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Problem 1.41
[Difficulty: 2]
Given:
Air in hot air balloon
Hg
mm
1
759
±
=
p
C
1
60
°
±
=
T
Find:
(a) Air density using ideal gas equation of state
(b) Estimate of uncertainty in calculated value
Solution:
We will apply uncertainty concepts.
Governing Equations:
ρ
p
RT
⋅
=
(Ideal gas equation of state)
2
1
2
1
1
1
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
±
=
L
x
R
u
x
R
R
x
u
(Propagation of Uncertainties)
We can express density as:
ρ
101 10
3
⋅
N
m
2
×
kg K
⋅
287 N
⋅
m
⋅
×
1
333 K
⋅
×
1.06
kg
m
3
=
=
ρ
1.06
kg
m
3
=
2
1
2
2
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
±
=
T
p
u
T
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Unformatted text preview: T u p p u ρ So the uncertainty in the density is: 1 1 = = ∂ ∂ RT RT p p Solving each term separately: u p 1 759 0.1318% ⋅ = = 1 2 − = − = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = ∂ ∂ RT p RT p T T T u T 1 333 0.3003% ⋅ = = ( ) ( ) [ ] ( ) ( ) [ ] 2 1 2 2 2 1 2 2 % 3003 . % 1318 . − + ± = − + ± = T p u u u Therefore: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × ± ± = − 3 3 m kg 10 47 . 3 % 328 . u...
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.
 Fall '07
 Lear
 Fluid Mechanics

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