Problem 4.45
[Difficulty: 2]
Outflow
CS
Given:
Data on airflow out of tank
Find:
Find rate of change of density of air in tank
Solution:
0
=
⋅
+
∂
∂
∫
∫
CS
CV
A
d
V
V
d
t
r
r
ρ
Basic equation
Assumptions:
1) Density in tank is uniform 2) Uniform flow 3) Air is an ideal gas
Hence
V
tank
d
ρ
tank
dt
⋅
ρ
exit
V
⋅
A
⋅
+
0
=
d
ρ
tank
dt
ρ
exit
V
⋅
A
⋅
V
tank
−
=
p
exit
V
⋅
A
⋅
R
air
T
exit
⋅
V
tank
⋅
−
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 Fall '07
 Lear
 Fluid Mechanics, Trigraph, 2 m, Texit ⋅ Vtank

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