Adiabatic chart

Wet adiabatic lapse rates can be determined from Fig. 4-7, which is a skew T-log P diagram (or adiabatic chart). On this chart, dry adiabats are lines having a nearly constant slope of 9.8°C/1000 m (5.4°F/1000 ft). The wet adiabats are curved and have slopes that not only vary with the temperature at which the adiabat originates but also change along the length of the adiabats. Note that the wet adiabats tend to approach the slope of the dry adiabats at low temperatures, where the absolute amount of moisture in saturated air is small (see Table 4-3). 

FIGURE 4-7 The skew T-log P diagram, or adiabatic chart. On this chart all lines of temperature versus altitude for dry conditions (i.e., no condensation of water vapor) are nearly straight lines with a slope corresponding to the dry adiabatic lapse rate of 9.8°C/1000 m (5.4°F/1000 ft). These are called dry adiabats and slope upward to the left. Wet adiabats have a variable slope and appear as curved lines. Horizontal lines denote altitude lines of constant temperature slope upward to the right. 

FIGURE 5 A typical tornadic thunderstorm sounding of the atmosphere plotted on a log pressure-skew temperature adiabatic chart. The thick solid lines represent environmental temperature and dew-point temperature measurements. The dashed line Is the temperature of a parcel lifted from the earth s surface. Plus and minus signs Indicated regions of positive and negative buoyancy experienced by the parcel. Since the parcel is 6°C warmer than the environment at 500 mbar, the lifted index (stability indicator) Is defined to be -6°C. [Adapted from Fawbush, E. J., and Miller, R. C. (1953). Bull. Am. Meteorol. Soc. 34, 235-244.]... 

Fig. 27. Rankine cycle in terms of (a) pressure and volume (b) temperature and entropy and (c) MoUier (enthalpy vs entropy) chart, where adiabatic...

Fig. 3. Humidity chart illustrating changes in air temperature and humidity in adiabatic direct-heat (convection) dryers. AB is an adiabatic saturation line.

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. 

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 ... 

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. 

In the case of thick-walled HP vessels, the strain energy in the vessel shell can contribute to the available energy, but for vessels below about 20 MN/m (200 barg) it is negligible and can be ignored. If a MoUier chart for the gas is available, the adiabatic energy can be measured directly. This is the preferred method, but in many cases the relevant chart is not available. 

Figure 28 shows the key features of the humidity chart. The chart consists of the following four parameters plotted as ordinates against temperature on the abscissas (1) Humidity H, as pounds of water per pound of dry air, for air of various relative humidities (2) Specific volume, as cubic feet of dry air per pound of dry air (3) Saturated volume in units of cubic feet of saturated mixture per pound of dry air and (4) latent heat of vaporization (r) in units of Btu per pound of water vaporized. The chart also shows plotted hiunid heat (s) as abscissa versus the humidity (H) as ordinates, and adiabatic humidification curves (i.e., humidity versus temperature). Figure 28 represents mixtures of dry air and water vapor, whereby the total pressure of the mixture is taken as normal barometric. Defining the actual pressure of the water vapor in the mixture as p (in units of mm of mercury), the pressure of the dry air is simply 760 - p. The molal ratio of water vapor to air is p/(760-p), and hence the mass ratio is ... 

Figure 12-12A. Illustration of isentropic path on log pressure-enthalpy diagram, showing Mollier chart method of finding final temperature and calculation of H for reversible and adiabatic compression. (Used by permission Edmister, W. C. Applied Hydrocarbon Thermodynamics, 1961. Gulf Publishing Company, Houston, Texas. All rights reserved.)...

After identifying the initial temperature (T) and pressure (P) values, the final temperature and both enthalpy values (H) can be read on the same entropy line of the appropriate gas Mollier chart. For the adiabatic process, the work done on the gas is equal to AH, see Figures 12-13A-D. The following is reproduced by permission of Edmister, W. C., Applied Hydrocarbon Thermodynamics, Gulf Publishing Company. ... 

This compares with 1,339 bhp calculated by the gas horsepower relation. The values should agree exacdy, and the difference may lie in the reading of charts to determine the polytropic head. Using the bhp calculated with the adiabatic efficiency, e. ... 

The specific enthalpy will increase with dry hulh (sensible heat of the air) and moisture content (sensible and latent heat of the water). The adiabatic (isoenthalpic) lines for an air-water vapour mixture are almost parallel with the wet bulb lines so, to avoid any confusion, the enthalpy scale is placed outside the body of the chart, and readings must be taken using a straight-edge. (See Figure 23.7.)... 

In order that hot condenser water may be re-used in a plant, it is normally cooled by contact with an air stream. The equipment usually takes the form of a tower in which the hot water is run in at the top and allowed to flow downwards over a packing against a countercurrent flow of air which enters at the bottom of the cooling tower. The design of such towers forms an important part of the present chapter, though at the outset it is necessary to consider basic definitions of the various quantities involved in humidification, in particular wet-bulb and adiabatic saturation temperatures, and the way in which humidity data are presented on charts and graphs. While the present discussion is devoted to the very important air-water system, which is in some ways unique, the same principles may be applied to other liquids and gases, and this topic is covered in a final section. 

Two methods of changing the humidity and temperature of a gas from Aidj. JP x i to B(()2. J 2) may be traced on the humidity chart as shown in Figure 13.11. The first method consists of saturating the air by water artificially maintained at the dew point of air of humidity (line AC) and then heating at constant humidity to 82 (line CB). In the second method, the air is heated (line AD) so that its adiabatic saturation temperature corresponds with the dew point of air of humidity JP2- It is then saturated by water at the adiabatic saturation temperature (line DC) and heated at constant humidity to 82 (line CB). In this second method, an additional operation — the preliminary heating—is carried out on the air, hut the water temperature automatically adjusts itself to the required value. 

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. 

From the humidity chart, Figure 13.4 in Volume 1, air at 294 K and of 40 per cent relative humidity has a humidity of 0.006 kg/kg. This remains unchanged on heating to 366 K. At the dryer inlet, the wet bulb temperature of the air is 306 K. In the dryer, the cooling takes place along the adiabatic cooling line until 60 per cent relative humidity is reached. 

For a system of constant diameter (giving a single potential choke point at the end of the pipe), and if the gas is ideal, then the Design Charts for adiabatic flow of gases, given in Perry111 or the Omega method with = 1 (see Annex 8) can be used to determine the flow capacity. is a parameter within these charts. 

This is less than that which can be achieved with a 10% back pressure, and so the actual back pressure, with a 0.15 m diameter pipe will be less than 10%. This method could be used iteratively with different guesses of the back pressure in order to find the actual back pressure. Alternatively, the Design Charts for adiabatic flow of gases given in Perry111 could be used instead of the Omega method as they are more rigorous for the gas-only relief case. However, their use has not been demonstrated here. 

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... 

Adiabatic flash calculation Liquid and vapor enthalpies off charts in the API data book are fitted with linear equations... 

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