In the following we show a schematic diagram
of a cooling tower in the context of a steam power plant:

__mass flow:__

Referring to the diagram above the mass flow rate of the makeup water is given by the difference in specific humidity ω at the inlet and outlet air streams multiplied by the mass flow rate of the dry air. Thus the mass flow balance equations for the cooling tower become:

__energy:__

Since no work is done and no heat transfered externally, the cooling tower energy equation reduces to an enthalpy balance equation. Combining the mass flow equations with the energy equation leads to the final equation relating the mass flow rate of the dry air to the circulating cooling water of the condenser, as follows:

The mass flow rate of the liquid water at stations
(3) and (4) is normally provided from the condenser energy equation
of the steam power plant. Recall from **Chapter
10a** that the specific humidity ω is related to the
various pressures and the relative humidity φ by the following
relations:

The pressure P_{v} is the partial pressure
of the vapor, P_{g} is the saturation pressure at temperature
T, and P is the total pressure (air + vapor), usually taken as
one atmosphere (101.325 kPa). In **Chapter
10b** we saw how all of these relations can be most conveniently
evaluated graphically on a **Psychrometric
Chart**. Notice that we have extended the moisture specific
humidity range on this chart from 30 to 40 grams/kg-air in order
to accomodate the extremely high humidity normally encountered
at station (2), which is the reason why we normally see a cloud
above the cooling tower.

Note that the enthalpies of the vapor (h_{1}
and h_{2}) and those of the liquid (h_{3}, h_{4},
h_{mu}) can be conveniently evaluated as follows:

The temperature T is in degrees Celsius, and
the specific heat capacity of dry air C_{P} is approximately 1.00 [kJ/kg°C] and that of liquid
water approximately 4.18 [kJ/kg°C]. In the above analysis
we have assumed that the temperature of the makeup water T_{mu}
equals the temperature of the cooled circulating water T_{3}.
Alternatively the values of enthalpy for the vapor (h_{1}
and h_{2}) can also be conveniently read directly from
the Psychrometric Chart.

**Solved
Problem 10.5 - Cooling Tower for the Supercritical
Steam Power Plant for Athens, Ohio**

**Problem
10.6 - Cooling Tower for the Cogeneration
Steam Power Plant for Ohio University**

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Engineering Thermodynamics by Israel Urieli is licensed under a
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Alike 3.0 United States License