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Chapter 3 - Theoretical considerations
∆x
B
h
p up
G x
z
G z
G
p dw
τ 0
α
Figure 3.4: Definition of the boundary shear stress as a gravity component
At a given distance z of the ground, the shear stress can be obtained with:
τ τ 0
1
z
= ⋅ ⎛ – --⎞
⎝ h⎠
(3.22)
b) Shear Reynolds number
The Shear Reynolds number is composed in analogy to the Reynolds number. The velocity is
replaced by the shear velocity and the flow depth by the size of the roughness ε .
Re∗ = -------------
V∗ ⋅ ε
(3.23)
ν
c) Densimetric and sediment Froude number
In analogy to the Froude number, two dimensionless numbers are defined to characterize the sediment
transport capacity of a river. The densimetric Froude number Fr 1 d and the sediment
Froude number Fr∗ are distinguished by the used velocity:
Fr d
= ----------------------------------
V
; Fr∗ = ----------------------------------
V∗
= θ
(3.24)
( s – 1) ⋅ g⋅
d
( s – 1) ⋅ g ⋅ d
1. The densimetric Froude number - combining the flow velocity with sediment related characteristics
- is frequently used in literature despite a less explicit physical meaning (compared to Fr∗ ).
page 30 / November 9, 2002
Wall roughness effects on flow and scouring