MAE 150A, Winter 2015
Assignment 1: Due Wednesday, January 14, 2015
H.P. Le
1. Problem 4.3 in Wilcoxs text.
2. Problem 4.15 in Wilcoxs text.
3. Problem 4.33 in Wilcoxs text.
4. Problem 5.29 in Wilcoxs text.
5. For the ow of an incompressible uid, the velo
MAE 150A
H.P. Le
HW4 Solutions
Problem 1 11-54
Problem: An arctic hut in the shape of a half-circular cylinder has radius R. A wind of velocity U
is blowing and creates a substantial aerodynamic force on the hut. This force is due to the difference
betwee
MAE 150A
H.P. Le
HW1 solutions
Problem 1
4.3 Chapter 4, Problem 3
Problem: For cylindrical coordinates, the acceleration in two-dimensional flow is
ar =
u ur
u2
ur
ur
+ ur
+
t
r
r
r
and
a =
u u
ur u
u
u
+ ur
+
+
t
r
r
r
Find the acceleration vector, a
MAE 150A, Winter 2009 J. D. Eldredge Homework 1, Due Friday, January 16
0. Read chapters 4 and 5 of Wilcox. 1. (Problem 4.1, Wilcox) Compute the acceleration vector for the following velocity vectors, where U , and a are constants. (a) u = U cos(x + at)i
MAE 150A, Winter 2015
Assignment 3: Due Wednesday, January 28, 2015
H.P. Le
1. Problem 11.5 in Wilcoxs text.
2. Problem 11.10 in Wilcoxs text.
3. Tornado damage to structures is often caused by an excess interior pressure on walls and
roofs when the atmos
MAE 150A, Winter 2007
J. D. Eldredge
Homework 7 (5 problems + 1 OPTIONAL), due Friday, March 6
1. Use Thwaites’ equation to compute θ(x) for a zero-pressure gradient ﬂow over a ﬂat plate. Compare this result to the Blasius solution.
2. Consider the decele
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University of California, L03 Angeles
Mechanical and Aerospace Engineering Department
MAE 150A
INTERMEDIATE FLUID MECHANICS
SECOND MIDTERM EXAM
D. Getsinger
Tuesday, November 20, 2012
Open‘to two pages (8 1/2” X 11”) of handwritten notes only
[ Problem
MAE 150A, Winter 2009 J. D. Eldredge Homework 2 (5 problems + 1 OPTIONAL), due Friday, January 23
1. Problem 4.23, Wilcox (4.24 in 2nd edition). 2. A vortex has a velocity distribution given by u = u e , where u = and and are constant. (a) Find the vortic
MAE 150A
H.P. Le
HW6 solutions
Problem1
Chapter 13, Problem 35
Problem: A semi-infinite viscous fluid is bounded by a flat porous plate at y = 0. At time t = 0, the
plate is impulsively set in motion at a constant velocity U in the x direction. At the sam
MAE 150A, Winter 2009
J. D. Eldredge
Homework 5 (4 problems + 2 OPTIONAL), due Friday, February 20
1. Problem 12.4, Wilcox
2. Problem 13.21, Wilcox.
3. Problem 13.23, Wilcox.
4. Two thin layers of viscous ﬂuids ﬂow down an inclined wall at angle β, as sho
MAE 150A, Winter 2015
Assignment 6: Due Wednesday, February 18, 2015
H.P. Le
1. Problem 13.35 in Wilcoxs text.
2. Problem 13.38 in Wilcoxs text.
3. A stepped bearing is shown in the gure below. The lower plate moves with respect to
the bearing sleeve at s
MAE 150A, Winter 2015
Assignment 5: Due Wednesday, February 11, 2015
H.P. Le
1. Problem 12.8 in Wilcoxs text.
2. Problem 13.27 in Wilcoxs text.
3. Problem 13.32 in Wilcoxs text.
4. Derive a nondimensional form of the Navier-Stokes equations without body f
MAE 150A
H.P. Le
HW2 solutions
Problem 1
5.46 Chapter 5, Problem 46
Problem: A baseball is traveling through air with speed U = 100 mph. The flow speeds at Points 2
and 3 are U2 = 40 mph and U3 = 10 mph. If the pressure difference between Points 3 and 4 i
MAE 150A, Winter 2015
Assignment 7: Due Monday, February 23, 2015
H.P. Le
1. Consider an approximation to the velocity prole for an incompressible at plate boundary
layer in the form of a third order polynomial:
u(x, y) = A3 y 3 + A2 y 2 + A1 y + A0
(a)
(
MAE 150A
H.P. Le
HW5 Solutions
Problem 1
12.8 Chapter 12, Problem 8
Problem: The exact solution for rigid-body rotation is ur = 0 and u = r, where is angular
velocity. Determine the streamfunction, (r, ). Show that no velocity potential, (r, ), exists and
MAE 150A, Winter 2015
Assignment 8: Due Wednesday, March 4, 2015
H.P. Le
1. Consider the adverse pressure gradient in a oweld that produces the velocity distribution
given by
U (x) = Uo 1
x
L
Compute the separation location using Thwaites method.
