ME220A: Fundamentals of Fluid Mechanics
Fall 2011
Course goals:
to develop a coherent picture of the fluid dynamics theory via physically
motivated examples and to introduce students to both the classical as well
as modern results
The topics to be covered
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Midterm Exam 2
(9:00-10:15 am on November 21, 2011)
Problem 1 (30 pts). A ow is described by the velocity eld, V = ay 2 + b , where
i
j
1 1
a = 1 m s and b = 2 m/s. Coordinates are measured in meters. Please answer the
following:
(a:5) Is the ow
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Midterm Exam 1
(9:00-10:15 am on October 24, 2011)
Problem 1 (60 pts). A solid cone of uniform density c and height H acts to plug a hole
at the base of a container as depicted in gure 1. The cone protrudes a distance h from
the bottom of the co
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Homework 5
(due at 5:00 pm on November 14, 2011)
Please complete the following problems (11 total).
Chapter 5: Problems 5.38, 5.43, 5.47, 5.51, 5.59, 5.66, 5.76, 5.91, 5.110, 5.113, 5.125
Please remember that these problems typically require a
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Homework 4
(due at 5:00 pm on November 7, 2011)
Please complete the following problems (11 total).
Chapter 4: Problems 4.23, 4.29, 4.36
Chapter 5: Problems 5.17, 5.23, 5.26, 5.98
Chapter 6: Problems 6.9, 6.16, 6.18, 6.34
Although spread over th
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Homework 3
(due at 12:30 pm on November 14, 2011)
Problem 1. Using the method of matched asymptotic expansion, solve
y y + y = 0, with y (0) = 0, y (1) = 1,
1.
Compare with the exact solution.
Problem 2. Develop a 2D version of the Kolmogorov-Obu
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Homework 3
(due at 5:00 pm on October 31, 2011)
Please complete the following problems (10 total).
Chapter 3: Problems 3.2, 3.6, 3.14, 3.22, 3.5, 3.9, 3.17, 3.24, 3.32, 3.37
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Homework 2
(due at 12:30 pm on October 31, 2011)
Problem 1. Using the ideas from kinetic theory of gases, estimate dynamic viscosity of
the ideal gas in terms of (1) mean free path, number of molecules per unit volume,
mass of a molecule, mean ve
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Homework 2
(due at 5:00 pm on October 17, 2011)
Please complete the following problems (11 total).
Chapter 2: Problems 2.2, 2.5, 2.18, 2.34, 2.36, 2.58, 2.72, 2.88, 2.94, 2.99, 2.104
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Homework 1
(due at 12:30 pm on October 17, 2011)
Problem 1. Prove the following vector identities
( a)
(b)
(a b) c = a (b c),
t (u v ) = u(t v ) v (t u),
(c)
(u v ) = (v
)u (u
)v + u(
v) v(
(d)
(u v ) = ( u
)v + ( v
)u + u (
u),
v) + v (
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Homework 4 / Take-home nal exam
(due at 12:30 pm on November 30, 2011)
Problem 1. Find the pressure distribution in the slipper bearing assuming that the uid
motion is in the Stokes regime (cf. gure 1).
z
Solid
z=h(x)
pa
pa
Fluid
0
x
L
U
Figure 1
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Final Exam
(8:00-11:00 am on December 7, 2011)
Problem 1 (30 pts). An inverted cylindrical container of diameter d and height l is initially lled with air heated to a temperature TO (this temperature is above that of the
ambient temperature Tamb