70
CHAPTER 3. PRINCIPLES OF SIMILITUDE
which can be solved for Ng and substituted into the time scale equation to get
\ N-y
For the time scale and any kinematic parameters, this substitution is meaningless
because Np/N-, is equal to Ng (which usually is equal to unity). However, it is useful
to express the scale ratios of dynamic scale parameters in terms of prototype and
model fluid properties because there are situations when the model and prototype
fluids are different (e.g., fresh and salt water), and we need to determine appropriate
force scaling factors.
The Reynolds similitude time scale is easily found by substituting Nv - Nl/Ni
into the Reynolds criterion
NvNlNp =
N,
and rearranging to get
..
(Nl)2Np
p.
,
Nt = i---------- -
Reynolds time scale
Np
Table 3.1 lists the derived scale ratios for common physical flow parameters for
both Froude and Reynolds scaling criteria.
Reynolds similitude is seldom invoked for most models of coastal processes, instead it is recognized that gravity forces predominate in freesurface flows; and consequently, most models are designed using the Froude
criterion. Nevertheless, the engineer must make efforts to reduce the effects
of viscosity in the model, otherwise the dissimilar viscous effects will constitute a scale effect. For example, viscous bottom friction in small scale
harbor models will be significantly greater than in the prototype. Therefore, waves that must travel over long distances in the model will undergo a
decrease in wave height greater than what occurs in the prototype. For this
particular problem the solution is either to avoid lengthy wave propagation
distances in the model, or to theoretically correct for the frictional losses
in the model by beginning with a larger initial wave height.
Normally, we can discount viscous effects in harbor models provided the
Reynolds number (based on flow depth) is greater than 1 x 104 (Hydraulic
Laboratory Techniques 1980). The same can be said for flow through the
pores of a breakwater, but in this case the length parameter in the Reynolds
number should be the average void dimension, and the Reynolds number
should be above 3 x 104 (Hudson, et al. 1979).
Generally, Reynolds numbers above 1 x 104 are in the range of turbulent
flow where the viscous force becomes independent of Reynolds number.
CHAPTER 3. PRINCIPLES OF SIMILITUDE
which can be solved for Ng and substituted into the time scale equation to get
\ N-y
For the time scale and any kinematic parameters, this substitution is meaningless
because Np/N-, is equal to Ng (which usually is equal to unity). However, it is useful
to express the scale ratios of dynamic scale parameters in terms of prototype and
model fluid properties because there are situations when the model and prototype
fluids are different (e.g., fresh and salt water), and we need to determine appropriate
force scaling factors.
The Reynolds similitude time scale is easily found by substituting Nv - Nl/Ni
into the Reynolds criterion
NvNlNp =
N,
and rearranging to get
..
(Nl)2Np
p.
,
Nt = i---------- -
Reynolds time scale
Np
Table 3.1 lists the derived scale ratios for common physical flow parameters for
both Froude and Reynolds scaling criteria.
Reynolds similitude is seldom invoked for most models of coastal processes, instead it is recognized that gravity forces predominate in freesurface flows; and consequently, most models are designed using the Froude
criterion. Nevertheless, the engineer must make efforts to reduce the effects
of viscosity in the model, otherwise the dissimilar viscous effects will constitute a scale effect. For example, viscous bottom friction in small scale
harbor models will be significantly greater than in the prototype. Therefore, waves that must travel over long distances in the model will undergo a
decrease in wave height greater than what occurs in the prototype. For this
particular problem the solution is either to avoid lengthy wave propagation
distances in the model, or to theoretically correct for the frictional losses
in the model by beginning with a larger initial wave height.
Normally, we can discount viscous effects in harbor models provided the
Reynolds number (based on flow depth) is greater than 1 x 104 (Hydraulic
Laboratory Techniques 1980). The same can be said for flow through the
pores of a breakwater, but in this case the length parameter in the Reynolds
number should be the average void dimension, and the Reynolds number
should be above 3 x 104 (Hudson, et al. 1979).
Generally, Reynolds numbers above 1 x 104 are in the range of turbulent
flow where the viscous force becomes independent of Reynolds number.