MAE135
Spring 2015
SOLUTIONS TO HW 4
PROBLEM 1 (30 points)
(a) The fact that the exit pressure pe is dierent from the ambient pressure pa indicates a cuto
of communication between the nozzle exit and its surroundings. The only way this can happen is
if th

MAE135
SOLUTIONS TO HW 3
Spring 2010
PROBLEM 1 (5 points) (a) Given M = 4, and that the ow is isentropic, the area-Mach number relation (Table A.1) gives A/A =10.72. (b) We need to gure out the test section static pressure p and temperature T . We are giv

MAE135
Spring 2015
SOLUTIONS TO HW 3
PROBLEM 1 (30 points)
The disturbance propagates from left to right with speed a =
the disturbance measures space (x) and time (t) according to
RT . An observer moving with
dx
=a
dt
The propagation time is thus governe

MAE135
Homework No. 6
Spring 2010
Date Assigned: Friday, May 7, 2010 Due date: 5:00 pm Tuesday, May 18, 2010 PROBLEM 1 (10 points)
(a)
Ae /A* =4.0
(d)
Ae /A* =4.0
p
0
M=1
Subsonic
p
0
12
Shock
p
a
p
a
(b)
A1/A =2.0
*
(e)
Ae /A* =4.0
Ae /A* =4.0
p
0
12
p
0

MAE135
SOLUTIONS TO HW 4
Spring 2010
PROBLEM 1 (15 points) The bottle ow rate determines the ow rate of the leak mi under the initial cabin conditions p0i and T0i . Since the pressure ratio across the rupture orice is innite, the ow must be choked: mi = C

MAE135
SOLUTIONS TO MIDTERM
Spring 2010
Problem 1 (5 points) C and D are wrong: C is the isentropic relation, which does not hold through the shock, because the shock is non-isentropic; D is the incompressible Bernoulli equation, which fails here because

MAE135
Solutions to Homework No. 1
Spring 2010
PROBLEM 1 (5 points) For calorically perfect gas, the internal energy e = cv T . With cv = 717 K/kg K for air and T = 290 K, e = (717)(290) = 207930 J/Kg. (Note that the units J/kg = m2 /s2 ). Therefore Kinet

MAE135
Homework No. 4
Spring 2010
Date assigned: Tuesday, April 20, 2010 Due date: 5:00 pm, Tuesday, April 27, 2010 PROBLEM 1 (15 points) A dangerous situation develops inside a spacecraft that requires careful calculation. The astronauts detect a leak (p

MAE135
MIDTERM
06-MAY-2010
Open book (Anderson only), notes and homeworks. Assume calorically-perfect air ( = 1.4, R = 287 J/KgK) for all problems. 80 minutes time limit
PROBLEM 1 (5 points) Consider ow through a normal shock. Are any of the following sta

MAE135
Spring 2012
SOLUTIONS TO MIDTERM
PROBLEM 1 (5 points)
Two relations are incorrect:
C. p + u2 =const. is incorrect. This relation is the inviscid 1D (purely one-dimensional) momentum
equation. It does not hold for flow with area variation.
RT = cons

MAE135
Spring 2017
SOLUTIONS TO HW 4
PROBLEM 1 (30 points)
(a) We have a duct where the flow goes from rest (reservoir) to supersonic speed at station 3. For
isentropic flow, the only way to transition from subsonic to supersonic speed is through a sonic

MAE135
Spring 2017
Homework No. 7
Date assigned: Monday, May 15, 2017
Due date: 5:00 pm Monday, May 22, 2017
Writeup should be neat and single-sided. All problems should be solved. Assume calorically-perfect gas with
=1.4 for all problems.
PROBLEM 1 (20 p

MAE135
Spring 2017
SOLUTIONS TO HW 5
PROBLEM 1 (50 points)
(a) The pressure imbalance between the pipe exit and the ambient can be supported only if the
exit flow is sonic or supersonic. Here the maximum possible Mach number is sonic, so we must
have M2 =

MAE135
Spring 2017
Homework No. 4
Date assigned: Monday, April 24, 2017
Due date: 5:00 pm Monday, April 31, 2017
Writeup should be neat and single-sided. All problems should be solved. Assume calorically-perfect gas with
=1.4 for all problems.
PROBLEM 1 (

MAE135
Spring 2017
Homework No. 6
Date assigned: Monday, May 8, 2017
Due date: 5:00 pm Monday, May 15, 2017
Writeup should be neat and single-sided. All problems should be solved. Assume calorically-perfect gas with
=1.4 for all problems.
PROBLEM 1 (50 po

MAE135
Spring 2017
SOLUTIONS TO HW 6
PROBLEM 1 (50 points)
The mass flow rate of air at sonic conditions is given by:
p0
A
m
= 0.0404
T0
This formula is general enough to be used in any situation, provided one uses the local values of
total pressure and