2. Prob
MAE 150A, Winter 2015
Assignment 9: Due Wednesday, March 11, 2015
H.P. Le
1. Problem 7.42 in Wilcoxs text
2. Problem 8.18 in Wilcoxs text
3. Problem 8.39 in Wilcoxs text
4. Problem 15.12 in Wilcoxs text
5. Problem 15.25 in Wilcoxs text
6. Problem 15.28 in
MAE 150A
H.P. Le
HW7 solutions
Problem 1
Assuming the 3rd order polynomial velocity prole for u(x, y):
y
u(x, y)
y
= A0 + A1
+ A2
U
2
+ A3
y
3
(a) Applying the appropriate BCs (need 4):
u(x, y = 0) = 0
u(x, y = ) = U
u
(x, y = ) = 0
y
2u
2u
(x, y = ) = 0
I would also accept conservation of energy.
Although derived from Euler's equations
(momentum conservation), Bernoulli also
represents a statement of mechanical energy
conservation.
MAE 150A
H.P. Le
HW8 solutions
Problem 1
U (x) = Uo 1
dU
U0
x
=
L
dx
L
The momentum thickness from the t:
2
0.45
= 6
U
=
x
5
U (x )dx
0
x/L
0.45L
Uo 1
L
= 0.075
Uo
x 6
L
1
0
1
x
L
6
x
L
5
x
L
d
1
Hence,
=
2 dU
x
= 0.075 1 1
dx
L
6
The separation locat
MAE 150A
H.P. Le
HW9 solutions
Problem 1
7.42 Chapter 7, Problem 42
Problem: With great care, laminar pipe flow can be realized for Reynolds number, ReD , as high as
5104 . For water with viscosity = 105 ft2 /sec flowing in a perfectly smooth pipe of diam
Turbulent ows
February 27, 2015
Turbulence
What do people say about turbulence?
Turbulence is the most important unsolved problem of
classical physics -Richard Feyman
I am an old man now, and when I die and go to heaven there
are two matters on which I
University of California, Los Angeles
Mechanical and Aerospace Engineering Department
MAE 150A
INTERMEDIATE FLUID MECHANICS
SECOND MIDTERM EXAM
H.P. Le
Wednesday, February 25, 2015
Open to two pages (8 1/2 x 11) of handwritten notes
Problem Score Maximum
University of California, Los Angeles
Mechanical and Aerospace Engineering Department
MAE 150A
INTERMEDIATE FLUID MECHANICS
FIRST MIDTERM EXAM
H.P. Le
Monday, February 2, 2015
Open to one page (8 1/2 x 11) of handwritten notes
Problem Score Maximum
1
10
1
MAE 150A
H.P. Le
HW3 solutions
Problem 1
11.5 Chapter 11, Problem 5
Problem: The streamfunction is (x, y) = x2 y 2 , where and are constants of dimensions T 1 .
(a) Compute the velocity components and locate all stagnation points.
(b) Determine the values
MAE 150A, Winter 2015
Assignment 2: Due Wednesday, January 21, 2015
H.P. Le
1. Problem 5.46 in Wilcoxs text.
2. Problem 5.49 in Wilcoxs text.
3. Problem 4.28 in Wilcoxs text.
4. Problem 11.26 (parts a and b only) in Wilcoxs text.
5. A tornado may be model
MAE 150A, Winter 2015
Assignment 4: Due Wednesday, February 4, 2015
H.P. Le
1. Problem 11.54 in Wilcoxs text.
2. Problem 11.62 in Wilcoxs text.
3. Problem 11.64 in Wilcoxs text.
4. Problem 11.78 in Wilcoxs text.
1
MAE 150A, Fall 2016
Kwitae Chong
Homework 5 (4 problems + 2 OPTIONAL), due Tuesday, November 8
1. Problem 12.6, Wilcox (5th edition)
2. Problem 13.30, Wilcox (5th edition)
3. Problem 13.32, Wilcox (5th edition)
4. Two thin layers of viscous fluids flow do
MAE 150A, Fall 2016
Kwitae Chong
Homework 4 (5 problems )
1. Problem 11.55, Wilcox (5th edition). Your answer should make sense when you set U = 0
(i.e. the force should depend on the dierence between internal pressure pi and outer pressure
p ).
2. Proble