314. In Figure 3.14 we have illustrated a crosssectional view of a barge loaded with stones.
The
barge has sprung a lead as indicated, and the volumetric flow rate of the leak is given by
o
leak flow rate
(
)
d
i
C
A
g h
h
=
−
Here
is a discharge coefficient equal to 0.6,
d
C
o
A
is the area of the hole through which the water
Figure 3.14
Leaking barge
is leaking,
h
is the height of the external water surface above the bottom of the barge, and
h
is the
internal height of the water above the bottom of the barge.
The initial conditions for this problem
are
i
I.C.
o
,
0 ,
i
h
h
h
t
=
=
0
=
and you are asked to determine when the barge will sink.
The length of the barge is
L
and the
space available for water inside the barge is
HwL
ε
.
Here
ε
is usually referred to as the void
fraction and for this particular load of stones
0.35
ε =
.
In order to solve this problem you will need to make use of the fact that the buoyancy force
acting on the barge is
buoyancy force
(
)
gh wL
=
ρ
where
is the density of water.
This buoyancy force is equal and opposite to the gravitational
force acting on the barge, and this is given by
ρ
gravitational force
mg
=
Here
m
represents the mass of the barge, the stones, and the water that has leaked into the barge.
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 Winter '10
 B.G.Higgins
 Force, Boundary value problem, Mass flow rate, Barge

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