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Coastal Engineering: Theory and Practice
Kinematic similitude
Kinematic similarity is the similarity of motions which implies both géométrie similarity and similarity of time intervals, in other words, it requires
that the model and prototype hâve the same length scale ratio and the same
time scale ratio; thus the velocity scale ratio will be the same for both.
Example. Estimate the scaling criterion necessary for kinematically similar wave motion for gravity waves whose length is given by
r
gT2
, 27vd
2tt
L
Solution. 2ird/L is dimensionless, this ratio for model and prototype
should be an invariant for geometrically similar model. If 27rd/L is the
same, the tangent of the hyperbola will also be the same therefore scaling
relation between L and T is arrived from prototype to model ratio of wave
length. Thus for a kinematic similarity of wave motion,
L„
[Ctanh^d/Z,)^
Lm
[^" tanh(27rd/L]
Since “g” is constant
T
T2
_ P
Al = (At)2
Therefore, the kinematic similarity of wave lengths can be achieved by
making Dynamic Similitude At — ^/Xl.
Dynamic similarity exists when the model and the prototype hâve the
same length scale ratio, time scale ratio, and the force scale (mass scale)
ratio. Thus, the ratio of any two forces in one System must be the same
as the ratio of the corresponding forces in the other System. Kinematic
similarity can be achieved without considering any properties of the fluid,
which is unlikely for dynamic similarity.
Fm _ Afm®m _ PmL^n
_ » >2
FP ~ Mpap ~ PpL*
Âï ~ ApÂL
Al \
At /
2
— Ao A? X2,
Figure 9.1 depicts a model of OWC showing the similitude between
model and prototype scaled down using Froude’s scaling law.