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
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