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ME 330 Fluid Mechanics
Spring 2007
Department of Engineering
Western Kentucky University
CHAPTER 4 HW  Homework Solutions
Problem #’s 477C, 478, and 479, Due February 16, 2007
477C
Solution
(
a
)
False
: The statement is backwards, since the conservation laws are naturally
occurring in the system form.
(
b
)
False
: The RTT can be applied to any control volume, fixed, moving, or deforming.
(
c
)
True
: The RTT has an unsteady term and can be applied to unsteady problems.
(d)
True
: The extensive property
B
(or its intensive form
b
) in the RTT can be any
property of the fluid – scalar, vector, or even tensor.
478
Solution
For the case in which
B
sys
is the mass
m
of a system, we are to use the RTT
to derive the equation of conservation of mass for a control volume.
Analysis
The general form of the Reynolds transport theorem is given by
General form of the RTT
:
sys
r
CV
CS
dB
d
bd
bV ndA
dt
dt
ρρ
=+
⋅
∫∫
V
r
r
(1)
Setting
B
sys
=
m
means that
b
=
m
/
m
= 1. Plugging these and
dm
/
dt
= 0 into Eq. 1 yields
Conservation of mass for a CV
:
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This homework help was uploaded on 04/19/2008 for the course ME 330 taught by Professor An during the Spring '08 term at Western Kentucky University.
 Spring '08
 an

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