Psychrometric ratio

Rearranging equation 32 and defining the ratio h -a/iky-ci-Cf ) as r, the psychrometric ratio, give... 

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)]. 

For systems other than air-water vapor, the value of h /k c, may differ appreciably from unity, and the wet-bulb and adiabatic-saturation temperatures are no longer equal. For these systems the psychrometric ratio may be obtained by determining h /k from heat- and mass-transfer an ogies such as the Chilton-Colburn analogy [Ind. Eng. Chem., 26, 1183 (1934)]. For low humidities this analogy gives... 

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 ...

A rate balance between evaporation and heat transfer when radiation occurs may be modified by means of the psychrometric ratio for air-water vapor mixtures to give ... 

Comparing equations 13.8 and 13.9, it is seen that the adiabatic saturation temperature i > equal to the wet-bulb temperature when s = h/hDpA. This is the case for most water vapour systems and accurately so when Jf = 0.047. The ratio (h/hopAs) = b is sometimes known as the psychrometric ratio and, as indicated, b is approximately unity for the air-water system. For most systems involving air and an organic liquid, b = 1.3 - 2.5 and the wet-bulb temperature is higher than the adiabatic saturation temperature. This was confirmed in 1932 by SHERWOOD and COMINGS 2 who worked with water, ethanol, n-propanol, n-butanol, benzene, toluene, carbon tetrachloride, and n-propyl acetate, and found that the wet-bulb temperature was always higher than the adiabatic saturation temperature except in the case of water. 

Jf.d and -WaW are the molal absolute humidity at Tg and t y, respectively (lb-mole vapor/lb-mole gas), hc/kn is known as the psychrometric ratio. 

The wet-bulb temperature is measured with a device called a psychrometer. A simple one can be made by attaching a wick or porous cotton cloth to the mercury bulb of a thermometer and then wetting the wick. As long as the gas flow past the wick is turbulent, readings are not affected by gas velocity and the psychrometric ratio is constant. Dropkin [4] showed that for the air-water system hG/kn — 0.227. 

In a countercurrent packed column, n-butanol flows down at the rate of 0.25 kg/m2 s and is cooled from 330 to 295 K. Air at 290 K, initially free of n-butanol vapour, is passed up the column at the rate of 0.7 m3/m2 s. Calculate the required height of tower and the condition of the exit air. Data Mass transfer coefficient per unit volume, hDa = 0.1 s 1. Psychrometric ratio, (h/hDpAs) = 2.34. Heat transfer coefficients, hL = 3hG. Latent heat of vaporisation of n-butanol, A = 590 kJ/kg. Specific heat capacity of liquid n-butanol, Cl = 2.5 kJ/kg K. Humid heat of gas , s = 1.05 kJ/kg K. 

Based on the approximation that the effect of mass transfer on heat transfer is negligible, the correlation for the psychrometric ratio is obtained by several investigators (Bl, C7, H3, L5, W4). 

Fig. 1. Comparison of correlations for psychrometric ratios with the experimental...

More recently, Henry and Epstein (H3) reported data on psychrometric ratios for cylinders in cross-flow and spheres. Their experimental results, which covered the Lewis number range of 3.7 to 7.2, were identical for spheres and cylinders. Furthermore, their results could best be represented by an equation similar to that of Bedingfield and Drew (Bl) as follows ... 

Figure 1 compares the experimental data of various investigators with Eqs. (11) and (12). Equation (11) compares more favorably with the experimental results at lower values of Schmidt to Prandtl number ratios, whereas Eq. (12) compares more favorably at higher values. It is evident that further work is needed to derive a theoretical relationship which encompasses the entire range of the experimental results. Furthermore, practically no data exist for the psychrometric ratio at high temperatures and high humidities. 

Approximate solutions can be obtained which will satisfy many drying problems. G is a function of Tr and the psychrometric ratio. The psy-chrometric ratio can be assumed constant for an approximate solution. 

Equation (23) contains G, S, and as parameters. G kg Pit,/hTR) is a function of Tr and the psychrometric ratio. The psychrometric ratio can be calculated and is fairly constant. Therefore G is a function of Tr only (Pr, being the vapor pressure at Tr). < is a function of Tr and S is a function of Tr and Tw. In Figs. 3 and 4, moisture concentration and time, in dimensionless coordinates, have been plotted with Tr and Tr — Tyr as parameters. Given Tr, Tyy, and BhTRAo/ KWy, one can determine the drying schedule by using these plots. A /W is the area of heat transfer per pound of water at the critical water content. 

The use of an expression such as (70) indicates that drying occurs by removal of water from the exposed areas on the external surface of the particle and in its capillaries. The treatment may not be applied for temperatures of the solids above the boiling point of water, when intense vapor streams completely alter the heat- and mass-transfer mechanism. The psychrometric ratios have little meaning if the temperatme of the air is much above 250°F. 

B Psychrometric ratio h. Radiation heat transfer coeffi-... 

A special psychrometric chart would need to be constructed for the acetone-nitrogen system to get first estimates (this can be done using PSYCHIC, as shown in Fig. 12-7). A humidity of 0.025 kg/kg at F = 60 C lies just below the adiabatic saturation line for — 40°C. The wet-bulb temperature will not be the same as Fas for this system as the psychrometric ratio p is less than 1, Fwb should be significantly above F. However, let us assume no good first estimate is available and simply take F b to be 0°C initially. 

The ratio (h/M Ay)> termed the psychrometric ratio, lies between 0.96 and 1.005 for air-water vapor mixtures thus it is nearly equal to the value of humid heat c,. If the effect of humidity is neglected, the adiabatic saturation and wet-bulb temperatures and T, respectively) are almost equal for the air-water system. Note, however, that and are conceptually quite different. The adiabatic saturation temperature is a gas temperature and a thermodynamic entity while the wet-bulb temperature is a heat and mass transfer rate-based entity and refers to the temperature of the liquid phase. Under constant drying conditions, the surface of the drying material attains the wet-bulb temperature if the heat transfer is by pure convection. The wet-bulb temperature is independent of surface geometry as a result of the analogy between heat and mass transfer. 

In order to use equation (8-15) for determination of T it is necessary to know the value of hGtkr known as the psychrometric ratio. Values of hG and ky can be estimated independently for the particular shape of the wetted surface by correlations like those presented in Chapter 2, using the heat- and mass-transfer analogy if necessary. Alternatively, experimental values of the psychrometric ratio can be used. Henry and Epstein (1970) have examined the data and methods of measurement and have produced some measurements of their own. For turbulent flow of gases past cylinders, such as wet-bulb thermometers, and past single spheres, the results of 18 gas-vapor systems are well correlated by... 

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