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Process Circuit Analysis 107

Over a small temperature range, the enthalpy of vaporization is essentially
constant. Thus, we may use the Clausius-Clapyeron equation, Equation 3.2.32, to
express the vapor pressure of water as a function of temperature. Next, calculate
the mole fraction of water in the exit air using Equation 3.2.28, where p,is, is the
2
vapor pressure of water at the exit-air temperature. We assume that heat capacity
of air and water vapor is constant over the temperature range of interest. Using
data taken from Reid et al. [2], calculate the heat capacities at 100 °F (37.8 °C).
Thus, Cp, = 8.2 Btu/lbmol-°F (34.3 kJ/kg mol-K) and c p2 = 7.2 Btu/lbmol-°F (30.1
kJ/kg mol-K). The heat capacity of water, 18.0 Btu/lbmol-°F (75.4 kJ/kg mol-K),
is also assumed constant. We select 32.0 °F as the reference temperature, R, to
t
correspond to the steam tables. Thus, Equations 37 to 42 in Table 3.2.2 are the
pure component enthalpies of all the components.
The next step in the problem solving procedure is to outline a solution pro-
cedure for the Equations listed in Table 3.2.2. There are algorithms available for
determining in what order to solve a set of algebraic equations, which is called the
precedence order. See, for example, Rudd and Watson [17] and Myers and Seider
[18] for a discussion of some of these algorithms. Sometimes, we can develop a
procedure by inspection of an equation set, as in the procedure given in Table
3.2.3.

Table 3.2.3 Calculation Procedure - Cooling-Tower Analysis_______

1. Obtain pw from the steam tables at tw (Equation 3.2.30 in Table 3.2.2)
2. Calculate ym from Equation 3.2.29.

3. Obtain Ahw from the steam tables at tiw, Equation 3.2.31.

4. Calculate yi,i from the psychrometric relation, Equation 3.2.27.
5. Assume an exit air temperature, t 2.

6. Calculate p 2,is from Equations 3.2.32 to 3.2.34.

7. Calculate y2,i from Equation 3.2.28.
8. Calculate mi, m 2 rot, yi 2 and y 22 from Equations 3.2.22 to 3.2.25 and Equation
3.2.44.

9. Calculate h-i, h 2, h 3, and h 4 from Equations 3.2.35 to 3.2.43.
10. Substitute h-i, h 2, ha, hu, mi, m 2, ma, and m 4 into Equation 3.2.26 to check the
assumed value of t 2.

11. Repeat steps 5 to 10 until Equation 3.2.26 is satisfied within a sufficient degree
of accuracy.

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