CETN IV-18
March 1999
2
V
τ o = ρω
(1)
Ck (h / d e )
1/8
where
w = mass density of water
V
= depth-averaged velocity
Ck = undetermined constant
h = water depth at maximum discharge
de = median grain-size diameter
The constant Ck is a boundary layer shape factor that includes the unknown relationship between
de and bottom roughness.
The Critical Shear Stress of the noncohesive sand bed is given by the Shields parameter as
τ cr = C s (ρ s - ρ w ) g d e
(2)
where
Cs = constant of proportionality
s = mass density of sand
de = median grain-size diameter
Equations 1 and 2 results in the expression
4
ρ
V
2
1
h
=
w
(3)
ρ s - ρ w
g d
d e (C e )8
e
where the two unknown constants, Ck and Cs, have been combined into Ce. The term in square
brackets on the right-hand side of Equation 3 is the ratio of grain-size Froude number to the
immersed specific gravity of the sand, and it is defined as the Grain Mobility Number (Yalin
1971).
2
Previous Page
