Sedimentation and Stratigraphy Geology 5142 Dr. Thieme

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Sedimentation and StratigraphyGeology 5142Dr.
Thieme

• Lecture 6 Sediment Transport, Unidirectional Flow

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Sediment Transport
Physics are similar to an "inclined plane"
experiment.

• Gravity -

Both are treated as "fluids" in which flow is
either laminar or turbulent.

• Wind
• Water

a "fluid" with very high viscosity? (also
sometimes explained by gravity physics)

• Ice -

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Gravity
A "angle of rest (repose)" the maximum angle
at which material is stable without falling
downslope. Typically between 30 and 35 degrees
from the horizontal.
N resisting force "normal" to the slope due to
friction. N W cos A
D driving force acting downslope D W sin A
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Fluid Dynamics

• A fluid in motion can move in one of two ways -
• laminar flows where molecules move parallel to
  each other in the direction of transport
• turbulent flows with some net movement in the
  direction of transport

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Reynolds experiment

• Pressure drops between inlet and outlet of a
  cyllindrical pipe
• Reynolds expected linear relationship with same
  ratio between pressure at inlet and outlet for
  different velocities
• found instead a much larger pressure drop at
  higher velocities due to more turbulent flow

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Reynolds number
Re r ul/v
r fluid density u velocity of flow l
diameter of pipe (depth of channel) v viscosity
of fluid
density of water 1 gm cm-3 viscosity of water
0.89 centipoise (at STP of 25C and 1 atm), i.e.
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Relt500 laminar flow 500ltRelt2000
transitional (both laminar and turbulent)
Regt2000 turbulent flow
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Reynolds number

• transition from laminar to turbulent flow most
  characteristic of water
• low kinematic viscosity of air compared to water
  explains why all natural air flows are turbulent
• high kinematic viscosity of ice and lava explains
  predominance of laminar flow
• viscosity decreases with T in water, increases
  with T in air

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Bedload Transport

• rolling is initiated when the frictional drag
  exerted by flowing water overcomes gravitational
  resistance

• saltation which moves particles upward into the
  flow must result from an additional force

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Bernoulli equation
potential
kinetic
pressure
Total Energy rgh ru2/2 P
Eloss
resistance
r density of the fluid g acceleration due to
gravity h height difference u velocity of
flow P pressure
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Bernoulli effect

• kinetic energy (velocity) and pressure terms of
  the Bernoulli equation must balance.

• there will be an increase in velocity as flow is
  narrowed above large clasts on the channel bottom

• the fluid pressure must be correspondingly
  reduced, and that exerts a lifting force on the
  clasts below

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Particle Movement

• saltation "jumps" become longer as flow velocity
  increases

• suspension is favored by more turbulent flow at
  higher velocity

• suspension is most effective on platy particles
  with largest surface area relative to mass (mica
  and clay)

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Hjulstrom diagram
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Shields diagram of particle Reynolds number vs.
bed shear stress, b -
b v du/dt change in velocity over time times
the viscosity
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Particle Settling
Re r ul/v r 2rus/v 2rus/v
2r twice the radius diameter us falling
velocity of particle in motionless fluid v
kinematic viscosity of the fluid particle
Reynolds number which can in turn be reduced to
gravitational force (FG) and drag force (FD) of
the "Navier-Stokes" equations
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Particle Settling
FG VDrg V volume of sphere 4pr3/3 Dr
difference in density between sphere and fluid g
acceleration due to gravity

• FD CDArus2/2
• CD "drag coefficient" fudge factor?
• A cross-sectional area of the sphere
• density of the fluid
• us falling velocity of the particle

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Stokes' "Law"

• us (2r)2Drg/18v
• us falling velocity of the particle
• v viscosity of the fluid

For water at 18oC, (density 0.999 gm cm-3,
viscosity 1.06 centipoise), particles are in the
Stokes range if their diameters are less than 0.1
mm. For air (density 0.0012 gm cm-3 and
viscosity 0.0183 centipoise), Stokes' law applies
to particles not larger than 5 microns.
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