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Chapter 9

Gas Power Systems

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Learning Outcomes

Performair-standard analysesof internalcombustion engines based on the Otto,

Diesel, and dual cycles, including:

sketchingp-vand T-sdiagrams and evaluatingproperty data at principal states.

applyingenergy, entropy, and exergy

balances.determiningnet power output, thermal

efficiency, and mean effective pressure.

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Learning Outcomes

Performair-standard analysesof gasturbine power plants based on the Brayton

cycle and its modifications, including:

sketchingT-sdiagrams and evaluatingproperty data at principal states.

applyingmass, energy, entropy, and exergy

balances.determiningnet power output, thermal

efficiency, back work ratio, and the effects of

compressor pressure ratio.

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Learning Outcomes

For subsonicand supersonic flowsthroughnozzlesand diffusers:

demonstrateunderstanding of the effects ofarea change, the effects of back pressure on

mass flow rate, and the occurrence of choking

and normal shocks.

analyzethe flow of ideal gases with constantspecific heats.

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Considering Gas Turbine Power Plants

Gas turbine power plants are more quicklyconstructed, less costly, and morecompactthan thevapor power plants considered in Chapter 8.

Gas turbines are suited for stationary powergenerationas well as for powering vehicles,

including aircraft propulsion and marine power

plants.

Gas turbines are

increasingly used for large-scale powergeneration, andfor such applications fueled primarily bynatural gas, which is relatively abundant today.

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Considering Gas Turbine Power PlantsGas turbines may operate on an openor closedbasis, asshown in the figures.

The open gas turbineis more commonly usedand is themain focus of our study of gas turbines.

Study of the individual components of these configurationsrequires the contro l volume formsof the mass, energy, and

entropy balances.Opento the atmosphere Closed

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The openmode gas turbine is an in ternal com bust ion

power plant.Airis continuously drawn intothe compressorwhere it is

compressed to a high pressure.

Combustion productsexit

at elevated temperatureandpressure.

Combustion productsexpand through the turbine

and then are discharged to the

surroundings.

Airthen enters the combustion

chamber(combustor) where itmixes with fueland combustion

occurs.

The remainder is

available as net work

output to drive an

electric generator, to

propel a vehicle, or

for other uses.

Part of the

turbine work

is used to

drive the

compressor.

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The closedgas turbine operates as follows:

A gascirculatesthrough four components: turbine,compressor, and two heat exchangers at higher and loweroperating temperatures, respectively.

The turbineand compressorplay the same roles as in theopen gas turbine.

As the gas passes through thehigher-temperature heat

exchanger, it receives energyby

heat transfer from an external

source.The thermodynamic cycle iscompleted by heat transfer to the

surroundingsas the gas passes

through the lower-temperatureheat exchanger.

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The heat transferassociated with the higher-temperature heat exchanger of the closedgasturbine originates from an external sou rce, which

may includeExternal com bus t ionofbiomass, municipal solidwaste, fossil fuels such as

natural gas, and other

combustibles.

Waste heatfrom industrialprocesses.

Solarthermal energy.A gas-cooled nuclear

reactor.

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To conduct elementaryanalyses of opengas turbine power

plants, simplifications are required. Although highly idealized,an air-standard analysiscan provide insightsand qualitative

informationabout actual performance.

An air-standard analysishas the following elements:

The working fluid is airwhich behaves as an ideal gas.Ideal gas relations are reviewed in Table 9.1.The temperature rise that would be brought about bycombustion is accomplished by heat transfer from an

external source.

With an air-standard analysis, we avoid the complexities ofthe combustion process and the change in composition

during combustion, which simplifies the analysis

considerably. Combustion is studied in Chapter 13.

In a co ldair-standard analysis, the specific heats are

assumed constantat their ambient temperature values.

Air-Standard Analysis of

Open Gas Turbine Power Plants

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Air-Standard Brayton Cycle

The schematic of a simple open air-standard gas turbine

power plantis shown in the figure.The energy transfersby heat and work are in thedirections of the arrows.

Aircirculates through the components:

Process1-2: the airiscompressedfrom state 1to

state 2.

Process2-3: Thetemperature risethat would be

achieved in the actual power

plant with combustion is

realizedhere by heat transfer,

At state 1, airis drawn into thecompressorfromthe surroundings.

