EGN 3353C Fluid Mechanics
Lou Cattafesta
MAE Dept.
University of Florida
Lecture 13
Reynolds Transport Theorem
Æ
provides link between system and control volume
approaches
±
Recall that all laws of mechanics are written for
systems (Lagrangian description).
±
System
Æ
arbitrary quantity of mass of fixed
identity
±
In fluid dynamics, it is more convenient to
study a region in space, called a
control
volume (CV)
o
Mass may cross the boundary of the CV
o
Boundary of control volume is the
control surface (CS)
o
CV may deform and move, but many
practical problems involve a fixed, non
deformable CV.
(a) follow the fluid as it leaves
Æ
system approach
(b) consider CV as can boundary & mass crosses
boundary
Æ
CV approach
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View Full DocumentEGN 3353C Fluid Mechanics
Lou Cattafesta
MAE Dept.
University of Florida
Examples of System Laws
1.
Conservation of Mass:
0
system
dM
dt
=
where
system
system
syste
M
m
d
M
md
ρ
∀
=
=∀
∫
∫
2.
Conservation of Linear Momentum:
system
dP
F
dt
=
G
G
where
system
system
M
Vdm
Vd
P
∀
∀
=
=
∫∫
G
G
G
3.
Conservation of Angular Momentum:
system
dH
T
dt
=
G
G
where
( ) ( )
system
system
M
rVd
m
Vd
H
r
∀
×
=
=
×∀
G
G
G
G
G
4.
Conservation of Energy:
First Law of Thermodynamics
N
N
rate of work
rate of heat
done by system
added to system
system
dE
QW
dt
−=
±
±
where
N
N
N
2
internal
potential
energy/mass
kinetic
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 Spring '07
 Lear
 Fluid Dynamics, Fluid Mechanics, dt, 3353C Fluid Mechanics, EGN 3353C Fluid, MAE dept, Lou Cattafesta

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