=

Specific gravity (2.65 for quartz)

Ss

Density of water (999 kg/m3, 1.94 slugs/ ft3)

=

ρ

Density of sediment (quartz 2,647 Kg/m3, 165.4 lb/ft3)

=

ρs

g

=

The relationships in Equations 3.43 and 3.44 are the fundamental relations between velocity,

depth, resistance to flow (Manning's n), density and a coefficient determined experimentally

for the beginning of movement of the sediment particles. This coefficient is called the

Shields coefficient. The equation can be solved for the following:

1. Critical velocity for beginning of sediment movement for a given depth, roughness,

Shields coefficient, and bed material size and density.

2. Critical size for a given velocity, depth, roughness, Shields coefficient, and bed material

density.

3. Clear-water scour depth for a given velocity, roughness, Shields coefficient, and bed

material size and density. This depth is the contraction scour depth at the end of a long

contraction.

Critical Velocity for the Beginning of Bed Material Movement. Rearranging Equations 3.43

and 3.44 to give the critical velocity for beginning of motion of bed material of size D for

depth y, Shield's parameter, and Manning's n results in:

K 1/ 2 (S s - 1)

1/ 2

D1/ 2 y1/ 6

Vc = s

s

(SI)

(3.45)

n

1.49 k 1/ 2 (S s - 1)1/ 2 D1/ 2 y1/ 6

s

s

Vc =

(English)

(3.46)

n

n = K nu D1/ 6

(3.47)

s

Knu = 0.041

(SI)

Knu = 0.0336

(English)

Vc = K u D1/ 3 y1/ 6

(3.48)

s

K 1/ 2 (S s - 1)

1/ 2

Ku = s

(SI)

(3.49)

K nu

1.49 K 1/ 2 (S s - 1)1/ 2

s

Ku =

(English)

K nu

where:

=

Critical velocity above which bed material of size D and smaller will be

Vc

transported, m/s, ft/s

=

Shields parameter

Ks

3.41

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