Table 5.7. Scale Ratios for Similitude.
Characteristic
Dimension
Re
Fr
We
Length
L
L
L
L
2
2
2
2
Area
L
L
L
L
3
3
3
3
Volume
L
L
L
L
2
1/2
3
1/2
Time
T
ρL /
(Lρ/γ)
(L ρ/σ)
1/2
1/2
Velocity
L/T
/Lρ
(Lγ/ρ)
(σ/Lρ)
2
2 2 3
2
L/T
/ρ L
γ/ρ
σ/L ρ
3
5/2
1/2
3/2
1/2
Discharge
L /T
L/ρ
L
(γ/ρ)
L
(σ/ρ)
3
3
3
Mass
M
L ρ
L ρ
L ρ
2
2
3
Force
ML/T
/ρ
L γ
Lσ
3
Density
M/L
ρ
ρ
ρ
2 2
2 2
2
Specific Weight
M/L T
/L ρ
σ/L
γ
2 2
Pressure
ML/T
/L ρ
Lγ
σ/L
2 2
2
7/2
1/2
5/2
1/2
Impulse & Momentum
ML /T
L
L (ργ)
L (ρσ)
2 2
2
4
2
Energy and Work
ML /T
L /ρ
Lγ
Lσ
2
3
3
2
7/2
3/2
-1/2
3/2
1/2
Power
ML /T
/Lρ
L
(Lρ)
γ
ρ
σ
Mobile Bed Models. In modeling highway crossings and encroachments in the river
environment, two- and three-dimensional mobile bed models are often used. These models
have the bed and sides molded of materials that can be moved by the model flow. Similitude
in mobile bed models implies that the model reproduces the fluvial processes such as bed
scour, bed deposition, lateral channel migration, and varying boundary roughness. It is
generally not possible to faithfully simulate all of these processes simultaneously on scale
models. Distortions of various parameters are often made in such models.
Two approaches are available to design mobile bed models. One approach is the analytical
derivation of distortions explained by Einstein and Chien (1956) and the other is based on
hydraulic geometry relationships given by Lacey, Blench, and others (Mahmood and Shen
1971). In both of these approaches, a first approximation of the model scales and distortions
can be obtained by numerical computations. The model is built to these scales and then
verified for past information obtained from the prototype. In general, the model scales need
adjusting during the verification stage.
Model verification consists of the reproduction of observed prototype behavior under given
conditions on the model. This is specifically directed to one or more alluvial processes of
interest. For example, a model may be verified for bed-level changes over a certain reach of
the river. The predictive use of the model should be restricted to the aspects for which the
model has been verified. The use is based on the premise that if the model has successfully
5.42
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