Problem 3.43
[Difficulty: 3]
Given:
Data on isothermal atmosphere
Find:
Elevation changes for 3% pressure change and 5% density change; plot of pressure and density versus elevation
Solution:
Assumptions:
Static, isothermal fluid,; g = constant; ideal gas behavior
Basic equations
dp
dz
ρ
−
g
⋅
=
and
p
ρ
R
⋅
T
⋅
=
Then
dp
dz
ρ
−
g
⋅
=
pg
⋅
R
air
T
⋅
−
=
and
dp
p
g
R
air
T
⋅
−
dz
⋅
=
Integrating
Δ
z
R
air
T
0
⋅
g
−
ln
p
2
p
1
⎛
⎜
⎝
⎞
⎟
⎠
⋅
=
where
TT
0
=
For an ideal gas with T constant
p
2
p
1
ρ
2
R
air
⋅
T
⋅
ρ
1
R
air
⋅
T
⋅
=
ρ
2
ρ
1
=
so
Δ
z
R
air
T
0
⋅
g
−
ln
ρ
2
ρ
1
⎛
⎜
⎝
⎞
⎟
⎠
⋅
=
C
−
ln
ρ
2
ρ
1
⎛
⎜
⎝
⎞
⎟
⎠
⋅
=
(1)
From Table A.6
R
air
287
Nm
⋅
kg K
⋅
⋅
=
Evaluating
C
R
air
T
0
⋅
g
=
287
⋅
kg K
⋅
⋅
30
273
+
()
×
K
⋅
1
9.81
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 Fall '07
 Lear
 Fluid Mechanics

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