2.2
ﬁfe/:9; Waf/ /&(x)
Cl. " *ﬁq— ‘ —— b
' a
l I
l I 3
: 8 EH“ C!’_c_' I
l ‘”" f f x

_._.’5J
W777
Amer Well (it (3}
Denote the pressure distributions on the upper and lower walls by pubs) and p a (x) reSpectively.
The walls are close enough to the mo
M&AE 150B
Spring 2014
HOMEWORK 7
Assigned:
Due:
Thursday, May 15
Thursday, May 22 (5 PM)
1) [10 points] (Anderson 5.2) Consider a circular vortex filament of strength and radius R. Find an
expression for the velocity (vector) a distance A along a line thr
M&AE 150B
Spring 2014
HOMEWORK #2
Assigned:
Due:
Thursday, April 10
Thursday, April 17 (5 PM)
1) [10 points] (Anderson 2.2) Consider an airfoil in a wind tunnel with horizontal top and bottom
walls. Using an analysis similar to the one in lecture (see fig
M&AE 150B
Spring 2014
HOMEWORK #4
Assigned:
Due:
Thursday, April 24
Thursday, May 1 (5 PM)
1) [5 points] (Anderson 4.2) Consider the NACA 2412 airfoil shown in fig. 4.10 with a 2m chord
and an airspeed of 50 m/s under standard sea level conditions. If th
M&AE 150B
Spring 2014
HOMEWORK #2
Assigned:
Due:
Thursday, April 10
Thursday, April 17 (5 PM)
1) [10 points] (Anderson 2.2) Consider an airfoil in a wind tunnel with horizontal top and bottom
walls. Using an analysis similar to the one in lecture (see fig
Differential Forms in Cartesian Coordinates:
Continuity (incompressible):
u v w
+ +
=0
x y z
u
u u
u
p
+u
+v + w = + g x
x y
z
x
t
Euler:
v
v v
v
p
+ u +v + w = + g y
x y
z
y
t
w
w w
w
p
+u
+v
+w
= + gz
t
x
y
z
z
Differential Forms in Polar Co
M&AE 150B
Spring 2014
HOMEWORK #1
Assigned:
Due:
Thursday, April 3
Thursday, April 10 (5 PM)
1) [10 points] (Anderson 1.4) Consider an infinitely thin flat plate with a 1.0m chord at an angle of
attack of 10 in a supersonic flow. The pressure and shear s
Differential Forms in Cartesian Coordinates:
Continuity (incompressible):
u v w
+ +
=0
x y z
u
u u
u
p
+u
+v + w = + g x
x y
z
x
t
Euler:
v
v v
v
p
+ u +v + w = + g y
x y
z
y
t
w
w w
w
p
+u
+v
+ w = + gz
t
x
y
z
z
Differential Forms in Polar Co
M&AE 150B
Spring 2014
HOMEWORK 8
Assigned:
Due:
Thursday, May 22
Thursday, May 29 (5 PM)
1) [10 points] (Anderson 5.9) The Supermarine Spitfire (Fig 5.19) had a maximum velocity of 362
mph at an altitude of 18,500 ft. It weighs 5,820 lbs, has a wing area
M&AE 150B
Spring 2014
HOMEWORK 9
Assigned:
Due:
Thursday, May 29
Thursday, June 5 (5 PM)
1) [6 points] (Anderson 9.2) Consider an oblique shock in a Mach 4 flow with a wave angle () of
30. At an altitude of 10 km, p = 26,500 Pa and T = 223.3 K. Calculate
’ g [jg/1b M
(W!) max/J} 7" (28% 65”) W (0 >
’ r3 4 (213: q
6* RC :20 K 5) HE ‘5 9r (73%): 2921 m ,2
«0 W
I
3;
M
"ﬂm
4
3,
AVON
if
m“;
5
v
i?” 1.6 on = c ,_, cosoc + ed sino:
Also, using the more accurate N’ rather than L' in Eq. (1.22), we have
1
X :£
M&AE 150B Name:
Spring 2014
MIDTERM EXAM
Thursday, May 8, 2014
1) [35 points] Consider inviscid flow over an airfoil with chord c at = 0. The lower
surface is flat and the upper surface is given by
2 x
yu = t sin
c
for 0
x 1
c 4
,
2 x 1
1 x
yu = t
5.2
* 3
Since (l5 and r are always perpendicular (by inspection of the ﬁgure),
.
rdrzx? 1‘02
40 3 ‘——
_,
dV
4;: r2
—.
I
By symmetry, the resultant velocity due to the entire loop must be along the x—axis. Hence,
G =_[ d‘_\} 0059:[};I
4.9 Magpoem I; made:
M‘ +2 c
0mm: ———1 =V c2 jg mom: (I)
_ V 2 :20
2pm ,3 c
C
=— 1 e
E; 2 ( cos )
d: = 3 sine d9
2
(1+co'59) °“ .
9 «12WD A —+ A smnt?
K) ° sin6 E n ]
With the above, Eq‘ (1) becomes
= j” Ao(1_00529)d9 z I An(l cose) sine sin n9 d9
1
4.2 qw= — pm Vw2= w; (1.23)(50)2 =1533 N/m2
.
L W =0.44
2
(lg—w—
qu * (1533)(2)
From Fig. 4.5,
_)
4.3 r=cj Vds
§=<§ £355+§ 95’s
Dds 2d?
Dt
Hence, the second term in Eq. (1) becomes
{74?}: d—Y—Z—=0
i if 2
From the momentum equation,
m7
V =  l Vp (neglec
M&AE 150B
Spring 2014
HOMEWORK 6
Assigned:
Due:
Thursday, May 8
Thursday, May 15 (5 PM)
1) [10 points] (Anderson 4.9) Starting with eqns. (4.35) and (4.43), derive eqn. (4.62). The following
integrals may come in handy (in addition to the orthogonality of
M&AE 150B
Spring 2014
HOMEWORK #5
Assigned:
Due:
Thursday, May 1
Tuesday, May 6 (5 PM)
1) [10 points] (Anderson 4.6) The NACA 4412 airfoil has a mean camber line given by
2
x x
x
0.25 0.8 for 0 0.4
c c
c
z
=
2
c
x x
x
0.111 0.2 + 0.8 for 0.4 1.
c c
MAE 150B, Aerodynamics
Su16, X. Zhong
Homework No. 1
Due: Wednesday, June 29, 2016
Problem 1: Problem 1.2 of Andersons text book
Problem 2: Problem 1.3 of Andersons text book
Problem 3: Problem 1.4 of Andersons text book
Problem 4: Problem 1.5 of Anderson