3.3. HYDRAULIC SIMILITUDE
69
Importance of Froude Scaling
For practically all coastal engineering problems (and at least 90 percent of
all hydraulic flow problems), the forces associated with surface tension and
elastic compression are relatively small, and thus, can be safely neglected
(Warnock 1950). This leaves selection of an appropriate hydrodynamic scaling law to an evaluation of whether gravity or viscous forces are dominant
in the phenomenon. For this reason ...
... the Froude and Reynolds number are important to
coastal engineers because similarity of one of these numbers, combined with geometric similarity, provides the
necessary conditions for hydrodynamic similitude in an
overwhelming majority of coastal models.
The scale requirements for any physical property can be derived for a
given model scaling criterion by dimensional considerations and/or Newton’s 2nd Law. Usually, the derived scale ratio will be expressed in terms
the scale ratios of various independent parameters; however, the ratio can
also include other derived ratios if so desired.
Example 3.5. Froude and Reynolds Time Scale
The Froude similarity criterion is given by
Nv = y/NgNL
Because velocity is dimensionally length/time (and also from consideration of preserving the Strouhal number), the scale ratio for velocity is dimensionally equivalent
to Nl/N(. Substituting into the Froude criterion and rearranging yields
Froude time scale
For all practical purposes, the gravitational scale is unity (i.e., Ng — 1), and the
Froude time scale is simplified to the common relationship
Nt = VNl
The Froude time scale can also be expressed in terms of the prototype and model
fluid parameters by noting the scale for specific weight is given as
= NpNg
69
Importance of Froude Scaling
For practically all coastal engineering problems (and at least 90 percent of
all hydraulic flow problems), the forces associated with surface tension and
elastic compression are relatively small, and thus, can be safely neglected
(Warnock 1950). This leaves selection of an appropriate hydrodynamic scaling law to an evaluation of whether gravity or viscous forces are dominant
in the phenomenon. For this reason ...
... the Froude and Reynolds number are important to
coastal engineers because similarity of one of these numbers, combined with geometric similarity, provides the
necessary conditions for hydrodynamic similitude in an
overwhelming majority of coastal models.
The scale requirements for any physical property can be derived for a
given model scaling criterion by dimensional considerations and/or Newton’s 2nd Law. Usually, the derived scale ratio will be expressed in terms
the scale ratios of various independent parameters; however, the ratio can
also include other derived ratios if so desired.
Example 3.5. Froude and Reynolds Time Scale
The Froude similarity criterion is given by
Nv = y/NgNL
Because velocity is dimensionally length/time (and also from consideration of preserving the Strouhal number), the scale ratio for velocity is dimensionally equivalent
to Nl/N(. Substituting into the Froude criterion and rearranging yields
Froude time scale
For all practical purposes, the gravitational scale is unity (i.e., Ng — 1), and the
Froude time scale is simplified to the common relationship
Nt = VNl
The Froude time scale can also be expressed in terms of the prototype and model
fluid parameters by noting the scale for specific weight is given as
= NpNg