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RecallRecall
[ ]nF RfC = [ ]nR FfC =
if the parameters on the right hand side have the same values for twogeometrically similar but different sized bodies, the flow pattern will bethe same for each.
[ ]nnT FRfC ,=
These Equations state that
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Ship SimilaritiesShip Similarities
Types of SimilaritiesTypes of Similarities
1. Geometrical Similarities1. Geometrical Similarities
2.2. KinematicKinematic SimilaritiesSimilarities
3. Kinetic Similarities3. Kinetic Similarities
Length, Area, VolumeLength, Area, Volume
Position, Velocity,Position, Velocity,AccelerationAcceleration
Forces, MomentsForces, Moments
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31
====
m
s
m
s
m
s
m
s
m
s
SS
DD
BB
LL
1. Geometrical Similarities1. Geometrical Similarities
Preserved dimension ratios
Preserved Coefficients
..........PmPsBmBs CCCC ==
S
Object
m
Object model
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Object could take any shape
Father and son Mother and daughter
Geometrically Similar but different scale
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GeometricallySimilarb
utdifferents
cale
OtherExa
mples
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Geometrically Similar but different scale
More Examples ..
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Ls
Ship
Lm
Model
31
====
m
s
m
s
m
s
m
s
m
s
SS
DD
BB
LL
..........PmPsBmBs CCCC ==
Geometric SimilaritiesGeometric Similarities
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10 m
1 m
Model
Example (1)Example (1) Ship ParticularsLs = 10.0 mBs = 3.0 mCBs =0.55Ss =27.6 m
2
Vols = 9.9 m3
Find model particulars
Ship
Fire rescue boat
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Ls
Ship
Lm
Model
m
s
m
s
BB
LL =
55.0== BmBs CCShip and boat are geometrically SimilarShip and boat are geometrically Similar
31
=
m
s
m
s
L
L
mB3
110 = mBm 3.0=
Similarly mDm 06.0=
Also,m
s
m
s
S
S
L
L =
mS
6.27
1
10= 2276.0 mSm =
31
9.9
1
10
=
m
33109.9 mxm
=
And,
Solu
tion
Solu
tion
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Ls
Lm
Ship
Model
2.2. KinematicKinematic SimilaritiesSimilarities
s
s
ns gL
VF =
m
mnm
gL
VF =
nmns FF =
=
m
m
s
s
gL
V
gL
V
m
s
m
s
L
L
V
V=
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Ls
Lm
Ship
Model
2.2. KinematicKinematic SimilaritiesSimilarities
s
sssns LVR
=
m
mmmnm
LVR
=
nmns RR =
m
mmm
s
sss LVLV
=
s
m
m
s
L
L
V
V=
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10 m
Ship
1 m
Model
Example (2)Example (2)Ship Particulars
Ls = 10.0 mBs = 3.0 mDs =0.60 mCBs =0.55
Ss =27.6 m2
Vols = 9.9 m3
Vs = 12 knots
Find model speed if the ship and model are
running at the sameFroudenumbersi.e. kinematically similar
Fire rescue boatVs = 12 knots
Vm
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Ship Particulars
Ls = 10.0 mBs = 3.0 mCBs =0.55Ss =27.6 m
2
Vols = 9.9 m3
Vs = 12 knots10 m
Ship
Fire rescue boatVs = 12 knots
1 m
ModelVm
nmns FF =
=
m
m
s
s
gL
V
gL
V
=
1*81.910*81.912 mV
knotsVm 79.3=
SolutionSolution
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1 m
Model
Example (2)Example (2)
Find model speed if the ship and model are
running at the sameReynoldsnumberi.e. kinematically similar
10 m
Ship
Ship Particulars
Ls = 10.0 mBs = 3.0 mCBs =0.55Ss =27.6 m
2
Vols = 9.9 m3
Vs = 12 knots
Fire rescue boatVs = 12 knots
Vm
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SolutionSolutionShip Particulars
Ls = 10.0 mBs = 3.0 mCBs =0.55Ss =27.6 m
2
Vols = 9.9 m3
Vs = 12 knots10 m
Ship
Vs = 12 knots
1 m
Model
Vmnmns RR =m
mmm
s
sss LVLV
=
mmss LVLV = 1*10*12 mV=
knotsVm 120=
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Case 1Case 1
Ls
Lm
Geometrically SimilarGeometrically Similar
nmns FF =
RmRs CC=
Hence,Hence,
Also,Also,
m
s
m
s
L
L
V
V
=2
2
2
2
m
s
m
s
L
L
S
S=
kinematicallykinematically SimilarSimilar
Find the ratioFind the ratio RRRsRs// RRRmRm
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Case 1 (Cont.)Case 1 (Cont.)
