The Reynolds Transport Theorem
(Section 45,
Ç
engel and Cimbala)
Recall from Thermodynamics:
•
A
system
is a quantity of matter of fixed identity.
No mass can cross a system
boundary
.
•
A
control volume
is a region in space chosen for study.
Mass
can
cross a control
surface
(the surface of the control volume).
•
The fundamental conservation laws (conservation of mass, energy, and momentum)
apply directly to systems
.
•
However, in most fluid mechanics problems,
control volume analysis is preferred
over system analysis
(for the same reason that the Eulerian description is usually
preferred over the Lagrangian description).
•
Therefore, we need to
transform the conservation laws from a system to a control
volume
. This is accomplished with the
Reynolds transport theorem
(
RTT
).
There is a direct
analogy
between the transformation from Lagrangian to Eulerian
descriptions (for differential analysis using infinitesimally small fluid elements) and the
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 Fall '05
 CIMBALA
 Fluid Dynamics, Fluid Mechanics, Thermodynamics, Derivative, Reynolds Transport Theorem

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