This document provides an overview of chapter 5 of a thermodynamics textbook, which covers mass and energy analysis of control volumes. The key objectives are to develop the conservation of mass and first law of thermodynamics as applied to control volumes. It defines concepts like mass flow rate, volume flow rate, enthalpy, and flow work. Examples are provided to demonstrate applying conservation of mass to problems involving steady and unsteady flow systems as well as compressible and incompressible fluids. The chapter also discusses applying the energy balance to steady flow systems like nozzles, compressors, and heat exchangers.

1. Thermodynamics I 1
Chapter 5
Mass and Energy Analysis of Control
Volumes

2. Homework #5 Due: TBA
2
Problems: 5.8
5.17
5.24
5.30
5.42
5.49
5.56
5.71E
5.75
5.90
5.114
5.155

3. 3
Objectives
• Develop the conservation of mass principle.
• Apply the conservation of mass principle to various systems
including steady- and unsteady-flow control volumes.
• Apply the first law of thermodynamics as the statement of the
conservation of energy principle to control volumes.
• Identify the energy carried by a fluid stream crossing a control
surface as the sum of internal energy, flow work, kinetic energy,
and potential energy of the fluid and to relate the combination of
the internal energy and the flow work to the property enthalpy.
• Solve energy balance problems for common steady-flow devices
such as nozzles, compressors, turbines, throttling valves, mixers,
heaters, and heat exchangers.

4. 4
CONSERVATION OF MASS
Mass is conserved even during chemical reactions.
Conservation of mass: Mass, like energy, is a conserved property,
and it cannot be created or destroyed during a process.
Closed systems: The mass of the system remain constant during a
process.
Control volumes: Mass can cross the boundaries, and so we must
keep track of the amount of mass entering and leaving the control
volume.

5. 5
Mass and Volume Flow Rates
Mass flow through a cross-sectional area per unit time is called the
mass flow rate.
Note the dot over the mass symbol indicates a time rate of change.
where
𝑉𝑛 = 𝑉. 𝑛

6. 6
Mass and Volume Flow Rates
Volume flow rate
The volume flow rate is the volume of fluid flowing through a cross
section per unit time.
where
If ρ=const. on cross section area:

7. Example
7
Refrigerant-134a at 200 kPa, 40% quality, flows through a 1.1-cm inside diameter,
d, tube with a velocity of 50 m/s. Find the mass flow rate of the refrigerant-134a.
At P = 200 kPa, x = 0.4 we determine the specific volume from
3
0.0007533 0.4(0.0999 0.0007533)
0.0404
f fgv v xv
m
kg
 
  

2
2
3
4
50 / (0.011 )
0.0404 / 4
0.117
ave aveV A V d
m
v v
m s m
m kg
kg
s


 



8. 8
Conservation of Mass Principle
Conservation of mass principle
for an ordinary bathtub.
The conservation of mass principle for a control volume: The net mass transfer
to or from a control volume during a time interval t is equal to the net change
(increase or decrease) in the total mass within the control volume during t.
General conservation of mass
or
or

9. 9
Mass Balance for Steady-Flow Processes
Conservation of mass
principle for a two-inlet–one-
outlet steady-flow system.
During a steady-flow process, the total amount of mass contained within a
control volume does not change with time (mCV = constant).
Then the conservation of mass principle requires that the total amount of mass
entering a control volume equal the total amount of mass leaving it.
For steady-flow processes, we are
interested in the amount of mass flowing per
unit time, that is, the mass flow rate.
Multiple inlets
and exits
Single stream
Many engineering devices such as nozzles,
diffusers, turbines, compressors, and pumps
involve a single stream (only one inlet and
one outlet).
If density and velocity don’t change on each
cross section area:

10. 10
Special Case: Incompressible Flow
During a steady-flow process, volume flow rates are not
necessarily conserved although mass flow rates are.
The conservation of mass relations can be simplified even further when
the fluid is incompressible, which is usually the case for liquids.
Steady,
incompressible
Steady, incompressible flow
(single stream)
For steady flow of liquids, the volume flow rates, as
well as the mass flow rates, remain constant since
liquids are essentially incompressible substances.
If velocity doesn’t change on each cross
section area:

11. Example
11
Discuss Example 5-1 in class:

12. Example
12
Discuss Example 5-2 in class:

13. 13
FLOW WORK AND THE
ENERGY OF A FLOWING FLUID
Schematic for flow work.
Flow work, or flow energy: The work (or energy)
required to push the mass into or out of the control
volume. This work is necessary for maintaining a
continuous flow through a control volume.
In the absence of acceleration, the force
applied on a fluid by a piston is equal to the
force applied on the piston by the fluid.

14. 14
Total Energy of a Flowing Fluid
The total energy consists of three parts for a nonflowing fluid and four parts for a
flowing fluid.
h = u + Pv
The flow energy is
automatically taken
care of by enthalpy.
In fact, this is the
main reason for
defining the
property enthalpy.

15. 15
Energy Transport by Mass
The product is the energy
transported into control volume by
mass per unit time.
iim
When the kinetic and potential energies
of a fluid stream are negligible
When the properties of the mass at
each inlet or exit change with time
as well as over the cross section

16. Example
16
Discuss Example 5-3 in class:

17. 17
ENERGY ANALYSIS OF STEADY-FLOW
SYSTEMS
Many engineering systems such
as power plants operate under
steady conditions.
Under steady-flow conditions, the mass
and energy contents of a control volume
remain constant.
Under steady-flow conditions,
the fluid properties at an inlet
or exit remain constant (do not
change with time).

18. 18
Mass and Energy balances
for a steady-flow process
A water
heater in
steady
operation.
Mass
balance
Energy
balance
Single stream

19. 19
Under steady operation,
shaft work and electrical
work are the only forms of
work a simple compressible
system may involve.
Energy balance relations with sign conventions
(i.e., heat input and work output are positive)
when kinetic and potential energy
changes are negligible
Some energy unit equivalents

20. 20
Note
At very high velocities, even small changes
in velocities can cause significant changes
in the kinetic energy of the fluid.