.inQ

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Airreturns to thesurroundingsat state 4with a

temperaturetypically muchgreater than at state 1.

After interacting with thesurroundings, each unit of mass

returns to the same condition asthe air entering at state 1,

thereby completing a

thermodynamic cycle.

Process 3-4: The high-pressure, high-temperature air

expands throughthe turbine. The turbine drives thecompressor and develops net power, .cycleW

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Airreturns to thesurroundingsat state 4with a

temperaturetypically much

greater than at state 1.After interacting with thesurroundings, each unit of mass

returns to the same condition as

the air entering at state 1,

thereby completing a

thermodynamic cycle.

Process 3-4: The high-pressure, high-temperature airexpands throughthe turbinefrom state 3to state 4. The

turbine drives the compressor and develops net power, .cycleW

We imagineprocess 4-1beingachieved by a heat exchanger, as

shown by the dashed line in the figure.

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Cycle 1-2-3-4-1is called the Brayton cyc le.

The com pressor p ressu re rat io, p2/p1, is a keyBrayton cycle operating parameter.

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Analyzing each component as a control

volume atsteady state, assuming thecompressorand turbine operate

adiabatically, and neglecting kineticand

potential energy effects, we get the following

expressions for the principal work and heattransfers, which are positive in accord with

our convention for cycle analysis.

Turbine

Compressor

(Eq. 9.15)

(Eq. 9.16)

(Eq. 9.17)

(Eq. 9.18)

Heat addition

Heat rejection
http://www.wiley.com/college/moran/0470495901/ig/Ch9/pages/eq_09_19.htmhttp://www.wiley.com/college/moran/0470495901/ig/Ch9/pages/eq_09_18.htmhttp://www.wiley.com/college/moran/0470495901/ig/Ch9/pages/eq_09_17.htmhttp://www.wiley.com/college/moran/0470495901/ig/Ch9/pages/eq_09_16.htm

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Air-Standard Brayton CycleThe thermal eff ic ienc yis

(Eq. 9.19)

The back work rat iois

(Eq. 9.20)

Since Eqs. 9.15through 9.20have been developed from massand energy balances, they apply equallywhen irreversibilities

are presentandin the absence of irreversibilities.

Note: A relatively large portion of the work developed by the

turbine is required to drive the compressor. For gas turbines,

back work ratios range from 20% to 80% compared to only 1-2%

for vapor power plants.
http://www.wiley.com/college/moran/0470495901/ig/Ch9/pages/eq_09_21.htmhttp://www.wiley.com/college/moran/0470495901/ig/Ch9/pages/eq_09_20.htm

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Ideal Air-Standard Brayton Cycle

The idealair-standard Brayton cycle provides an

especially simple setting for study of gas turbine powerplant performance. The ideal cycle adheres to additional

modeling assumptions:

Frictional pressure drops are absent during flows through

the heat exchangers. These processes occur at constantpressure. These processes are isobaric.

Flows through the turbine and pumpoccur adiabaticallyandwithout irreversibility. These processes are isentropic.

Accordingly, the ideal Brayton cycleconsists of twoisentropic processesalternated with two isobaric processes.In this respect, the ideal Brayton cycle is in harmony with

the ideal Rankine cycle, which also consists of two

isentropic processes alternated with two isobaric processes

(Sec. 8.2.2).

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Since the ideal Brayton cycle involves internally

reversible processes, results from Sec. 6.13apply.On the p-vdiagram, the work per unit of massflowing isvdp. Thus on a per unit of mass flowingbasis,

Area 1-2-a-b-1represents the

compressor work input.

Area 3-4-b-a-3

represents the turbinework output.

Enclosed area 1-2-3-4-1represents the net work

developed.

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Area 2-3-a-b-2represents

the heat added.Area 4-1-b-a-4representsthe heat rejected.

Enclosed area 1-2-3-4-1

represents the net heataddedor equivalently, the

net work developed.


On the T-sdiagram, the heat transfer per unit ofmass flowing is Tds. Thus, on a per unit of massflowing basis,

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Effects of Compressor Pressure Ratio on

Brayton Cycle Performance

That the compressor pressure ratio, p2/p1, is animportant operating parameter for gas turbines is

brought out simply by the following discussions

centering on the T-sdiagram:

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Increasing the compressor pressure ratio from p2/p1top2/p1changes the cycle from 1-2-3-4-1to 1-2-3-4-1.

