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
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 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
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
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 #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
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
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
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
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
’ 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 :£
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
MAE150B: Aerodynamics
Spring 2009, F. P. Tsai
Homework No. 4
Due Tuesday, May 12, 2009 Put your name and UID on EACH page of your homework to make sure they will be properly credited. 1. For the symmetric airfoil described in Problem 4.5 on page 388 of Te
MAE150B: Aerodynamics
Spring 2009, F. P. Tsai
Homework No. 3
Due Tuesday, April 21, 2009 Put your name and UID on EACH page of your homework to make sure they will be properly credited. 1. 2. 3. Problem 3.17 on page 292 of Textbook Problem 4.5 on page 388
MAE150B: Aerodynamics
Spring 2009, F. P. Tsai
Homework No. 2
Due Thursday, April 16,2009 Put your name and UID on EACH page of your homework to make sure they will be properly credited. 1. In a 2D planar flow of an incompressible fluid, the xcomponent o