Problem 1.49
[Difficulty: 4]
Given:
Dimensions of soda can:
D = 66 mm, H = 110 mm
Find:
Measurement precision needed to allow volume to be estimated with an
uncertainty of ± 0.5 percent or less.
Solution:
Use the methods of Appendix F:
Computing equations:
1
2
2
22
HD
DH
4
uu
u
π
∀
∀=
⎡⎤
∂∀
∂∀
⎛⎞
=±
+
⎢⎥
⎜⎟
∀∂
⎝⎠
⎣⎦
Since
2
4
, then
2
D
H4
∂∀
∂
=
and
DH
D2
∂∀
∂
=
.
Letting
D
D
u
x
δ
= ±
and
H
H
u
x
= ±
, and substituting,
1
1
2
2
2
2
2
4H
D
4D
DH
2
u
DH 4 H
DH 2
D
H
D
xx
x
x
πδ
ππ
∀
⎛
⎞
⎛
⎞
+
+
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
Solving,
2
2
21
2
u(
)
H
D
x
δδ
∀
⎡
⎤
⎛⎞⎛
⎞
⎛
⎞⎛
⎞
=+
=
+
⎢
⎥
⎜⎟⎜
⎟
⎜
⎟⎜
⎟
⎝⎠⎝
⎠
⎝
⎠⎝
⎠
⎢
⎥
⎣
⎦
()
11
2
2
12
110mm
66mm
u
0.005
0.158 mm
() ()
x
∀
⎡
⎤
+
+
Check:
3
H
3
D
0.158 mm
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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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