EGN 3353C Fluid Mechanics
Lou Cattafesta
MAE Dept.
University of Florida
Lecture 22
We will now apply the Reynolds Transport Theorem (RTT) to the Conservation of Angular Momentum
We will restrict our analysis to an inertial CV (CV in a non-accelerating 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
ρ
ρ
=
∀ +
⋅
∫
∫
G
G
For angular momentum,
r
B
V
H
m
=
=
×
G
G
G
so
b
r
V
=
×
G
G
and so
N
N
N
(
)
(
)
sum of all external
moments acting on CV
rate of change of
net flux of a
angular momentum in CV
= 0 for steady flow
r
r V
r V
CV
CS
system
r
CV
CS
dH
d
b d
b
V
ndA
dt
dt
d
M
r
V
d
r
V
V
ndA
dt
ρ
ρ
ρ
ρ
×
×
=
∀ +
⋅
=
×
∀ +
×
⋅
∫
∫
∑
∫
∫
G
G
G
G
G
G
G
G
G
G
G
G
G
G
±²²³²²´
ngular
momentum out of CV
±²²²³²²²´
o
We need to worry about external moments due to body forces, pressure, shear forces, and any other
external moments.
Simplifications
of
(
)
(
)
r
CV
CS
d
M
r
V
d
r
V
V
ndA
dt
ρ
ρ
=
×
∀ +
×
⋅
∑
∫
∫
G
G
G
G
G
G
G
o
For a fixed CV
, the relative velocity
CS
r
V
V
V
=
−
G
G
G
V
=
G

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