Since the average temperature of heataddition is greater in cycle 1-2-3-4-1, and

both cycles have the same heat rejectionprocess, cycle 1-2-3-4-1has the greater

thermal efficiency.

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thermal efficiency.

Accordingly, the Brayton cycle thermal

efficiency increases as the compressorpressure ratio increases.

60

th(%)

2 4 6 8 10

CompressorPressure Ratio

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thermal efficiency.

Accordingly, the Brayton cycle thermal

efficiency increases as the compressorpressure ratio increases.

The turbine inlet temperature alsoincreases with increasing compressor

ratiofrom T3to T3

.

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The figure shows theT

-sdiagrams of two idealBrayton cycles having the same turbine inlet temperature

but different compressor pressure ratios.

Cycle Ahas the greatercompressor pressure ratioand

thus the greater thermal efficiency.

Cycle Bhas the larger enclosedarea and thus the greater net work

developed per unit of mass flow.

For Cycle Ato develop the samenet power as Cycle B, a larger

mass flow rate would be required

and this might dictate a larger

system.

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Accordingly, for turbine-powered vehicles, wheresize and weight are constrained, it may be

desirable to operate near the compressor pressure

ratio for greater net work per unit of mass flowand

not the pressure ratio for greater thermal efficiency.

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Gas Turbine Power Plant Irreversibility

The most significant irreversibility by faris the

i r revers ib i li ty of combust ion. This type of irreversibility isconsidered in Chap. 13, where combustion fundamentals

are developed.

Irreversibi l i t iesrelated to f low through the turb ine andcompressoralso significantly impact gas turbine

performance. They act todecreasethe work developed by the turbineandincreasethe work required by the compressor,thereby decreasingthe net work of the power plant.

m

W

m

W

m

W

ctnet

marked decrease in net

work of the power plantirreversibilites decrease

turbine work

irreversiblities increase

compressor work

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Gas Turbine Power Plant Irreversibility

)(

)(

)/(

)/(

12

1s2

c

scc hh

hh

mW

mW

h

Isentropic compressor efficiency, introduced in Sec.6.12.3, accounts for the effects of irreversibilities within the

compressorin terms of actual and isentropic compressor work

input, each per unit of mass flowing through the compressor.

work input for the actual process from compressor

inlet state to the compressor exit pressure

work input for an isentropic process from

compressor inlet state to exit pressure

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Gas Turbine Power Plant Loss

The exhaust gas temperature of a s implegasturbine is typically well above the ambient

temperature. Thus, the exhaust gas has

considerable thermodynamic utility (exergy) that

would be irrevocably los twere the gas dischargeddirectly to the ambient.

Regenerat ivegas turbines (Sec. 9.7) and gas

turbine-based com bined cy c les(Sec. 9.9) aim toavoid such a significant loss by using the hot

exhaust gas cost-effectively.

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The regeneratorallows air exiting thecompressor to be preheated, process 2-x,

as the turbine exhaust gas cools, process

4-y.

Preheating reduces the heat added perunit of mass flowing(and thus the amount

of fuel that must be burned):

Regenerative Gas Turbines

)( x3in hhmQ

The hotturbine exhaust can be utilized with a preheater

called a regenerator.

)( 23in hhmQ

The net work per unit of mass flowing is not altered with theinclusion of a regenerator. Accordingly, since the heat added is

reduced, thermal efficiency increases.

With Regeneration Without Regeneration

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Since a finite temperature difference must exist

between the two streams of the regenerator for heattransfer to take place between the streams, the cold-

side exiting temperature, Tx, must be less than the

hot-side entering temperature, T4.

Regenerator Effectiveness

As the stream-to-streamtemperature difference becomes

small Txapproaches T4, but

cannot exceed it. Accordingly,

Tx T4.

As the enthalpy of the airvaries only with temperature, we

also haveh

x h

4.

T4

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In practice, regenerator effectiveness values

range from 60-80%, approximately. Thus, thetemperature Txat the combustor inlet is invariably

below the temperature T4at the turbine exit.

