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Problem 3.13
[Difficulty: 3]
Given:
Model behavior of seawater by assuming constant bulk modulus
Find:
The percent deviations in (a) density and (b) pressure at depth h = 6.5
mi, as compared to values assuming constant density.
Plot results over the range of 0 mi  7 mi.
Solution:
From Table A.2, App. A:
SG
o
1.025
=
E
v
2.42 GPa
⋅
3.51
10
5
×
psi
⋅
=
=
h
6.5 mi
⋅
=
Governing Equations:
dp
dh
ρ
g
⋅
=
(Hydrostatic Pressure  h is positive downwards)
(Definition of Bulk Modulus)
E
v
dp
d
ρ
ρ
=
Then
dp
ρ
g
⋅
dh
⋅
=
E
v
d
ρ
ρ
⋅
=
or
d
ρ
ρ
2
g
E
v
dh
=
Now if we integrate:
ρ
o
ρ
ρ
1
ρ
2
⌠
⎮
⎮
⎮
⌡
d
0
h
h
g
E
v
⌠
⎮
⎮
⌡
d
=
After integrating:
ρρ
o
−
o
⋅
gh
⋅
E
v
=
Therefore:
ρ
E
v
ρ
o
⋅
E
v
ρ
o
g
⋅
h
⋅
−
=
and
ρ
ρ
o
1
1
ρ
o
g
⋅
h
⋅
E
v
−
=
Δρ
ρ
o
o
−
ρ
o
=
ρ
ρ
o
1
−
=
1
1
ρ
o
g
⋅
h
⋅
E
v
−
1
−
=
11
ρ
o
g
⋅
h
⋅
E
v
−
⎛
⎜
⎝
⎞
⎟
⎠
−
1
ρ
o
g
⋅
h
⋅
E
v
−
=
ρ
o
g
⋅
h
⋅
E
v
1
ρ
o
g
⋅
h
⋅
E
v
−
=
Δρ
ρ
o
ρ
o
g
⋅
h
⋅
E
v
1
ρ
o
g
⋅
h
⋅
E
v
−
=
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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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