6.3. BEDLOAD-DOMINATED TRANSPORT MODELS
257
6.3.3 Best Model Requirements
The Best Model comes the closest to satisfying all five sediment transport
criteria, hence the name. It also is perhaps the hardest to conduct in
practice because of the restrictions that arise from fulfilling three of the
five criteria.
Maintaining the prototype-to-model ratio of relative length gives the
requirement
Nx = Nj or Nd = Nl
(6.31)
where Nl is the model length scale. This means that sediment grains must
be geometrically reduced according to the model length scale.
The scale ratio of relative sediment density yields
Np. = Np
(6.32)
Assuming that the model fluid is water, then Np ~ 1 and the model sediment should have nearly the same density as the prototype. The combination of having the same fluid and sediment densities in the model as in the
prototype means that the immersed sediment specific weight ratio will also
be unity, i.e.,
= 1
(6.33)
The scale ratio of grain size Reynolds number can be derived by solving the criterion Np, — 1 for the ratio, Nv,y and substituting it into the
expression for Nr, to get
Nr, =
NytNdV/2 Nd
Np )
N„
(6.34)
For the Best Model, Nyt
Nv, = ^/Nl and
= Np =
= 1 and Nd = NL, resulting in
Nr. = Nl12
(6.35)
The sediment fall speed is approximately proportional to the grain diameter within the range 0.13 mm - 1.0 mm. For the special case when both the
prototype and model median grain sizes fall within this range (and knowing that prototype and model sand both have the same immersed specific
weight), the sediment fall speed scale ratio can be approximated for the
Best Model as Nw = Nd = NL- The relative fall speed scale then becomes
Nv„ = x/N~l
(6.36)
257
6.3.3 Best Model Requirements
The Best Model comes the closest to satisfying all five sediment transport
criteria, hence the name. It also is perhaps the hardest to conduct in
practice because of the restrictions that arise from fulfilling three of the
five criteria.
Maintaining the prototype-to-model ratio of relative length gives the
requirement
Nx = Nj or Nd = Nl
(6.31)
where Nl is the model length scale. This means that sediment grains must
be geometrically reduced according to the model length scale.
The scale ratio of relative sediment density yields
Np. = Np
(6.32)
Assuming that the model fluid is water, then Np ~ 1 and the model sediment should have nearly the same density as the prototype. The combination of having the same fluid and sediment densities in the model as in the
prototype means that the immersed sediment specific weight ratio will also
be unity, i.e.,
= 1
(6.33)
The scale ratio of grain size Reynolds number can be derived by solving the criterion Np, — 1 for the ratio, Nv,y and substituting it into the
expression for Nr, to get
Nr, =
NytNdV/2 Nd
Np )
N„
(6.34)
For the Best Model, Nyt
Nv, = ^/Nl and
= Np =
= 1 and Nd = NL, resulting in
Nr. = Nl12
(6.35)
The sediment fall speed is approximately proportional to the grain diameter within the range 0.13 mm - 1.0 mm. For the special case when both the
prototype and model median grain sizes fall within this range (and knowing that prototype and model sand both have the same immersed specific
weight), the sediment fall speed scale ratio can be approximated for the
Best Model as Nw = Nd = NL- The relative fall speed scale then becomes
Nv„ = x/N~l
(6.36)