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Problem 3.87
[Difficulty: 4]
Given:
Canoe, modeled as a right semicircular cylindrical shell, floats in water of depth d. The shell has outer radius R and leng
R
1.2 ft
⋅
=
L1
7
f
t
⋅
=
d1
f
t
⋅
=
Find:
(a) General expression for the maximum total mass that can be floated, as a function of depth,
(b) evaluate for the given conditions
(c) plot for range of water depth between 0 and R.
Solution:
We will apply the hydrostatics equations to this system.
Governing Equations:
dp
dy
ρ
g
⋅
=
(Hydrostatic Pressure  y is positive downwards from
free surface)
F
v
A
y
p
⌠
⎮
⎮
⌡
d
=
(Vertical Hydrostatic Force)
Assumptions:
(1) Static fluid
(2) Incompressible fluid
(3) Atmospheric pressure acts on free surface of the liquid.
dF
y
θ
d
θ
max
y is a function of
θ
for a given depth d:
y
d
R
R cos
θ
()
⋅
−
−
=
dR
−
R cos
θ
⋅
+
=
The maximum value of
θ
:
θ
max
acos
Rd
−
R
⎡
⎣
⎤
⎦
=
A freebody diagram of the canoe gives:
Σ
F
y
0
=
Mg
⋅
F
v
−
=
where
F
v
is the vertical force of the water on the canoe.
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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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