ABSTRACT
From a mathematical point of view, the interrelation between specific water flow and sediment transport conditions for a one-dimensional phenomenon without changes in the shape of the cross section can be described by the following equations (Cunge, 1980): • Continuity equation for water movement:
∂A
∂t + ∂Q
∂x = 0 (5.1)
• Dynamic equation for water movement: ∂h
∂x + v
C2R + ∂z
∂x + v
g
∂v
∂x + 1
g
∂v
∂t = 0 (5.2)
• Friction factor predictor which can be given as a function of: C = f (d50, v, h, So) (5.3)
• Continuity equation for sediment transport: (1 − p)B∂z
∂t + ∂Qs
∂x = 0 (5.4)
• Sediment transport equation which can be given as a function of: Qs = f (d50, v, h, So) (5.5)
Where: Qs = sediment discharge (m3/s) B= bottom width (m)
d50 =mean diameter of sediment (m) p= porosity (dimensionless) z= bottom level above datum (m) v= average velocity (m/s) h= y=water depth (m) So = bottom slope (m/m) R= hydraulic radius (m)
74 to Sediment Transport
These five equations form a non-linear partial differential system, which cannot be solved analytically, but instead by a numerical method (Cunge, 1980). These implicit equations are not independent; they depend on each other. For instance, the water flow influences the roughness coefficient and, vice versa, the sediment transport depends strongly on the water flow.
