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TRANSCRIPT
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Chapter 6
MASS AND ENERGY
ANALYSIS OF CONTROLVOLUMES
Fundamentals of Thermal-Fluid Sciences, 3rd EditionYunus A. Cengel, Robert H. Turner, John M. Cimbala
McGraw-Hill, 2008
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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.
Apply the energy balance to general unsteady-flow processes with
particular emphasis on the uniform-flow process as the model for
commonly encountered charging and discharging processes.
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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 aprocess.
Control volumes: Mass can cross the boundaries, and so we mustkeep track of the amount of mass entering and leaving the controlvolume.
Mass m and energy Ecan be converted to each other according to
where cis the speed of light in a vacuum, which is c = 2.9979 108 m/s.
The mass change due to energy change is absolutely negligible.
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Mass and Volume Flow Rates
The average velocity Vavg is
defined as the average speed
through a cross section.
The volume flow rate is the
volume of fluid flowing through a
cross section per unit time.
Definition of
average velocity
Mass flow
rate
Volume flow rate
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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 Dtis equal to the net change
(increase or decrease) in the total mass within the control volume duringD
t.
General conservation of mass
General conservation of mass in rate form
or
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Mass Balance for Steady-Flow Processes
Conservation of mass principle for a two-
inletone-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 inletsand exits
Single
stream
Many engineering devices such as nozzles,
diffusers, turbines, compressors, and
pumps involve a single stream (only oneinlet and one outlet).
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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)There is no such thing as a conservation of volume
principle.
However, for steady flow of liquids, the volume flow
rates, as well as the mass flow rates, remain
constant since liquids are essentially incompressible
substances.
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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 controlvolume. 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.
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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.
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Energy Transport by Mass
The product is the energy
transported into control volume by
mass per unit time.
iimq&
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
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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 volumeremain constant.
Under steady-flow conditions,
the fluid properties at an inlet
or exit remain constant (do not
change with time).
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Mass and Energy balances
for a steady-flow process
A water
heater in
steady
operation.
Mass
balance
Energy
balance
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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
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SOME STEADY-FLOW ENGINEERING DEVICES
A modern land-based gas turbine used for electric power
production. This is a General Electric LM5000 turbine. It
has a length of 6.2 m, it weighs 12.5 tons, and produces
55.2 MW at 3600 rpm with steam injection.
Many engineering devices operate essentially under the same conditions
for long periods of time. The components of a steam power plant (turbines,
compressors, heat exchangers, and pumps), for example, operate nonstop for
months before the system is shut down for maintenance. Therefore, these
devices can be conveniently analyzed as steady-flow devices.
At very high velocities,
even small changes invelocities can cause
significant changes in
the kinetic energy of the
fluid.
Total electric power generation of Korea: 55,000 MW
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Nozzles and Diffusers
Nozzles and diffusers areshaped so that they cause large
changes in fluid velocities and
thus kinetic energies.
Nozzles and diffusers are commonly
utilized in jet engines, rockets,
spacecraft, and even garden hoses.
A nozzle is a device that increasesthe velocity of a fluidat the expense
of pressure.
A diffuseris a device that increases
the pressure of a fluidby slowing it
down.
The cross-sectional area of a nozzle
decreases in the flow direction for
subsonic flows and increases for
supersonic flows. The reverse is true
for diffusers.
Energy
balance for
a nozzle or
diffuser:
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Turbines and
Compressors Turbine drives the electric generator In
steam, gas, or hydroelectric power plants.
As the fluid passes through the turbine,
work is done against the blades, which
are attached to the shaft. As a result, the
shaft rotates, and the turbine produces
work.
Compressors, as well as pumps and
fans, are devices used to increase the
pressure of a fluid. Work is supplied to
these devices from an external sourcethrough a rotating shaft.
A fan increases the pressure of a gas
slightly and is mainly used to mobilize a
gas.
A compressoris capable of compressing
the gas to very high pressures. Pumps work very much like compressors
except that they handle liquids instead of
gases.
Energy balance for the
compressor in this figure:
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Throttling valvesThrottling valves are any kind of flow-restrictingdevices
that cause a significant pressure drop in the fluid.
What is the difference between a turbine and a
throttling valve?
The pressure drop in the fluid is often accompanied by alarge drop in temperature, and for that reason throttling
devices are commonly used in refrigeration and air-
conditioning applications.
The temperature of an ideal gas does
not change during a throttling
(h = constant) process since h = h(T).
During a throttling process, the enthalpy
of a fluid remains constant. But internal
and flow energies may be converted to
each other.
