3.3. HYDRAULIC SIMILITUDE
67
M? = C = Ca
(3.20)
E
The Mach number is used in studies of air flow having high velocities.
Equating the prototype value of the Cauchy number with the model
value results in the Cauchy modeling criterion, expressed in scale ratios
as
NpNv =1
Ne
°r NCa = 1
(3-21)
This criterion also has little application in coastal engineering problems
involving fluid flow because the fluid can usually be considered incompressible. A possible exception might be the force on a structure caused by
compression of air trapped by a breaking wave.
The Cauchy similitude criterion is important in the design of structural
models where elastic forces are important. For example, we apply the
Cauchy criterion when scaling the elastic properties of mooring lines for a
floating body subjected to hydrodynamic loading in a wave model. This
aspect of Cauchy similitude is developed in Chapter 5.
Euler Criterion
Although pressure is usually taken as the dependent force in Eqn. 3.6, it
is possible to have situations in which pressure forces are the dominant
force acting on the flow. If this is the case, the Euler Number gives an
indication of the relative importance of pressure and inertia, i.e.,
pressure force _ pL2 _ p
,
inertial force
pL2V2
pV2
The Euler model criterion is found by equating prototype and model
values of the Euler number, i.e.,
or
P
pV2
which is given in terms of scale ratios as
Np
,
NPN2
or Neu — 1
(3.23)
(3-24)
(3.25)
67
M? = C = Ca
(3.20)
E
The Mach number is used in studies of air flow having high velocities.
Equating the prototype value of the Cauchy number with the model
value results in the Cauchy modeling criterion, expressed in scale ratios
as
NpNv =1
Ne
°r NCa = 1
(3-21)
This criterion also has little application in coastal engineering problems
involving fluid flow because the fluid can usually be considered incompressible. A possible exception might be the force on a structure caused by
compression of air trapped by a breaking wave.
The Cauchy similitude criterion is important in the design of structural
models where elastic forces are important. For example, we apply the
Cauchy criterion when scaling the elastic properties of mooring lines for a
floating body subjected to hydrodynamic loading in a wave model. This
aspect of Cauchy similitude is developed in Chapter 5.
Euler Criterion
Although pressure is usually taken as the dependent force in Eqn. 3.6, it
is possible to have situations in which pressure forces are the dominant
force acting on the flow. If this is the case, the Euler Number gives an
indication of the relative importance of pressure and inertia, i.e.,
pressure force _ pL2 _ p
,
inertial force
pL2V2
pV2
The Euler model criterion is found by equating prototype and model
values of the Euler number, i.e.,
or
P
pV2
which is given in terms of scale ratios as
Np
,
NPN2
or Neu — 1
(3.23)
(3-24)
(3.25)