2.2 Purpose and Significance
11
Fig. 2.1 A technical framework to verify the SSPM
across-the-board comparison was possible as the soil erosion processes in the three
models were all implemented in the laboratory using simulated rainfall.
2.3 Similarity Requirements
The similarity degree between the prototype and model is based on the geometrical,
kinematic and dynamic similarity. Geometrical similarity in a model may be achieved
when each geometrical length L p in the prototype has a constant ratio corresponding
to the model length L m in the model. Subscripts p and m stand for prototype and
model parameters respectively. This ratio is called the length scale number λ L of
the model (λ L = L p /L m ). In the proposed downscaled model experiment, horizontal
length scale is equal to the vertical length scale; therefore, the dam height scale
number λ H equals the length scale number. Likewise, due to geometrical similarity,
the watershed area scale number λ A could be calculated as λ
2
L where the subscript A
is the area of the watershed.
Dynamic similarity indicates that the corresponding forces in the prototype and
model must have a constant ratio. For the flow under its own gravity, e.g., the free
surface flow, requires geometrical similarity and equality of the Froude number (Fr)
in the model and prototype; namely λ Fr = 1.0. In a field observation or laboratory
11
Fig. 2.1 A technical framework to verify the SSPM
across-the-board comparison was possible as the soil erosion processes in the three
models were all implemented in the laboratory using simulated rainfall.
2.3 Similarity Requirements
The similarity degree between the prototype and model is based on the geometrical,
kinematic and dynamic similarity. Geometrical similarity in a model may be achieved
when each geometrical length L p in the prototype has a constant ratio corresponding
to the model length L m in the model. Subscripts p and m stand for prototype and
model parameters respectively. This ratio is called the length scale number λ L of
the model (λ L = L p /L m ). In the proposed downscaled model experiment, horizontal
length scale is equal to the vertical length scale; therefore, the dam height scale
number λ H equals the length scale number. Likewise, due to geometrical similarity,
the watershed area scale number λ A could be calculated as λ
2
L where the subscript A
is the area of the watershed.
Dynamic similarity indicates that the corresponding forces in the prototype and
model must have a constant ratio. For the flow under its own gravity, e.g., the free
surface flow, requires geometrical similarity and equality of the Froude number (Fr)
in the model and prototype; namely λ Fr = 1.0. In a field observation or laboratory