Lecture 25: CV analysis of mass and momentum conservation I
3/24/2008
ME203002/004
Objectives:
1.
Control volume analysis – mass conservation
()
cv
cs
dV
V
n dA
t
Why there is a minus sign? What is the meaning of A,
Vn
?
2.
Linear momentum conservation
Dt
D
sys
V
d
V
=
t
.
.
V
C
V
d
V
+
.
.
S
C
V
(
V
·
n
)
d
=
on
contents
F
a. When is this equation valid?
b. When we solve a problem, we always write down the three(x, y & z)
Components of this vector equation, please try to write them down.
c. What is the meaning of
.
.
S
C
V
(
V
·
n
)
d
?
“Momentum transport
through control surfaces
because of flow
”
1
2
3
Need to understand ((
V
.
n
)
d
)’s meaning and calculation
d. What do we mean by
F
oncontent
?
1.
only externally force matters
2 .
Body force gravity
Acting on fluids
Normal force: pressure
Surface force
F
oncontents
Shear force: shear
Body force.
..
Acting on solid
Reaction force
3.
What is the general procedure of using C.V. analysis (7 steps)
define coordinate system: has to be inertia system
draw schematics, list assumptions (may need to introduce more assumption
during problem solving)
define CV:
o
label transport process across control surfaces
o
label surface normal direction
o
label force acting on contents of the CV (necessary only for momentum
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 Spring '08
 JimQiao
 Force, 15 cm, 0.2 M, 1 m/s, 5 m/s, 10 ft

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