Page 124 - Industrial Ventilation Design Guidebook

86 CHAPTER 4 PHYSICAL FUNDAMENTALS
Comparing the results for (a) and (b), we see that pressure has a consider-
able effect on the result. This is important to remember, especially in industrial
ventilation and process measurements with notable underpressures and over-
pressures.
We will now derive an approximation for Eq. (4.116) that can be used
when the partial pressure of water vapor in air is low compared with the total
pressure.
First we note that with fairly good accuracy it is valid that

where using Eq. (4.83) leads to the approximation

where x'(6 M) is the humidity of saturated air at temperature 0 M when the
total pressure of air is p.
Substituting approximations (4.120) and (4.121) to Eq. (4.116), we
obtain

The Lewis number for air is approximately 1 (see Example 6), so with good
accuracy Le = 1 , and we get an approximation from Eq. (4.122):

Above we considered the question of which temperature the damp cloth
settles to when it is thermally insulated against all surroundings but the air-
flow, and when it can be assumed that there is no radiation heat transfer be-
tween the cloth and the airflow. In this consideration the state of the air has
been constant.
If, instead, the air is damped adiabatically with the wet cloth, so that the
state of the air varies, the cloth will settle to a slightly different temperature.
Each state of air (9, x) is represented by a certain wet bulb temperature 0 M,
which can be calculated from Eq. (4.116) or its approximation (4.123), when
the partial pressures of water vapor are low compared with the total pressure.
When the state of air reaches the saturation curve, we have an interesting spe-
cial case. Now the temperatures of the airflow and the cloth are identical. This
equilibrium temperature is called the adiabatic cooling border or the thermo-
dynamic wet bulb temperature (0 atj).
When air is humidified with water flow rh v and when the incoming and
outgoing humid airflows are denoted rh^ and m 2, the energy balance of the
conditioning chamber can be written as

Equation (4.124) is illustrated in Fig. 4.11.