±±±±
D
EPARTMENT OF
O
CEAN
E
NGINEERING
M
ASSACHUSETTS
I
NSTITUTE OF
T
ECHNOLOGY
2.20
Marine Hydrodynamics
SAMPLE
FINAL EXAM
THREE HOURS
CLOSED BOOKS
INSTRUCTIONS:
For the problems in section A, fill in the required answers where indicated by ______________, (or in the
provided space). When a list of options, [ . . . ] [ . . . ] [ . . . ], is provided select (by circling) all (none, one or
more of) the options which apply. For problems in section B, write your solutions in the exam book provided.
Unless otherwise indicated, use gravitational acceleration
g
=
s
m
10
2
, water density
=
ρ
10
3
kg
m
3
, and
2
−
2
kinematic viscosity
=
ν
10
−
6
m
s
; and air density
=
ρ
kg
1
m
3
, and kinematic viscosity
=
ν
10
5
m
s
. Give all
your numerical results in SI (
s
,
m
,
kg
) units. For numerical answers, you MUST give also the proper units (e.g.,
m
5
2
s
not 5).
There are a large number of problems and each individual answer can only be worth that many points, do NOT
spend a disproportionate amount of time on any one problem.
YOUR NAME:
If you want us to post your course grade
so that you can know it next week, please provide a
nontrivial alphanumeric code here (don’t forget your code):
2.20  SAMPLE
FINAL EXAM
Page 1
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SECTION A [35%]
A1. A 2D point vortex of circulation
Γ
is placed at a point A (1, 1) in a
corner created by the two walls x = 0 and y = 0. The horizontal force
on the vortex (in terms of
ρ
and
Γ
) is
F
= _____________________
Neglecting gravity, the pressure difference between the two points
O(0,0) and B(1,0) is:
(
P
O
−
P
B
)/
ρ
=_______________________
A2. A thin square plate (density
ρ
s
= 2
ρ
) of dimension 1cm
×
1cm and thickness 1mm is released in water
from rest. If the plate falls parallel to the square side (figure (a) below), its terminal velocity is
U
p
= ____________________________________ (use friction coefficient
C
f
= 1.328
R
L
1/2
for laminar,
and
C
f
= 0.0725
R
L
1/5
for turbulent boundary layer).
A teardropshaped streamlined body has the same length (1cm) and total wetted area (
S
=2cm
2
) as the
flat plate above, and has a weight in water (weight minus buoyancy)
W
=1.5·10
3
N. When dropped from
rest vertically (figure (b) below), the terminal velocity of this body is found to be
U
b
= 0.25m/s. Based
on this information, the form drag (total drag minus friction drag) of the teardropshaped body can be
estimated to be
D
= _______________________.
A3. A 2D circle has an unsteady horizontal velocity
U(t)
in an infinite fluid. The fluid itself has a uniform
horizontal acceleration (to the right) of
A
= 1m/s
2
. At some instant t =
τ
, the total horizontal
&
hydrodynamic force on the circle is zero. Assuming potential flow, at t =
τ
,
U
(
τ
)
= ____________m/s
2
to the [right] [left].
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 Spring '05
 DickK.P.Yue
 Fluid Dynamics

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