Problem *3.105
[Difficulty: 2]
F
B
W
H
= 60 cm
θ
h
= 5 cm
y
x
Given:
Data on river
Find:
Largest diameter of log that will be transported
Solution:
Basic equation
F
B
ρ
g
⋅
V
sub
⋅
=
and
Σ
F
y
0
=
Σ
F
y
0
=
F
B
W
−
=
where
F
B
ρ
g
⋅
V
sub
⋅
=
ρ
g
⋅
A
sub
⋅
L
⋅
=
WS
G
ρ
⋅
g
⋅
V
⋅
=
SG
ρ
⋅
g
⋅
A
⋅
L
⋅
=
From references (e.g. CRC Mathematics Handbook)
A
sub
R
2
2
θ
sin
θ
()
−
⋅
=
where R is the radius and
θ
is
the included angle
Hence
ρ
g
⋅
R
2
2
⋅
θ
sin
θ
−
⋅
L
⋅
SG
ρ
⋅
g
⋅
π
⋅
R
2
⋅
L
⋅
=
θ
sin
θ
−
2SG
⋅
π
⋅
=
2
0.8
×
π
×
=
This equation can be solved by manually iterating, or by using a good calculator, or by using Excel's Goal Seek
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 Fall '07
 Lear
 Fluid Mechanics

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