Problem *3.108
[Difficulty: 3]
H
= 8 ft
h
= 7 ft
θ
= 60
o
Floating
Sinking
Given:
Data on boat
Find:
Effective density of water/air bubble mix if boat sinks
Solution:
Basic equations
F
B
ρ
g
⋅
V
⋅
=
and
Σ
F
y
0
=
We can apply the sum of forces for the "floating" free body
Σ
F
y
0
=
F
B
W
−
=
where
F
B
SG
sea
ρ
⋅
g
⋅
V
subfloat
⋅
=
V
subfloat
1
2
h
⋅
2 h
⋅
tan
θ
⋅
⎛
⎜
⎝
⎞
⎠
⋅
L
⋅
=
L h
2
⋅
tan
θ
( )
=
SG
sea
1.024
=
(Table A.2)
Hence
W
SG
sea
ρ
⋅
g
⋅
L
⋅
h
2
⋅
tan
θ
( )
=
(1)
We can apply the sum of forces for the "sinking" free body
Σ
F
y
0
=
F
B
W
−
=
where
F
B
SG
mix
ρ
⋅
g
⋅
V
sub
⋅
=
V
subsink
1
2
H
⋅
2 H
⋅
tan
θ
⋅
⎛
⎜
⎝
⎞
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 Fall '07
 Lear
 Fluid Mechanics

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