THEORY

The cooling tower experiment is applied from the First Law of Thermodynamics, which is

the conservation of energy. The energy cannot be created nor destroyed. The high energy

content must be transferred to low energy content.

Firstly, the energy that enters the cooling tower is in the form of hot water. The other

energy that contributes such as heat generation from friction of both air and water, energy

losses from pipes are ignored. Besides that, the hot water was cooled from temperature T1 to a

temperature of T2. Furthermore, the cooling of the hot water in the form of forced convection by

which air at T1 was blown over the hot water and the water exited the cooling tower at some

temperature T2. Both of the opening and the closing temperatures of the air and water were

recorded but when this data is recorded, an energy balance can be conducted on the system.

Moreover, the energy balance is a form of book keeping that accounts for the energy

entering and exiting the system. The main component of the energy balance is the enthalpy

which is defined as:

H=U+PV (1)

Where H is enthalpy, U is internal energy, P is pressure and V is volume.

The joint terms U+PV is the enthalpy, which means to heat flow. The enthalpy can be

calculated or referred from tables of data for the fluid being used. In this experiment, the fluids

used by the cooling tower are air and water. The enthalpy values can be obtained from the

thermodynamics textbook. As an example, since both initial and final temperature of the input

hot water and the output cool water were measured, the temperature T in can be referred and the

enthalpy can be recorded. Besides that, the enthalpy of the output cooled water can be similarly

referenced and an energy balance can be conducted for the water.

The equation below displays the general method to start an energy balance:

∑ ∆ H ¿=∑ ∆H out (2)

∆ H=H ¿−H out .

A similar method is used for conducting the energy balance for air entering and leaving

the system. Besides that, there are two methods to determine the change in enthalpy. When the

air is at low pressure, it can be treated as an ideal gas and the enthalpy change can be

calculated through the use of the following equation:

∆ H=Cp∆T (3)

∆ H is the change in enthalpy, ∆T is the change in temperature and C p is the specific heat with

respect to constant pressure.

Hence, the specific heat relation does not take into account the percent of water in the

air, a psychromatic chart is used to determine the enthalpy change between the entrance and

the exit air. Furthermore, to use the psychromatic chart efficiently, some information is needed

for the input and the output air.

The information that are needed are the dry bulb and the wet bulb temperatures of the

inlet and the outlet air. In addition, both the input and the output air flow are measured with a

sling psychromatic. Moreover, the sling psychrometer is the equipment that has two

thermometers. The thermometers is used for measuring the wet bulb temperature has a wetted

cotton sleeve over the bulb end while the dry bulb thermometer is a regular thermometer. In the

end, the wet bulb and the dry bulb temperatures of the inlet and outlet air have been measured,

each can be referred on the psychrometric chart and the enthalpy of it is recorded. When the

enthalpies for the input and the output water and air conditions are identified, energy balances

can be conducted on the system.

For convective heat transfer from a solid to a fluid the rate of heat transmission (dq/dt) is given

by the following equation:

dq = hA1 ( T - TA) dt

Where h = heat transfer coefficient for the fluid

A1 = area normal to the direction of heat flow

T = surface temperature of solid

TA = temperature of fluid

The fall in temperature dT of the solid in time dt is given by

dq dt = m.c.dt

Where m = mass of solid

c = specific heat capacity of solid

Combining equations (1) and (2) the following equation is obtained:

−dT

(T−Ta) = hA1 dt / m

Integrating gives

log10 (T - TA) − log10 (To - TA) = - hA1t / 2.303.m.c

log10 (T - TA) = (− hA1t / 2.303. m.c) − log10 (To - TA)

Where To = element temperature at t = 0.

This is an equation of the straight line form y = Mx + C, with

y = log10 (T - TA)

M = −hA1t/ 2.303. m.c

x = t and

C = log10 (To - TA)

A plot of log10 (T - TA) versus t will give M and hence h can be found.

h = − 2.303mc M / A1

The velocity V1, developed by the gas of density, expanding freely under the influence of

pressure difference p is given by

V12 / 2 = p

Since velocity is given in terms of the velocity head H1 (cm of water) and 1cmH2O = 98.1N/m2

V12 / 2 = 98.1H1

The density of the air under pressure PA at temperature TA is given by

PA / = RTA

where R = 287

Therefore,

V1 = 237.3

For the effective velocity(V) past a bank of tubes, the velocity based on full cross section has to

be adjusted according to the flow area available. When a single element is being studied, the

diameter of one elements under study is one tenth the diameter of the working section, so the

flow area is 9/10 of the full area. Hence, the effective velocity, V = 10/9* V1.

Nusselt’s number, Nu, is the ratio of the conductive thermal resistance of the gas to the

convective thermal resistance of the gas while Reynold’s number, Re, is the ratio of the inertia

force of the gas to the viscous force of the gas.

Nu and Re for a gas with density , viscosity , speed V, thermal conductivity k and heat

transfer coefficient h can be found using the following equations:

Nu = hD / k Re = VD /

where De is the equivalent diameter through which the gas is passing, which is given by the

following formula:

where SL and ST are the longitudinal pitch and transverse pitch of the elements and d is

diameter of the elements.

AIMS

The objectives of this experiment are:

i. To investigate the effect of cooling load on wet bulb approach

ii. To investigate the effect of air velocity on wet bulb approach and the pressure drop through the packing

APPARATUS

Water

SOLTEQ Water Cooling Tower (Model HE 152)

Figure 1: SOLTEQ Water Cooling Tower (Model HE 152)