Selection of a regenerator is largely aneconomic decision.

Regenerator Effectiveness

With regeneration less fuel is consumedby thecombustor but another component, the

regenerator, is required.

When considering use of a regenerator, thetrade-off between fuel savings and regenerator

cost must be weighed.

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A modification of the Brayton cycle that increases

the net work developed is mult is tage expansionwith reheat.

The figure shows a cycle with two turbine stagesand a reheat combustor between the stages.

Gas Turbines with Reheat and Regeneration

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Cycle with reheat

The ideal Brayton cycle with reheatis 1-2-3-a-b-4-1.

The ideal Brayton cycle without reheatis 1-2-3-4-1.The reheat cyclehas a larger enclosed areathanthe cycle without reheat and thus a greater net work

developed per unit of mass flowing, which is the aim.


Cycle without reheat

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The figure also shows that the temperature at the exitof the second-stage turbine, state 4, is greaterthan at

the exit of the single turbine of the cycle without reheat,

state 4. Accordingly, with reheat the potential for

regeneration is also enhanced.

When reheat and regeneration are used together, thethermal efficiency can increase significantlyover that for

the cycle without reheat.


T4

T4

G T bi ith

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Another modification of the Brayton cycle thatincreases the net work developed is compress ionwith intercool ing.

The figure shows two compressor stages and an

intercooler between the stages.

Gas Turbines with

Intercooling and Regeneration

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Gas Turbines with

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Recalling that for such internally reversible processes the

work input per unit of mass flowing is given by vdp, thefollowing area interpretationsapply, each per unit of mass

flowing:

Gas Turbines with


With intercooling, area 1-c-d-2-a-b-1

represents the work input.Without intercooling, area 1-2-a-b-1represents the work input.

The cross-hatched areac-d-2-2-c

represents the reduction in workachieved with intercooling.

If the total turbine work remains the same, a reduction incompressor work results in an increase in the net work

developed, which is the aim.

Gas Turbines with

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While compression with andwithout intercooling each

bring the air to the same final pressure, p2, the finaltemperature with intercooling, T2, is lowerthan the final

temperature without intercooling, T2.

Gas Turbines with


Comparing states 2and 2on the T-sdiagram, T2< T2.

The lower temperature at the compressor exitwithintercooling enhances the potential for regeneration.

T2

T2

Gas Turbines with

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Gas Turbines with

Intercooling and RegenerationWhen compression with intercoolingis used together with

regeneration, the thermal efficiency can increase significantlyover that for the cycle without intercooling.

The T-sdiagram also shows that for cooling to thesurroundings the temperature Tdat the intercooler exit

cannot be less thanT1, the temperature of the air enteringthe compressorfrom the surroundings: Td T1.

T1

Td

R ti G T bi

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Shown here is a regenerative gas turbinethatincorporates reheat and intercooling.

With these modifications to the basic Brayton cycle:

Regenerative Gas Turbine

with Reheat and Intercooling

The net work

outputisincreased.

The thermalefficiency is

increased.

R ti G T bi

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Applying mass and energy ratebalancesat steady state, weobtain the following expressions,

each per unit of mass flowing:



Totalturbine work:

(h6h7) + (h8h9) = ht1(h6h7s) + ht2(h8h9s)m

W

t

=

where t1and t2denote the isentropic efficienciesof turbines 1and 2,

respectively.

Totalcompressor work:

(h2h1) + (h4h3) = (h2sh1)/hc1+ (h4sh3)/hc2m

W

c

=

where c1and c2denote the isentropic efficienciesof compressors 1

and 2, respectively.

R ti G T bi

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Applying mass and energy ratebalancesat steady state, weobtain the following expressions,

each per unit of mass flowing:



Totalheat added:

(h6h5) + (h8h7)m

Q

in

=

In this application, the regenerator effectivenessis:

(h5h4)/(h9h4)hreg=

For cooling to the surroundings, the temperature at theexit of the intercooler, T3, cannot be less than the

temperature of the air entering the compressor from the

surroundings: T3 T1.

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The exhaust temperature of the simple gas turbine

is typically well above the ambient temperature, andthus the hot gas exiting the turbine has significant

thermodynamic utility (exergy) that can be used cost-

effectively.

