Lecture
7
 Marine
Hydrodynamics
Lecture
7
Chapter
3
–
Ideal
Fluid
Flow
The
structure
of
Lecture
7
has
as
follows:
In
paragraph
3.0
we
introduce
the
concept
of
inviscid
ﬂuid
and
formulate
the
governing
equations
and
boundary
conditions
for
an
ideal
ﬂuid
ﬂow.
In
paragraph
3.1
we
introduce
the
concept
of
circulation
and
state
Kelvin’s
theorem
(a
conservation
law
for
angular
momentum).
In
paragraph
3.2
we
introduce
the
concept
of
vorticity.
⎧
Inviscid
Fluid
ν
=0
⎪
⎨
+
Ideal
Fluid
Flow
≡
⎪
Dρ
⎩
Incompressible
Flow
(
§
1.1)
or
∇·
±v
Dt
1
2.20  Marine Hydrodynamics, Spring 2005
2.20
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Governing
Equations
and
Boundary
Conditions
for
Ideal
Flow
•
Inviscid
Fluid,
Ideal
Flow
Recall
Reynolds
number
is
a
qualitative
measure
of
the
importance
of
viscous
forces
compared
to
inertia
forces,
UL
inertia
forces
R
e
=
=
ν
viscous
forces
For
many
marine
hydrodynamics
problems
studied
in
13.021
the
characteristic
lengths
and
velocities
are
L
≥
1m
and
U
≥
1m/s
respectively.
The
kinematic
viscosity
in
water
is
ν
water
=10
−
6
m
2
/s
leading
thus
to
typical
Reynolds
numbers
with
respect
to
U
and
L
in
the
order
of
R
e
=
≥
10
6
>>>
1
⇒
ν
1
viscous
forces
∼
±
0
R
e
inertia
forces
This
means
that
viscous
eﬀects
are
<<
compared
to
inertial
eﬀects
 or
conﬁned
within
very
small
regions.
In
other
words,
for
many
marine
hydrodynamics
prob
lems,
viscous
eﬀects
can
be
neglected
for
the
bulk
of
the
ﬂow.
Neglecting
viscous
eﬀects
is
equivalent
to
setting
the
kinematic
viscosity
ν
=
0,
but
ν
=0
⇔
inviscid
ﬂuid
Therefore,
for
the
typical
marine
hydrodynamics
problems
we
assume
incompressible
ﬂow
+
inviscid
ﬂuid
≡
ideal
ﬂuid
ﬂow
which
turns
out
to
be
a
good
approximation
for
many
problems.
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 Spring '05
 DickK.P.Yue

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