Problem *3.107
[Difficulty: 4]
Given:
Cylindrical timber, D = 1 ft and L = 15 ft, is weighted on the lower end so that is floats vertically with 10 ft
submerged in sea water. When displaced vertically from equilibrium, the timber oscillates in a vertical direction
upon release.
Find:
Estimate the frequency of the oscillation. Neglect viscous forces or water motion.
Solution:
We will apply the hydrostatics equations to this system.
Governing Equations:
F
buoy
ρ
g
⋅
V
d
⋅
=
(Buoyant force is equal to weight of displaced fluid)
d =
10 ft
(Equilibrium
Depth)
D
= 1 ft
L
Assumptions:
(1) Static fluid
(2) Incompressible fluid
(3) Atmospheric pressure acts everywhere
(4) Viscous effects and water motion are negligible.
At equilibrium:
Σ
F
y
F
buoy
Mg
⋅
−
=
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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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