CHEMICAL ENGINEERING

326 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

toHG 2 D 78 .5 kJ/kg is 300 K. From Fig. 13.5 the exit air therefore has a humidity of
0.02 kg/kg which from Fig. 13.4 corresponds to a percentage humidity of 90%.

PROBLEM 13.9

Water is to be cooled in a small packed column from 330 to 285 K by means of air
flowing countercurrently. The rate of flow of liquid is 1400 cm^3 /m^2 s and the flowrate
of the air, which enters at 295 K with a humidity of 60% is 3.0m^3 /m^2 s. Calculate the
required height of tower if the whole of the resistance to heat and mass transfer can be
considered as being in the gas phase and the product of the mass transfer coefficient and
the transfer surface per unit volume of column is 2 s^1. What is the condition of the air
which leaves at the top?

Solution

As in Problem 13.8, assuming the relevant latent and specific heat capacities:

HG 1 D 1. 003  295  273 CH 2495 C 2. 006  295  273 

From Fig. 13.4, atD295 and 60% humidity,HD 0 .010 kg/kg and hence:

HG 1 D 1. 003 ð 22 C 0. 010  2495 C 44. 13 D 47 .46 kJ/kg

In the inlet air, water vapourD 0 .010 kg/kg dry air or  0. 010 / 18 / 1 / 29 D
0 .016 kmol/kmol dry air.

Thus the flow of dry airD 1  0. 016  3. 0 D 2 .952 m^3 /m^2 s.
Density of air at 295 KD 29 / 22. 4  273 / 293 D 1 .198 kg/m^3.
and mass flow of dry airD 1. 198 ð 2. 952 D 3 .537 kg/m^2 s.
Liquid flowD 1. 4 ð 10 ^3 m^3 /m^2 s
and mass flow of liquidD 1. 4 ð 10 ^3 ð 1000 D 1 .4 kg/m^2 s.
The slope of the operating line is thus:LCL/GD 1. 40 ð 4. 18 / 3. 537 D 1 .66 and the
coordinates of the bottom of the line are:

L 1 D285 K,HG 1 D 47 .46 kJ/kg

From these data, the operating line may be drawn in as shown in Fig. 13b and the top
point of the operating line is:

L 2 D330 K,HG 2 D122 kJ/kg

Again as in Problem 13.8, the relation between enthalpy and temperature at the interface
Hfvs.fis drawn in Fig. 13b. It is seen that the operating line cuts the saturation curve,
which is clearly an impossible situation and, indeed, it is not possible to cool the water to
285 K under these conditions. As discussed in Section 13.6.1, with mechanical draught
towers, it is possible, at the best, to cool the water to within, say, 1 deg K of the wet