Reynolds Number Re

1
Reynolds Number (Re)
Driving Forces
Re
Resisting Force
Re VR(?/?), where
R A/P V mean velocity ?/? ? (which is
kinematic viscosity)
Re lt 500 Laminar Flow Re gt 750 Turbulent Flow
2
Flow Types

• Laminar
• Water particles move along paths that do not
  disrupt the movement of neighboring particles.
• Most resistance is caused by intermolecular
  viscous forces.
• Resistance is ? velocity

• Turbulent Flow
• Water particles move in all directions and
  velocity constantly fluctuates
• Most resistance is generated along channel
  perimeter related to channel shape, particle
  size, and concentration.
• Resistance is ? square of velocity

3
Manning EquationDescribes Flow and Resistance in
Open Channels
V 1.49/n(R2/3)(S1/2) n Mannings
roughness Coefficient Slope water surface
slope Assumes English units.
4
Velocity Distribution in Open Channels
5
Sediment Transport Terminology

• Entrainment the processes that initiate the
  motion of a particle.
• Competence the size of the largest particle a
  stream can entrain under any give set of
  hydraulic conditions.
• Capacity the maximum amount of sediment that the
  stream can carry given the current hydraulic
  conditions.
• Load amount of sediment that is actually carried
  by the stream.
• Sediment discharge time rate of movement through
  a cross-section (weight/time tons/day)

6
Load TypesClassification Based on Mode of
Transport

• Suspended Load Particles transported mainly or
  entirely in suspension through the supporting
  action of turbulence.
• Bedload Sediment which moves by skipping,
  sliding, and rolling along the channel bed.
  Remains within a few grain diameters of the
  channel bed.

7
Load TypesClassification Based on
BottomSediment Characteristics

• Wash Load Particles so fine that they are not
  found in appreciable amounts in the channel bed.
• Bed Material Load Particle sizes that are found
  in great quantities in the stream bed.
• Most bed material load is actually transported
  in suspension.

8
Variations in Suspended SedimentConcentration
with Discharge
9
Influence of Mannings n on Resistance and
Suspended Sediment
10
Methods Used to Describe Entrainment

• Critical Bed Velocity
• Impact or momentum of the water mass on the
  exposed part of the particle.
• 6th power law Size of particle entrained
  increases with the 6th power of the velocity.
• Very difficult to measure

Velocity (V)
?
Water
11
Methods Used to Describe Entrainment

• Critical Tractive Force
• Dragging force is exerted on the exposed part of
  the particle.
• ? ?DS
• (Duboys Equation)
• Fairly Easy to measure

Water Surface
Depth (D)
?
Slope (S)
12
Shields Dimensionless Values

• Dimensionless Shear Stress

Dimensionless Reynolds Numbers
?
Vd
?
R
(?f - ?s) d
?
? - Specific weight of solid and fluid
V (gRS)1/2
d Intermediate grain diameter
R Hydraulic Radius
13
Dimensionless Shields Plot
14
Hjulstrom Plot
15
Tractive Force vs. Critical Velocity?
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Stream Power

• ? ? QS
• ? ? wdvS
• ? (?dS)v
• ? ?S

17
East Fork River Bedload Trap
Flow
Bedload Trap