where g is the acceleration due to gravity and ρ and ρs are the water and sediment density,
respectively. The shear stress is computed by the formula:
1
2
τc = ρ f U
(6)
2
where f is a dimensionless friction factor calculated assuming a logarithmic velocity profile (see
for example Sleath, 1984):
-2
8⎡
⎛ d ⎞⎤
f ( H ) = ⎢1 + ln ⎜ 50 ⎟⎥
(7)
25 ⎣
⎝ 15H ⎠⎦
where d50 is the median grain size. The critical shear stress is computed from the critical Shields
parameter which is either estimated as a constant or calculated using the formula proposed by
Soulsby and Whitehouse (1997).
Using Eqs. (5) - (7) the sediment transport formula can be written in the form of Equation
(3) with n = 3 and
A given by the
function:
1.5
⎛
τ ⎞
⎛1
⎞
A = C ⎜ ρ f ⎟ exp ⎜ -4.5 cr ⎟
(8)
τc ⎠
⎝2
⎠
⎝
Note that A is a monotonically increasing function of τc and therefore U.
7