lines of constant humid volume. The value of Twb corresponding to a given line can be read at the intersection of the line with the saturation curve. 

The diagonal scale above the saturation curve on the psychrometric chart shows the enthalpy of a unit mass (1 kg or 1 Ibm) of dry air plus the water vapor it contains at saturation. The reference states are liquid water at 1 atm and 0°C (32°F) and dry air at 1 atm and 0°C (Figure 8.4-1) or O F (Figure 8.4-2). To determine the enthalpy from the chart, follow the constant wet-bulb temperature line from the saturation curve at the desired temperature to the enthalpy scale. 

This result (which is far from obvious) allows us to perform adiabatic cooling calculations with relative ease using the psychrometric chart. First locate the initial state of the air on the chart then locate the final state on the constant wet-bulb temperature line that passes through the initial state (or on the 100% humidity curve if cooling below the adiabatic saturation temperature takes place) and finally perform whatever material and energy balance calculations are required. Example 8.4-7 illustrates such a calculation for an adiabatic humidification operation. 

The psychrometric chart for most gas-liquid systems would show a family of adiabatic saturation curves in addition to the families of curves shown on Figures 8.4-1 and 8.4-2. However, for the air-tvater system at 1 atm, the adiabatic saturation curve through a given state coincides with the constant wet-bulb temperature line through that state, so that Tas = Twb- The simple material and energy balance procedure for adiabatic cooling outlined in this section is possible only because of this coincidence. 

For practical purposes, the properties of humid air are recorded on psychrometric (or humidity) charts such as those of Figures 9.1 and 9.2, but tabulated data and equations also are available for greater accuracy. A computer version is available (Wiley Professional Software, Wiley, New York). The terminal properties of a particular adiabatic humification of air are located on the same saturation line, one of those sloping upwards to the left on the charts. For example, all of these points are on the same saturation line (7)//) = (250,0.008), (170, 0.026) and (100,0.043) the saturation enthalpy is 72 Btu/lb dry, but the individual enthalpies are less by the amounts 2.5, 1.2, and 0, respectively. 

When both wet- and dry-bulb temperatures have been found, the humidity is read from the psychrometric chart in the following way. The point on the saturation curve corresponding to the wet-bulb temperature is found first. An adiabatic cooling line is then interpolated and followed until the coordinate corresponding to the dry-bulb temperature is reached. The humidity is read from the other axis. 

The psychrometric chart can be used for a number of other purposes since it is really just a graphical means of presenting the mathematical relationships between the material and energy balances in the air/water vapor systems. It may be pointed out that psychrometric charts exist for systems other than air/water vapor. The charts may be drawn in different ways, but they usually include a basic temperature (dry bulb) and humidity (absolute humidity) set of coordinates (Fig. 1). Additional lines or parameters that are usually included are ... 

One can approximate the results of these calculations by using a psychrometric chart (Fig. 1). Actually, a psychrometric chart is created from these kinds of calculations. To use the chart to obtain the same results as above, first locate the dry-bulb temperature on the abscissa (50 C or 120 F). Follow the vertical line up until it intersects with the curve labeled 50% humidity. At the intersection, follow the horizontal line to the left, which ends at the absolute humidity of 0.04. 

The adiabatic cooling lines are lines of almost constant enthalpy for the entering air-water mixture, and you can use them as such without much error (1 or 2%). However, if you want to correct a saturated enthalpy value for the deviation which exists for a less-than-saturated air-water vapor mixture, you can employ the enthalpy deviation lines which appear on the chart and which can be used as illustrated in the examples below. Any process that is not a wet-bulb process or an adiabatic process with recirculated water can be treated by the usual material and energy balances, taking the basic data for the calculation from the humidity charts. If there is any increase or decrease in the moisture content of the air in a psychrometric process, the small enthalpy effect of the moisture added to the air or lost by the air may be included in the energy balance for the process to make it more exact as illustrated in Examples 4.47 and 4.49. 

FIG. 12-3 Mollier psychrometric chart for the air-water system at standard atmospheric pressure, 101,325 Pa SI units, plots humidity (abscissa) against enthalpy (lines sloping diagonally from top left to bottom right). Source Aspen Technolo. )... 

Aspen Technology httpy/www.aspentech.com. PSYCHIC, one of the Process Tools, generates enstomized psychrometric charts. Mollier and Bowen enthalpy-hnmidity charts are prodneed in addition to Grosvenor. Any gas-vapor system can be handled as well as air-water data supplied for common organic solvents. Can draw operating lines and spot points, as shown in Fig. 12-7. 

From Sonntag equation (12-4),p, = 19,948 Pa difference from Antoine is less than 0.5 percent. Relative humidity = 100 x 3915/19,948= 19.6 percent. From a psychrometric chart, e.g.. Fig. 12-1, a humidity of 0.025 kg/kg at T = 60°C lies very close to the adiabatic saturation line for 35°C. Hence a good first estimate for Tas and T b will be 35°C. Refining the estimate of Twb by using the psychrometer equation and iterating gives... 

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