294
CHAPTER 6. SEDIMENT TRANSPORT MODELS
(assuming the falling sediment particle is moved in the horizontal direction
at the same speed as the fluid). Prototype-to-model preservation of the
ratio given by Eqn. 6.97 assures that the relative times for particle motion
remain similar.
Le Méhauté (1970) proposed a kinematic condition of similarity for suspended sediment that is essentially the same as given by Valembois (1960).
Le Méhauté stated that sediment in suspension travels distances in the horizontal (X) and vertical (Z) that are proportional to its horizontal velocity
(D) and fall speed (u>), respectively or
X _ U
Z ~ w
The similitude relationship obtained from Eqn. 6.98 (or Eqn. 6.97) is
formed as the prototype-to-model ratio
or in terms of scale ratios
g = 7F
(6100)
The scaling criteria given by Eqn. 6.100 allows for geometric distortion.
Le Méhauté assumed that the hydrodynamics were scaled according to
the Froude criterion, so he replaced the horizontal velocity scale with its
Froude law equivalent based on vertical length scale, i.e., Nu = y/NgNzThe model geometrical distortion was then given as
Nx
Nz
N3NZ\1/2
)
(6.101)
For a geometrically undistorted model, Q — 1, and the similitude condition
reduces to
= x/ÂÇÀÇ
(6.102)
Neither Valembois (1960) nor Le Méhauté (1970) presented any experimental evidence to support their proposed relationship between the fall
speed scale and the model length scales. That was to come somewhat
later.
CHAPTER 6. SEDIMENT TRANSPORT MODELS
(assuming the falling sediment particle is moved in the horizontal direction
at the same speed as the fluid). Prototype-to-model preservation of the
ratio given by Eqn. 6.97 assures that the relative times for particle motion
remain similar.
Le Méhauté (1970) proposed a kinematic condition of similarity for suspended sediment that is essentially the same as given by Valembois (1960).
Le Méhauté stated that sediment in suspension travels distances in the horizontal (X) and vertical (Z) that are proportional to its horizontal velocity
(D) and fall speed (u>), respectively or
X _ U
Z ~ w
The similitude relationship obtained from Eqn. 6.98 (or Eqn. 6.97) is
formed as the prototype-to-model ratio
or in terms of scale ratios
g = 7F
(6100)
The scaling criteria given by Eqn. 6.100 allows for geometric distortion.
Le Méhauté assumed that the hydrodynamics were scaled according to
the Froude criterion, so he replaced the horizontal velocity scale with its
Froude law equivalent based on vertical length scale, i.e., Nu = y/NgNzThe model geometrical distortion was then given as
Nx
Nz
N3NZ\1/2
)
(6.101)
For a geometrically undistorted model, Q — 1, and the similitude condition
reduces to
= x/ÂÇÀÇ
(6.102)
Neither Valembois (1960) nor Le Méhauté (1970) presented any experimental evidence to support their proposed relationship between the fall
speed scale and the model length scales. That was to come somewhat
later.