Due Sep. 11
Problem Set #2: Work, Paths and Gas State Equations
Always indicate any assumptions you make. If you use any results or equations
from the class notes or text in you solutions, please note and reference them (but you
better be sure they are a
AE3450/Seitzman
Spring 2013
Due Fri., Jan. 25
Problem Set #3: State Equations Ideal Gases
Homework solutions should be neat and logically presented, see format requirements
at (www.ae.gatech.edu/people/jseitzma/classes/ae3450/homeworkformat.html).
Alway
Due Tue., Sept. 2
Problem Set #1: Units, Significant Figures, Energy and Systems
Always indicate any assumptions you make. If you use any results or equations
from the class notes or text in you solutions, please note and reference them (but you
better b
AE3450/Seitzman
Spring 2013
Due Fri., Jan. 18
Problem Set #2: Work, Paths and Enthalpy
Homework solutions should be neat and logically presented, see format requirements
at (www.ae.gatech.edu/people/jseitzma/classes/ae3450/homeworkformat.html).
Always i
AE3450/Seitzman
Fall 2013
Solution for Problem Set #9: Nozzle Flow
Problem 1. Supersonic Exhaust System
Given: Air flow facility shown in picture.
Find: a) To1 with respect to facility
b) A1/A2 required to choke facility if
isentropic
Assume: air is tpg a
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Already derived differential
forms of steady conservation eqs.
no body forces
neglect viscous work
Mass
d 1 dv 2 dA
+
+
=0
2
2 v
A
p
x
T
v
A
dx
h q
(VI.9)
p+dp
T+dT
+d
v+dv
A+dA
h+dh
Recall, 1-D valid
only for dA/dx sma
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State Equations
Relationship between TD properties
can find one TD properties based on values of
some number of other properties
Example
p(,T) or p(v,T) or T(p,v) or
relation between p, v, T sometimes known as
the EOS
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Example: P.G. State Eqns.
Given: Piston-cylinder containing CO
initially at 400. K, 1.0 atm. At later time
gas is at 800. K and 10. atm.
1
2
Find:
?
2
Change in specific volume (v1v2)
Change in internal energy (u2-u1)=u12
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Control Volume Derivation
How to convert our relationships for a closed
system (control mass) to an open system (control
volume)
For mass conservation, our control mass law was
dm sys
=0
CM
dt
In integral form (integrati
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General Thermodynamic Problem
Solving Approach
For solving most engineering problems using thermodynamics,
can use the following recipe:
1. Draw picture of system that includes control surface
2. List givens (properties, c
AE3450/Seitzman
Fall 2013
Solution for Problem Set #7: Entropy and the Second Law
Problem 1. Reversible vs. Irreversible Processes
Given: Gas undergoing either of two compression processes: one frictionless and the
other not. For both processes, the initi
AE3450/Seitzman
Fall 2013
Solution for Problem Set #8: Stagnation Properties and Isentropic Flow
Problem 1. Turbine Stagnation Properties
Q0
Given: Adiabatic turbine with conditions shown
Find: a) To1
Reversible?
b)
T1 628K
po1 14atm
Assume: 1) flow is st
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CM Energy and Enthalpy Examples: #1
Given: Piston-cylinder but piston is
locked in place, fluid inside being
heated. No other work being done
(only pdV work possible)
m
Q
Find:
How much heat (transfer) required to change
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Equilibrium Diagrams and
Saturated Liquid/Vapor Systems
In equilibrium, different phases of matter
gas, liquid, solid (also multiple solid phases,
e.g., different crystalline structures of steel)
So far looked at individ
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Mach Angle and Mach Number
Looking for relationship between speed of sound and flow
speed (or speed of body moving through fluid)
Consider small body (point) moving in stagnant fluid
continuously launches weak pressure d
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Speed of Sound
Consider adiabatic, 1-D propagation of weak
(infinitessimal) pressure wave traveling through
initially stationary (nonmoving), simple
compressible substance
Can think of piston given
small push
p
time t1
F
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Entropy Approach to 2nd Law for CM
Start with existence of entropy as a thermodynamic
property (measure of microscopic disorder of system,
or better, energy states of system)
S=S(U,V) function of two indep. variables
Ima
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Classical Approach to 2nd Law for CM
Start with observations about the ability to build devices
(thermodynamic cycles)
Clausius Statement of 2nd Law
concerns cycles that cause heat transfer from low
temperature body to h
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Isentropic Processes
Isentropic (process or system)
no change in entropy
dS=0 or S=dS=0
2nd Law for control mass
dS= Q/T+ 3s
So two ways to get no entropy change
production (irreversibilities) balanced by cooling
(hea
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Differential Form of Energy Conservation
For Quasi-1D, Steady Flow
Also assume no work but flow work (e.g., no
viscosity), thermally/calorically perfect gas
v2
1
= c p dT + dv 2
q = dh o = dh + d
2
2
q dT
1
=
+
dv 2
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Energy CVAnalysis: Example 1
Given: Steady flow in wind tunnel with air intake at
30 m/s, 300 K and exit at 300 m/s
m1
Find: T2
Assume: Adiabatic (insulated)
v1=30 m/s
No work but PV work
T1=300 K
Air is ideal gas
Unifor
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2nd Law Development for Closed Systems
At least two approaches for developing
mathematical form of 2nd Law for Closed Systems
(i.e. Control Masses)
1. Entropy Approach: start with existence of
entropy as TD property, find i
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Entropic State Eqns. Ideal Gases
du
p
dv
T
T
cv dT R
for ideal gas
dv
T
v
s2
T2 c dT
v2 R
v
integrate
ds
dv
s1
T1
v1 v
T
T2 c dT
v2 dv
s2 s1 v R
T1
v1 v
T
Recall Gibbs eqn.
