EGR 4347 Analysis and Design of Propulsion Systems

Review

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EGR 4347 - Review

Explain the difference between units and dimensions.

Dimensions – physical quantity that can be characterized EX. length, mass

Units – arbitrary magnitudes assigned to the dimensions EX. meter, feet

April 22, 2023 EGR 4347 3

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Explain extensive and intensive properties.

Extensive depends on system

Intensive is independent of system

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Give at least four forms of energy which make up the term total energy, E.

1. Thermal 2. Mechanical3. Potential 4. Electric5. Chemical 6. Nuclear7. Kinetic 8. Magnetic

April 22, 2023 EGR 4347 5

EGR 4347 - Review

Give the unit of mass in the SI, Old English and English Engineering system.

SI - kgOld English - lbm

English Engineering - slug

April 22, 2023 EGR 4347 6

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What is gc and how is it used?

Conversion constant - used with mass

What is a simple compressible substance?The only important reversible work mode is volume change or pdv work.

April 22, 2023 EGR 4347 7

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What is the state postulate?

The state of a simple compressible system is completely specified by two independent, intensive properties.

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What is a perfect or ideal gas (physical meaning)?No dissociation Intermolecular forces negligibleOccurs at low pressures and high temperatures (compared to critical point)

What is the ideal gas law?P = R T

April 22, 2023 EGR 4347 9

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Explain R in the ideal gas law.Specific Gas Constant-depends on

molecular weight

Give the equation for and define the Conservation of Mass.

dm/dt = 0

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Give the equation for and define Continuity.

outin mm..

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Give the equation for and define 1st Law for a Control Volume.

outoutoutout

inininin

kepehmWQ

kepehmWQ

)(

)(...

...

April 22, 2023 EGR 4347 12

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Give the equation for and define the 2nd law for a Control Volume.

0TQSsmsmS

k

kgen

.

ee

.

ii

..

CV

April 22, 2023 EGR 4347 13

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Define adiabatic.No heat interaction.

Define reversible.A process that can be reversed without leaving any trace on the surroundings.

Define isentropic.ds=0

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Is an adiabatic, reversible process isentropic?Yes

Is an isentropic process always adiabatic and reversible?No

Is an isentropic, adiabatic process reversible?Yes

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Is an isentropic, reversible process always adiabatic?No

What is a calorically perfect gas?cp/cv = constant =

For a calorically perfect gas what is du?du=cvdT

April 22, 2023 EGR 4347 16

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For a calorically perfect gas what is dh?dh=cpdT

What is Gibbs Equation?Tds=dh-vdp=du+pdv

What is specific enthalpy?h=u+pdv

April 22, 2023 EGR 4347 17

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Define total properties.Fluid brought to rest isentropically (or

adiabatically)Write the equation for total enthalpy and total

temperature.ht=h+V2/(2gc) Tt=T+V2/(2gccp)

April 22, 2023 EGR 4347 18

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Explain the concept of isentropic efficiency as it applies to a turbine.

s21

a21

s

aT hh

hhww

workturbineIsentropicworkturbineActual

April 22, 2023 EGR 4347 19

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Draw the T-s diagram showing Turbine Isentropic Efficiency.

April 22, 2023 EGR 4347 20

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Derive cp = cv+ R from h = u + pv using the ideal gas law

h = u+pv = u+RTdh = du + RdT +TdR dR=0dh/dT = du/dT + Rcp = cv + R

April 22, 2023 EGR 4347 21

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What is Mach number? V/a where a is the speed of sound

Using Gibbs equation Tds = du + pdv finds = cv ln(T2/T1) + R ln(v2/v1).

1

2

1

2 lnlnvvR

TTcs

vdvR

TdTcds

Tpdv

Tduds

v

v

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Find the following in terms of using cp=cv+R

1) R/cv

R/ cv = (cp/ cv) - 1 = - 1

2)R/ cp

R/ cp = 1 - (cv / cp) = 1 - (1/ ) = ( - 1)/

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3) (cv - R) / cp

(cv - R)/ cp = (cv / cp) - (R / cp) = 1/ - ( -1) / = (2- )/

4) (cv - R) / cv

(cv - R)/ cv = 1 - ( - 1) = 2 -

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Use s = cp ln(T2/T1) - R ln(p2/p1) to find the isentropic relationship for pressure and temperature

cp ln(T2/T1) = R ln(p2/p1) ln(T2/T1) = (R/cp ) ln(p2/p1) R/cp=(-1)/raise “e” to this power(T2/T1) = (p2/p1) (-1)/

April 22, 2023 EGR 4347 25

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Use Tt=T+V2/(2gccp) to find Tt/T in terms of and Mach numberV = M a where a is SQRT(gc RT)

Tt=T+M2 RTgc /(2gccp)

(Tt/T) = 1 - M2 ( R)/(2cp) R/cp=(-1)/

(Tt/T) = 1 - M2 (-1)/2