In this course we consider three types of Control Volume Systems - Steam Power Plants, Refrigeration Systems, and Aircraft Jet Engines. Fortunately we will be able to separately analyse each component of the system independent of the entire system, which is typically represented as follows:

In addition to the energy flow across the control
volume boundary in the form of heat and work, we will also have
mass flowing into and out of the control volume. We will only
consider **Steady Flow** conditions throughout, in which there is no energy
or mass accumulation in the control volume, thus we will find
it convenient to derive the energy equation in terms of power
[kW] rather than energy [kJ]. Furthermore the term Control Volume
indicates that there is no boundary work done by the system, and
typically we have shaft work, such as with a turbine, compressor
or pump.

Consider an elemental mass **d**m flowing
through an inlet or outlet port of a control volume, having an
area A, volume **d**V, length **d**x, and an average steady
velocity , as follows.

Thus finally the mass flow rate can be determined as follows:

The fluid mass flows through the inlet and
exit ports of the control volume accompanied by its energy. These
include four types of energy - internal energy (u), kinetic enegy
(ke), potential energy (pe), and flow work (w_{flow}).
In order to evaluate the flow work consider the following exit
port schematic showing the fluid doing work against the surroundings
through an imaginary piston:

It is of interest that the specific flow work is simply defined by the pressure P multiplied by the specific volume v. In the following section we can now develop the complete energy equation for a control volume.

Consider the control volume shown in the following figure. Under steady flow conditions there is no mass or energy accumulation in the control volume thus the mass flow rate applies both to the inlet and outlet ports. Furthermore with a constant mass flow rate, it is more convenient to develop the energy equation in terms of power [kW] rather than energy [kJ] as was done previously.

The total power in due to heat and mass flow through the inlet port (1) must equal the total power out due to work and mass flow through the outlet port (2), thus:

The specific energy e can include kinetic and
potential energy, however will always include the combination
of internal energy (u) and flow work (Pv), thus we conveniently
combine these properties in terms of the property enthalpy (as
was done in **Chapter 3a**), as
follows:

Note that z is the height of the port above
some datum level [m] and g is the acceleration due to gravity
[9.81 m/s^{}2].
Substituting for energy e in the above energy equation and simplifying,
we obtain the final form of the energy equation for a single-inlet
single-outlet steady flow control volume as follows:

Notice that enthalpy h is fundamental to the energy equation for a control volume.

When dealing with closed systems we found that
sketching *T-v* or *P-v* diagrams was a significant
aid in describing and understanding the various processes. In
steady flow systems we find that the Pressure-Enthalpy (*P-h*)
diagrams serve a similar purpose, and we will use them extensively.
In this course we consider three pure fluids - water, refrigerant
R134a, and carbon dioxide, and we have provided *P-h* diagrams
for all three in the **Property
Tables** section. We will illustrate their use in the following
examples. The *P-h* diagram for water is shown below. Study
it carefully and try to understand the significance of the distinctive
shapes of the constant temperature curves in the compressed liquid,
saturated mixture (quality region) and superheated vapor regions.

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Engineering Thermodynamics by Israel Urieli is licensed under a
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