1 Basic Free Surface Effects WE 1
Transcript of 1 Basic Free Surface Effects WE 1
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MASTER COPY – No Unauthorised Copying Property of Warsash Maritime Acade
© Southampton Solent University 2007
Worked Example 1: Pool
• A box shaped vessel has a length of 50 metres, a beam
of 8 metres and a lightship draft of 2 metres. Thelightship KG is 3 metres.
•The vessel has a swimming pool, with the base of the
pool 4 metres above the keel. The pool is 15 metres
long, and 8 metres wide.
•Determine the effective GM of the vessel if the pool is
filled to a depth of 1 metre with fresh water.
.
Worked Example 1: Pool
• The lightship displacement can be found from the
geometry, draft and water density:
tonnes8201.0252850
∆=ρLBT
∆=ρ×
=×××
×
∇
.
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MASTER COPY – No Unauthorised Copying Property of Warsash Maritime Acade
© Southampton Solent University 2007
Worked Example 1: Pool
• To start with, we treat the fluid as a solid cargo. The
process of calculation is identical to loading a solidcargo:
tonnes120=1.000×1×8×15=MassCargo
metres5.4=2
1+4=KGCargo
2
DepthFluid+KeelAboveFluidOf Base=KGCargo
.
Worked Example 1: Pool
• A loading table can be used to find the solid KG of the
vessel:
24603820Lightship
3000940Totals
5404.5120Pool Water
MomentKGMassItem
m19.3=940
3000=
MassTotal
MomentTotal=KGSolid
.
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© Southampton Solent University 2007
Worked Example 1: Pool
• The draft, BM,KB and GM can be found in the loaded
(solid) condition:
m2921.025850
940T
ρLB
∆T
.=××
=
×=
metres1512
292
2
T=KB .
.
== metres332292850
12
850I
=BM
3
.
.
=××
×
=∇
metres0.283.19-2.331.15GM
KG-BM+KB=GM
=+=
.
Worked Example 1: Pool
• The free surface effect can now be calculated:
metres68.0=1×940
1.000×12
8×15
=GMInLoss
n×∆
ρ×I=GMInLoss
2
3
2
F/SF/S
metres-0.40=0.68-0.28=GMFluid
GMInLoss-GMSolid=GMFluid
.
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MASTER COPY – No Unauthorised Copying Property of Warsash Maritime Acade
© Southampton Solent University 2007
Worked Example 1: Pool
• Clearly the vessel is dangerously unstable. Free surface
effect is strongly influenced by the beam of the freesurface. Reducing the beam by adding longitudinal
watertight baffles in the fluid. This is modelled by the n
value (not the tank length and beam).
metres17.0=2×940
1.000×12
8×15
=GMInLoss
n×∆
ρ×I=GMInLoss
2
3
2
F/SF/S
metres11.0=0.17-0.28=GMFluidGMInLoss-GMSolid=GMFluid
.