MAE135
Spring 2015
Solutions to Homework No. 1
PROBLEM 1 (20 points)
For a calorically perfect gas, the internal energy e = cv T . The ratio of kinetic to internal energy
therefore is:
1 2
1 2
V
V
Kinetic energy
= 2
= 2
Internal energy
e
cv T
Air has cv =

MAE135
Spring 2015
SOLUTIONS TO HW 2
PROBLEM 1 (30 points)
Assuming that the process from the freestream () to the combustor entrance (c) is adiabatic, we
have
h0 = h0c
1 2
1
cp T + V = cp Tc + Vc2
2
2
If we assume that the velocity in the combustor is ne

MAE135
Spring 2017
Homework No. 5
Date assigned: Monday, May 1, 2017
Due date: 5:00 pm Monday, May 8, 2017
Writeup should be neat and single-sided. All problems should be solved. Assume calorically-perfect gas with
=1.4 for all problems.
PROBLEM 1 (50 poi

MAE135
Spring 2017
Homework No. 8
Date assigned: Monday May 22, 2017
Due date: 5:00 pm Tuesday, May 30, 2017
Writeup should be neat and single-sided. Assume calorically perfect gas with = 1.4 where needed.
Use of gas dynamic tables and charts is fine wher

MAE135
Homework No. 8
Spring 2010
Date assigned: Tuesday May 25, 2008 Due date: 5 pm Thursday June 3, 2010 PROBLEM 1 (6 points)
=0 1
o
1
2
=? 2
1=1. 7
A planar supersonic nozzle with area ratio A/A = 1.7 is connected to a reservoir with p0 = 150 psia. The

MAE135
Homework No. 5
Spring 2010
Date assigned: Tuesday, April 27, 2010 Due date: 5:00 pm, Tuesday, May 4, 2010 PROBLEM 1 (10 points)
Combustion chamber
pa= 100 kPa p01=300 kPa T01=300 K
1
Frictionless injector
2
T01=300 K
Designed assumed T02=300 K In r

MAE135
Homework No. 2
Spring 2010
Date assigned: Tuesday, April 6, 2010 Due date: 5:00 pm Tuesday, April 13, 2010
Assume calorically-perfect gas with =1.4 for all problems.
PROBLEM 1 (10 points)
Consider the SR-71 at ight Mach number M1 =3.0 with ambient

MAE135
Homework No. 1
Spring 2010
Date assigned: March 24, 2010 Due date: 5:00 pm, Tuesday, April 6, 2010
Assume calorically-perfect gas with =1.4 for all problems.
PROBLEM 1 (5 points) The internal energy per unit mass is e = cv T while the kinetic energ

MAE135
Solutions to HW 7
Spring 2010
PROBLEM 1 (10 points) First we calculate that, in region 1, p01 /p1 =36.7. Case (a) From 1 to 2: M1 = 3.0 and = 20o Oblique shock charts: = 37.5o M1n = M1 sin = 1.83 p02 Normal shock table: M1n = 1.83 p2 /p1 = 3.74, p0

MAE135
SOLUTIONS TO HW 6
Spring 2010
PROBLEM 1 (10 points) In the rst three cases the outow is subsonic, therefore the exit pressure naturally matches the ambient pressure, pe = pa . (a) This is an isentropic ow which reaches M = 1 at the throat, then dec

MAE135
SOLUTIONS TO HW 2
Spring 2010
PROBLEM 1 (10 points) Since ow is isentropic, both T0 and p0 are conserved. In other words, T02 = T01 p02 = p01 Since we know the conditions in the freestream (1), we evaluate the total temperature and total pressure f

MAE135
SOLUTIONS TO HW 7
Spring 2017
PROBLEM 1 (20 points)
(a) For Ai /A = 1.3, the supersonic branch of the Mach number-area relation gives M = 1.66. This
is the ideal flight Mach number, for which compression is entirely isentropic.
(b) Flow after the s

MAE135
Spring 2017
SOLUTIONS TO HW3
PROBLEM 1 (40 points)
The acoustic disturbance propagates from left to right with the speed of sound a =
observer moving with the disturbance measures space (x) and time (t) according to
RT . An
dx
=a
dt
The propagation

MAE135
Spring 2017
SOLUTIONS TO HW 2
PROBLEM 1 (30 points)
Assuming that the process from the freestream () to the combustor entrance (c) is adiabatic, we
have
h0 = h0c
1 2
1
cp T + V
= cp Tc + Vc2
2
2
If we assume that the velocity in the combustor is ne

PROBLEM 3 (30 points)
V = 2Vsin
V
T
For incompressible potential flow the velocity on the surface of a cylinder is
V = 2V sin
where V is the freestream velocity and is the polar angle, defined here with respect to the
x-axis and positive clockwise. Lets

MAE135
Spring 2017
Homework No. 3
Date assigned: Monday, April 17, 2017
Due date: 5:00 pm Monday, April 24, 2017
Writeup should be neat and single-sided. All problems should be solved. Assume calorically-perfect gas with
=1.4 for all problems.
PROBLEM 1 (