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Hyd 4

The document discusses the stability of floating bodies, detailing key concepts such as righting and overturning moments, metacenter, and metacentric height. It includes sample problems related to ship stability and calculations for submerged depth and metacentric height for various scenarios. Practical problems are provided for practice, focusing on the stability of a barge and a wooden cone in water.

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116 views2 pages

Hyd 4

The document discusses the stability of floating bodies, detailing key concepts such as righting and overturning moments, metacenter, and metacentric height. It includes sample problems related to ship stability and calculations for submerged depth and metacentric height for various scenarios. Practical problems are provided for practice, focusing on the stability of a barge and a wooden cone in water.

Uploaded by

patriciamaycalumpong08
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Review Innovations CE Review for Apr 2024 – Hydraulics 4

Stability of Floating Bodies I


MBo = - approximate
V

θ = angle of tilting
v = volume of the wedge of immersion/emersion (m3)
s = horizontal distance between the centroids of v’s (m)
I = moment of inertia of an area which is the top view of the
body at the level of the liquid surface with respect to the axis
of tilting (m4)

B = width of the body (m).


D = draft or depth of flotation (m).
V = total volume submerged (m3).
G = center of gravity of the body in the upright position.
Bo = center of buoyancy of the body in the upright position.
Bo’ = center of buoyancy of the body in the tilted position.

Righting Moment

Overturning Moment

Sample Problems:

Situation 1
The center of gravity of a ship in the upright position is 11.5
m above the center of gravity of the portion below water, the
displacement being 16 MN. The ship tilts 30º causing the
center of buoyancy to shift sidewise 9.2 m.
1. Is the moment righting or overturning?
2. What is the magnitude of this moment?
M = metacenter; point of intersection between the buoyant
force and the tilted axis of the body which determines its
Situation 2
stability.
A rectangular scow 9 m wide, 15 m long and 3.6 m high
MG = metacentric height (m); distance between the
weighs 3304kN.
metacenter and the center of gravity of the body which
3. What is the draft in sea water weighing 10.20 kN/m3?
measures its stability.
4. What is the metacentric height if its center of gravity is
2.7 m above the bottom?
For rectangular sections:
5. If the scow tilts until one side is just at the point of
B2 
MBo = 1 + 0.5tan2θ submergence, determine the righting couple.
12D  

For other sections:


vs
MBo = - exact
Vsinθ
Manila/Cebu/Baguio FB: @ReviewInnovationsOfficial Davao FB: Review Innovations Davao Branch
 (02) 8735-9161 0919-227-9194  (082) 221-1121 0930-256-0998
Review Innovations CE Review for Apr 2024 – Hydraulics 4
Situation 3
It is desired to float in fresh water a wooden cone, 18 cm in
diameter and 25 cm high, with the apex downward. If the sg
of the cone is 0.60:
6. Compute the submerged depth.
7. Compute the distance of the metacenter from the center
of buoyancy.
8. Locate the metacenter from the center of gravity.

Problem for Practice:

Situation 4
The waterline section of a 1500-kN barge is as shown. Its
center of gravity is 1.5 m above the center of buoyancy.
9. Compute the initial metacentric height against rolling.
(2.93 m)
10. Compute the initial metacentric height against pitching.
(26.32 m)

Manila/Cebu/Baguio FB: @ReviewInnovationsOfficial Davao FB: Review Innovations Davao Branch


 (02) 8735-9161 0919-227-9194  (082) 221-1121 0930-256-0998

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