1.7^b. Properties of air saturated with water vapor.
Air, stored in a 30-m³ container at 340 K and 101.3 kPa is saturatedwith water vapor. Determine the following properties of the gas mixture:
a) Mole fraction of water vapor.
b) Average molecular weight of the mixture.
c) Total mass contained in the tank.
d) Mass of water vapor in the tank.

Solution

a) Antoine equation for water vapor:

For a saturated mixture

b)

c)

d)

1.8^c. Water balance around an industrial cooling tower.
The cooling water flow rate to the condensers of a big coal-fired power plant is 8,970 kg/s. The water enters the condensers at 29 °C and leaves at 45 °C. From the condensers, the water flows to a cooling tower where it is cooled down back to 29 °C by countercourrent contact with air (see Figure 1.11). The air enters the cooling tower at the rate of 6,500 kg/s of dry air, at a dry-bulb temperature of 30 °C and a humidity of 0.016 kg of water/kg of dry air. It leaves the cooling tower saturated with water vapor at 38 °C.
a) Calculate the water losses by evaporation in the cooling tower.

Solution

Consider the air leaving the tower saturated at 38 °C.

Antoine equation for water vapor:

E = water lost by evaporation in the air

b) To account for water losses in the cooling tower, part of the effluent from a nearby municipal wastewater treatment plant will be used as makeup water. This makeup water contains 500 mg/L of dissolved solids. To avoid fouling of the condenser heat-transfer surfaces, the circulating water is to contain no more than 2,000 mg/L of dissolved solids. Therefore, a small amount of the circulating water must be deliberately discarded (blowdown). Windage losses from the tower are estimated at 0.2% of the recirculation rate. Estimate the makeup-water requirement.

Solution

W = windage losses x_m = 500 ppm x_c = 2000 ppm
M = makeup water rate B = blowdown rate

Initial estimates

Water balance

Solids balance: