vector
Fluids
– Lecture 7
Notes
1. Momentum Flow
2. Momentum Conservation
Reading: Anderson 2.5
Momentum Flow
Before
we
can apply
the principle of momentum conservation to
a
fixed permeable control
volume, we must
first
examine the effect
of ﬂow through its surface. When material ﬂows
through the surface, it
carries not
only
mass, but
momentum as well. The
momentum
ﬂow
can be
described as
−→
−→
momentum ﬂow = (mass ﬂow)
×
(momentum
/
mass)
where
the
mass ﬂow
was defined earlier, and the momentum/mass is simply
the velocity
vector
vector
V
. Therefore
−→
�
�
˙
vector
vector
n
A
vector
V
momentum ﬂow =
m V
=
ρ
V
·
ˆ
V
=
ρ V
n
A
vector
vector
n
as
before.
Note
that
while
mass
ﬂow
is
a
scalar,
the
momentum
ﬂow
is
a
where
V
n
=
V
·
ˆ
vector, and points in the same direction as
vector
V
. The momentum ﬂux
vector
is defined simply
as the
momentum ﬂow per
area.
−→
momentum ﬂux
=
ρ V
n
V
A
n
^
m
.
m
.
V
ρ
V
Momentum
Conservation
Newton’s
second law
states that
during
a
short
time interval
dt
, the impulse of
a
force
vector
F
P
applied
to some
affected mass, will produce a
momentum change
d
vector
a
in that
affected mass.
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 Fall '05
 MarkDrela
 Force, Momentum, Momentum Conservation, integral momentum equation

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