Energy
balance
t
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[Example 6-8] Expansion(throttling) of R-134a [p.221]R-134a enters the capillary tube.Inlet (State 1): 0.8 MPa, sat. liquidExit (State 2): 0.12 MPaFind (1) exit quality, (2) exit temperatureAssume steady flow, KPE=0Then first law of thermodynamics becomes 21 hh =
kJ/kg47.951 =hable A-12 (p.1008)kJ/kg47.952 =h
( )fgf hhxhh -+= 22fg
f
hh
hhx
-
-=
2
2
3403.0
49.2297.236
49.2247.952 =
-
-=x
C32.22 o2 -=t
Table A-12 (p.1008)
Table A-12 (p.1008)
C31.31 o1 =t
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Mixing chambers
In engineering applications, the section
where the mixing process takes place is
commonly referred to as a mixingchamber.
The T-elbow of an ordinary shower
serves as the mixing chamber for the
hot- and the cold-water streams.
Energy balance for the
adiabatic mixing chamber in
the figure is:
10C
60C
43C
140 kPa
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Heat exchangers
Heat exchangers are
devices where two moving
fluid streams exchange heatwithout mixing. Heat
exchangers are widely used
in various industries, and
they come in various
designs.
A heat exchanger
can be as simple as
two concentric pipes.
Mass and energy
balances for the adiabatic
heat exchanger in the
figure is:
The heat transfer associated with a heat
exchanger may be zero or nonzero depending on
how the control volume is selected.
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[Example 6-10] Heat exchanger, cooling R-134a by water [p.224]Water (State 1): 15, 300 kPa comp. liquidWater (State 2): 25, 300 kPa comp. liquidR-134a (State 3): 6 kg/min, 1 MPa, 70 sup. vaporR-134a (State 4): 35, 1 MPa comp. liquidFind (1) flow rate of water, (2) heat transfer fromrefrigerant(R-134a) to water
Assume steady flow, insulated (Q=0), KPE=0, W=0Then first law of thermodynamics becomes43213311 hmhmhmhm &&&& +=+
+=+outin
hmWhmQ &&&&st law
kJ/kg982.621 =hable A-4 (p.994) kJ/kg83.1042 =hTable A-13 (p.1010) kJ/kg85.3033 =hTable A-11 (p.1007) kJ/kg865.1004 =h
minkg1.29
minkg6
982.6283.104865.10085.3033
12
431 =
--=
--= mhhhhm &&
2111 hmhmQ waterref &&& =+ ( )121 hhmQ waterref -= &&
( ) kJ/min1218982.6283.1041.29 =-=waterrefQ&
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Pipe and duct flow
The transport of liquids or gases in
pipes and ducts is of great importance
in many engineering applications. Flowthrough a pipe or a duct usually satisfies
the steady-flow conditions.
Heat losses from
a hot fluid
flowing through
an uninsulated
pipe or duct tothe cooler
environment
may be very
significant.
Pipe or duct flow may involve more than
one form of work at the same time.
Energy balance
for the pipe flow
shown in the
figure is
for liquid ( )1212 TTChh p --
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[Example 6-11] Electric heating of air [p.227]Duct with electric heater (15 kW)Air in (State 1): 100 kPa, 17, 150 m3/minHeat loss 0.2 kWFind the exit temperature of airAssume air as an ideal gas with constant Cp,KPE=0
2211 hmWhmQ &&&& +=+st law
( ) ( )1212 ttCmhhmWQ p -=-=- &&&&
( )kg
m8327.0
100
15.27317287.03
1
11 =
+==
P
TRu
s
kg00.3
min
kg14.180
kg
m
8327.0
min
m150
3
3
1
1 ====u
Vm
&
&
C9.2117005.100.3
)15(2.0 o12 =+
---=+
-= t
Cm
WQt
p&
&&
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[Example 6-12] Charging of a rigidinsulated tank by steam [p.230]Tank: initially evacuatedSupply steam: 1 MPa, 300Steam enters the tankFinal state of tank inside: 1 MPaDetermine the final temperatureAssume KPE=0, Q=0, W=01st law WhmumumhmQ eeii ++-=+ 1122
22umhm ii =
kJ/kg6.3051=ihable A-6 (p.999)2mmi = 2uhi =
Final state (state 2) kJ/kg6.30512 =uMPa,12 =P
T () u (kJ/kg)400 2957.9T2 = ? u2 = 3051.6500 3125.0
Linear interpolationC1.456 o2 =T
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Summary
Conservation of mass
Mass and volume flow rates
Mass balance for a steady-flow process
Mass balance for incompressible flow
Flow work and the energy of a flowing fluid
Energy transport by mass
Energy analysis of steady-flow systems Some steady-flow engineering devices
Nozzles and Diffusers
Turbines and Compressors
Throttling valves
Mixing chambers and Heat exchangers
Pipe and Duct flow