ds
cv dT
v
R ln 2
T
v1
T2 c dT
s12 s2 s1
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Energy Conservation for Control Volumes:
Integral Form
Start with Reynolds Transport Theorem (RTT):
r
dB
d
=
dV + CS (v rel n )dA
dt CM dt CV
Energy
1
B = Etot = U + Ekinetic = U + mv 2
2
v2
= etot = u +
uo
2
will put
AE3450/Seitzman
Fall 2013
(Brief) Solution for Supersonic Inlet Computer Problem
CD Diffuser
M
Design
The design areas for the M=1.75 inlet can be
found from the A/A* value required for isentropic
flow at M and for the required mass flow rate
required at
AE3450/Seitzman
Fall 2013
Solution for Problem Set #6: Energy Conservation for Control Volumes
Problem 1. High Temperature Wind Tunnel
Given: CO2 wind tunnel with
conditions given in picture,
CO2=1.30 and no external
work
Test Section Atest=225 cm2
Tin=21
Entropy Change by Heat Transfer
Define Thermal Energy Reservoir (TER)
Constant mass, constant volume
No work - Q only form of energy transfer
T uniform and constant
S
TER
dS
1
=
U V
dU
T
dS
1
dU = dQ
=
dQ
T
dS TER = Q /T
=
T,dU
dQ
Entropy Change by H
Energy Equation
1st Law of Thermodynamics
Energy cannot be created or destroyed.
(see Conservation of Mass for
exception)
It can, however, change from one form
to another; transfer from one system to
another.
Energy conservation is a Postulate
Closed S
State Postulate
According to the State Postulate the
number of intensive variable needed to
specify all other intensive variables
equals the number of relevant, reversible
work modes plus one.
This course deals with one such mode
(mechanical work); i.e.,
Problem 2
Problem 1
Given:
Find:
Solution
Answer:
Answer:
Problem 3
Solution
Page 1
Problem 4
Page 2
Problem 5
Solution
Solution
Problem 6
Solution
Page 3
Problem 7
Solution
Problem 8
Solution
Page 4
Problem 10
Problem 9
Solution
Solution
Given:
Find:
Ans
AE 3450: THERMODYNAMICS AND COMPRESSIBLE FLOWS (FALL 2014)
Assignment No. 3
Instructor: Dr. K. K. Ahuja
Tel: 404 407 7865
Email: krish.ahuja@ae.gatech.edu
Due: September 18, 2014
Total Points: 60
This Home work is based upon your independent reading as we
AE 3450: THERMODYNAMICS AND COMPRESSIBLE FLOWS (FALL 2013)
Assignment No. 2
Instructor: Dr. K. K. Ahuja
Tel: 404 407 7865
Email: krish.ahuja@ae.gatech.edu
Due: September 5, 2013
Total Points: 60
This Home work is based upon your independent reading as wel
AE 3450: THERMODYNAMICS AND COMPRESSIBLE FLOWS (FALL 2013)
Assignment No. 8
Instructor: Dr. K. K. Ahuja
Tel: 404 407 7865
Email: krish.ahuja@ae.gatech.edu
Work to be completed by November 29
Can be submitted any time until December 5, 2013
Total Points: 5
AE 3450: THERMODYNAMICS AND COMPRESSIBLE FLOWS (FALL 2014)
Assignment No. 7
Instructor: Dr. K. K. Ahuja
Tel: 404 407 7865
Email: krish.ahuja@ae.gatech.edu
Due: November 13, 2014
Total Points: 50
This Home work is based upon your independent reading as wel