EGN 3353C Fluid Mechanics
Lou Cattafesta
MAE Dept.
University of Florida
Chapter 6:
MOMENTUM ANALYSIS OF FLOW SYSTEMS
Lecture 19
±
We will now apply the Reynolds Transport Theorem (RTT) to the Conservation of Linear Momentum
±
We will restrict our analysis to an inertial CV (CV in a nonaccelerating reference frame)
±
Recall we derived the RTT for the general case of a CV that can move and deform
r
system
CV
CS
dB
d
bd
bV
ndA
dt
dt
ρρ
=∀
+
⋅
∫∫
G
G
±
For momentum,
B
Pm
V
=
=
GG
so
b
V
=
G
and Newton’s second law becomes
NN
rate of change of
net flux of
momentum in CV
momentum out of CV
= 0 for steady flow
r
r
CV
C
VV
CV
CS
system
S
dP
d
bd
b V ndA
dt
dt
d
FV
d
V
V
n
d
A
dt
+
⋅
+
⋅
∑
∫
∫
G
G
G
±²³²´
±²²³
G
G
G
²²´
±
surface
body
F
F
F
+
=
∑
∑∑
G
G
G
o
only body force we will consider in this course is gravitational
grav
CV
F
gd
ρ
=
∀
∫
G
G
o
surface forces
Æ
pressure and shear
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View Full DocumentEGN 3353C Fluid Mechanics
Lou Cattafesta
MAE Dept.
University of Florida
±
pressure
PA
F
d
= −
∫
G
G
(already considered this in fluid statics)
•
We only consider the net pressure forces on a CV
•
Consider the CV shown at left
o
If only a uniform pressure (e.g.,
atm
P
) acts on all sides
(which acts in the – normal direction)
±
pressure forces cancel
o
In general, only need to consider the gage pressure
1
atm
gage
PP
P
−
=
o
Note:
Subsonic flows have
exit
atm
=
!
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 Spring '07
 Lear
 Fluid Mechanics, Force, 3353C Fluid Mechanics, EGN 3353C Fluid, MAE dept, Lou Cattafesta

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