Ls
Lm
Rmmmm
Rssss
Rm
Rs
CVS
CVS
R
R2
2
212
1
=
2
2
mmm
sss
Rm
Rs
VS
VS
R
R
=
m
s
m
s
m
s
Rm
Rs
L
L
L
L
R
R2
2
=
3
3
m
s
m
s
Rm
Rs
L
L
R
R
=
m
s
m
s
Rm
Rs
R
R
=
m
s
Rm
Rs
R
R
=
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Case 2Case 2 Geometrically SimilarGeometrically Similar
nmns RR =
FmFs CC=
Hence,Hence,
Also,Also,
s
m
m
s
L
L
V
V
=2
2
m
s
m
s
L
L
S
S=
KinematicallyKinematically SimilarSimilar
Find the ratioFind the ratio RRFsFs// RRFmFm
Ls
Ship
Lm
Model
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Case 2 (Cont.)Case 2 (Cont.)
Ls
Lm
Fmmmm
Fssss
Fm
Fs
CVS
CVS
R
R2
2
21
21
=
2
2
mmm
sss
Fm
Fs
VS
VS
R
R
=
2
2
2
2
s
m
m
s
m
s
Fm
Fs
L
L
L
L
R
R
=
m
s
Fm
Fs
R
R
= 1=
Fm
Fs
R
R
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Case 3Case 3
Ls
Lm
Geometrically SimilarGeometrically Similar
nmns RR =Hence,Hence,
Also,Also,
s
m
m
s
L
L
V
V=
KinematicallyKinematically SimilarSimilar
nmns FF =
TmTs
CC =
m
s
m
s
L
L
V
V=
ms LL =s
m
m
s
L
L
L
L=
2
=
s
m
m
s
L
L
L
L
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Case 3 (Cont.)Case 3 (Cont.)
Ls
Ship
Lm
Model
Lm
Ship and Model are identical
Sisters
Practically Impossible
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Case 3 (Cont.)Case 3 (Cont.)
Tmmmm
Tssss
Tm
Ts
CVS
CVS
R
R2
2
2
12
1
=
2
2
mmm
sss
Tm
Ts
VS
VS
R
R
=
1=Tm
Ts
R
R
Ls
Ship
Lm
Model
Find the ratioFind the ratio RRTsTs// RRTmTm
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Ls
Lm
Ship
Model
3. Kinetic Similarity3. Kinetic Similarity
The ship and the model areThe ship and the model are GeometricallyGeometrically SimilarSimilar
ThenThen
This is calledThis is called KineticKinetic SimilaritySimilarity
nmns FF =
RmRs CC =
The ship and the model areThe ship and the model areKinematicallyKinematically SimilarSimilar
IfIf
andand
where,where,
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Ls
Ship
Lm
Model
3. Kinetic Similarity3. Kinetic Similarity
The ship and the model areThe ship and the model are GeometricallyGeometrically SimilarSimilar
ThenThen
This is calledThis is called KineticKinetic SimilaritySimilarity
nmns RR =
FmFs CC =
The ship and the model areThe ship and the model areKinematicallyKinematically SimilarSimilar
IfIf
andand
where,where,
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Ls
Ship
Lm
Model
3. Kinetic Similarity3. Kinetic Similarity
The ship and the model areThe ship and the model are GeometricallyGeometrically SimilarSimilar
ThenThen
This is calledThis is called KineticKinetic SimilaritySimilarity
nmns FF =
TmTs CC =
The ship and the model areThe ship and the model areKinematicallyKinematically SimilarSimilar
IfIf
andand
where,where, andand nmns RR =
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Kinetic SimilarityKinetic Similarity
IfIf
Geometrical SimilaritiesGeometrical Similarities
KinematicKinematic SimilaritiesSimilarities
Kinetic SimilaritiesKinetic Similarities
SatisfiedSatisfied
satisfiedsatisfied
Automatically satisfiedAutomatically satisfied
andand
thenthen
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AIR
Air-WaterInterface
Water
Thank You for Your Attention!