Fluids
– Lecture 6
Notes
1. Control Volumes
2. Mass Conservation
3. Control Volume Applications
Reading: Anderson 2.3, 2.4
Control Volumes
In developing
the equations of aerodynamics we will invoke the firmly
established and time
tested physical laws:
Conservation of Mass
Conservation of Momentum
Conservation of Energy
Because
we
are not
dealing
with isolated point
masses, but
rather
a
continuous deformable
medium, we will require new
conceptual and mathematical techniques to
apply
these laws
correctly.
One
concept
is the
control volume
, which can be either
finite or
infinitesimal. Two
types of
control volumes can be employed:
1)
Volume
is fixed in space (Eulerian type).
Fluid can freely
pass through the volume’s
boundary.
2) Volume
is attached to
the ﬂuid (Lagrangian type). Volume is freely carried along with the
ﬂuid, and no
ﬂuid passes through its
boundary. This is essentially
the same as the freebody
concept
employed in solid mechanics.
V
V
Eulerian Control Volume
Lagrangian Control Volume
fixed in space
moving with fluid
Both
approaches
are
valid. Here
we
will
focus on the fixed control
volume.
Mass Conservation
Mass
ﬂow
Consider
a small patch of
the
surface
of the fixed,
permeable control
volume.
The patch
has
1
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area
A
, and
normal unit
vector
ˆ
n
. The plane of ﬂuid particles which are on the surface
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 Fall '05
 MarkDrela
 Dynamics, Thermodynamics, Derivative, Mass, Aerodynamics

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