Waysto utilize this potential include:The regenerative cyc lepreviously considered.A combined cyc lenamely, a cycle thatcouples two power cycles such that the energy

discharged by heat transfer from the higher-

temperature cycle is used as a heat input for the

lower-temperature cycle.

Gas Turbine-Based Combined Cycle

C G C

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Illustrated here is a combined cycleinvolving gas and vapor power cycles:

The cycles are combined using aninterconnecting heat-recovery

steam generatorthat serves as the

boiler for the vapor power cycle.

The combined cycle has the gasturbines high average temperature ofheat additionand the vapor power

cycles low average temperature ofheat rejection.

Thermal efficiency is greaterthaneither cycle would have individually.

Combined Gas Turbine-Vapor Power Cycle

Increasingly, combined gas turbine-vapor power plants arebeing used world-widefor electric power generation.

C bi d G T bi V P C l

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Combined Gas Turbine-Vapor Power Cycle

The net power developed by thecombined cycleis the sum of the net

power developed by each cycle.

The thermal efficiency of thecombined cycleis the net power

output divided by the rate of heat

addition.

For an adiabatic heat recovery steamgenerator, mass and energy rate

(Eq. 9.28)

balances reduce to give the following relationship involving the

mass flow rates of the two cycles:

(Eq. 9.29)

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Combined-cycle District Heating

Alternatively, steam exitingthe turbinemay be sent

directly to the community

while its condensate returns

to the pump, thereby

eliminating the condenser.

Shown here is a combined gas turbine-vapor power cycle

applied for dis tr ict heating. District heating plants arelocated within communities to deliver steam or hot watertogether with electricityfor domestic,

commercial, and industrial use.

G T bi f Ai ft P l i

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Because of their favorable power-to-weight ratio, gasturbines are well suited for aircraft propulsion. Theturbojet eng ineis commonly used for this purpose.

The figure provides the schematic of a turbojet engine.

Gas Turbines for Aircraft Propulsion

Va V5


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Va V5

The increasein velocityfrom diffuser inlet, Va, to nozzleexit, V

5

, gives rise to the th rus tdeveloped by the engine

in accord with Newtons second law of motion (Eq. 9.31).In harmony with air-standard analysis, we assume airmodeled as an ideal gasflows through the engine shown

in the schematic and the temperature rise that would be

obtained with combustion is achieved by heat transfer

from an external source.



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Va V5

If the air flows through the components of the turbojet enginewithout irreversibilities and stray heat transfer,air undergoes

the five processesshown on the T-sdiagram:


Process a-1: Air at velocity Vaenters the diffuser anddecelerates isentropically, while experiencing an increase in

pressure.

Process 1-2: The air experiences a further increase inpressure isentropically, owing to work done by the compressor.


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Va V5


Process 2-3: The temperatureof the air increasesat constantpressure as it receives a heat transferfrom an external source.

Process 3-4: The high-pressure, high-temperature air

expands isentropicallythrough the turbine, driving thecompressor.




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Va V5


Process 4-5: The air continues to expand isentropicallythrough the nozzle, achieving a velocity, V5, at the engine exit

much greater than the velocity, Va, at the engine inlet, and

thereby developing th rus t.



Review: Nozzle and Diffuser Modeling

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If the change in potential energy from inlet to exit is

negligible, g(zize) drops out.

If the heat transfer with surroundings is negligible,

drops out.

)(

2

)V(V)(0

22

cvcv eiei

ei zzghhmWQ

Review: Nozzle and Diffuser Modeling

.0cvW

2

VV)(0

22ei

ei hh

cvQ

The one-inlet, one-exit energy rate balance atsteady state reads:

For a control volume enclosing a nozzle or diffuser,

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Theenergy rate balanceapplicable to the nozzle

takes the form


2

VV)(0

25

24

54 hh

)(2V

2

V545

25

54 hhhh

h4V4 0

4

5

h5V5

For the nozzle, i= 4and e= 5. Then,

2VV)(0 22 eiei hh

Since inlet velocity is negligible, the energy ratebalance reduces to


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Since the final expressions obtained for thediffuser and nozzle are deduced from massand

energy rate balances, they apply equally when

irreversibilities are present and in the absence of

irreversibilities.


ch09 pt2

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