Problem 3.67
[Difficulty: 3]
Given:
Block hinged and floating
Find:
SG of the wood
Solution:
Basic equation
dp
dh
ρ
g
⋅
=
Σ
M
z
0
=
Computing equations
F
R
p
c
A
⋅
=
y'
y
c
I
xx
Ay
c
⋅
+
=
Assumptions:
Static fluid;
ρ
= constant; p
atm
on other side; no friction in hinge
For incompressible fluid
p
ρ
g
⋅
h
⋅
=
where p is gage pressure and h is measured downwards
The force on the vertical section is the same as that on a rectangle of height d and width L
F
1
y’
F
2
Mg
y
x
Hence
F
1
p
c
A
⋅
=
ρ
g
⋅
y
c
⋅
A
⋅
=
ρ
g
⋅
d
2
⋅
d
⋅
L
⋅
=
ρ
g
⋅
L
⋅
d
2
⋅
2
=
The location of this force is
y'
y
c
I
xx
c
⋅
+
=
d
2
Ld
3
⋅
12
1
⋅
×
2
d
×
+
=
2
3
d
⋅
=
The force on the horizontal section is due to constant pressure, and is at the centroid
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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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