3.2. REQUIREMENTS OF SIMILITUDE
57
Most scale models are geometrically similar, and this certainly aids in visual
recognition of processes as they occur in the model.
Geometrically similar models are also known as geometrically undistorted models. Geometrically undistorted models are models in which
the vertical and horizontal scales are the same, and they represent the
true geometric reproduction (usually a miniature version) of the prototype.
Geometric scaling may include the finest geometric details, such as surface
roughness, which can significantly influence certain types of flows. However,
characterizing and reproducing every geometric detail of the prototype may
be very difficult or impossible, in which case the deviation from geometric
similitude must be carefully considered (Munson, et al. 1990).
Often some definite objectives can be met by departing from geometric
similarity and using a model in which the horizontal and vertical length
scales are different. The implications of geometrically dissimilar models are
discussed in a later section.
Example 3.2. Geometrically Similar Beach Profiles
An equilibrium beach profile given by the equation
h = Ax2'3
is to be constructed in a wave tank using a length scale of Nl = 25. Determine the
scale ratio of the shape parameter, A.
Taking the ratio of the equation for the equilibrium profile in the prototype to the
equation in the model value gives
k
_ A
r 2/3
'Im —
hp = ApXp2/3
57
Most scale models are geometrically similar, and this certainly aids in visual
recognition of processes as they occur in the model.
Geometrically similar models are also known as geometrically undistorted models. Geometrically undistorted models are models in which
the vertical and horizontal scales are the same, and they represent the
true geometric reproduction (usually a miniature version) of the prototype.
Geometric scaling may include the finest geometric details, such as surface
roughness, which can significantly influence certain types of flows. However,
characterizing and reproducing every geometric detail of the prototype may
be very difficult or impossible, in which case the deviation from geometric
similitude must be carefully considered (Munson, et al. 1990).
Often some definite objectives can be met by departing from geometric
similarity and using a model in which the horizontal and vertical length
scales are different. The implications of geometrically dissimilar models are
discussed in a later section.
Example 3.2. Geometrically Similar Beach Profiles
An equilibrium beach profile given by the equation
h = Ax2'3
is to be constructed in a wave tank using a length scale of Nl = 25. Determine the
scale ratio of the shape parameter, A.
Taking the ratio of the equation for the equilibrium profile in the prototype to the
equation in the model value gives
k
_ A
r 2/3
'Im —
hp = ApXp2/3