Herrera Environmental Consultants, Inc. Seattle Portland Missoula

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Open Channel Flow Way Abbreviated

• an introduction to the basics of open channel
  flow, and a guide to channel design tools

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Todays Topics

• The Open-Channel Toolbox TM Peter Wilcock
• Stable Channel Design
• Tools

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The Open-Channel Toolbox TM Peter Wilcock

• Conservation Relations
• Conservation of Mass (Continuity)
• Conservation of Energy
• Conservation of Momentum

• Constitutive Relations
• Flow Resistance
• Sediment Transport

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Conservation of Mass (Continuity)

• Mass is neither created nor destroyed
• Inputs outputs
• Inputs and outputs for fluid flow are discharge
• Vel x Flow Area

U1A1 U2A2
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Conservation of Momentum (Force-balance)

• Newtons Second Law
• In steady, uniform flow,
• Depth-slope product

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Flow Resistance

• Relation between velocity, flow depth, basal
  shear stress, and hydraulic roughness
• A variety of relations exist including
• Mannings
• Chezy
• Empirical
• The big unknown n

Using continuity,
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Estimating roughness

• Best approach is to measure discharge and then
  calculate n from Mannings equation
• A variety of empirical formulas exist for
  calculating Mannings n
• Based upon sediment size
• Limerinos, 1970
• Strickler, 1923
• Based upon slope and hydraulic radius
• Jarrett, 1984
• Note Units of R and d are meters

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Estimating roughness

• Visual inspection using Barnes, 1967 to estimate
  roughness
• Tables of n values can also be found in the
  HEC-RAS Hydraulic Reference Manual, and Open
  Channel Hydraulics, Chow, 1959
• For a detailed comparison of these and other
  methods, see An evaluation of methods for
  estimating Mannings n in small mountain
  stream, Marcus, W.A. et al, 1992

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Sediment transport
Emmett and Wolman (2001)

• Directly expressed in terms of sediment supply
  and water supply
• Shear stress is a descriptor of transport rate

Meyer-Peter and Muller
General Form
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Conservation of Energy

• Energy is neither created nor destroyed
• Two components
• kinetic ( )
• potential (zh)
• Energy is also converted to heat, hf
• H1 H2 hf

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Stable Channel Design

• Two types of stability
• rigid (static)
• moveable (dynamic)
• incoming sediment supply sediment transport
  rate
• Rigid case
• channel boundary materials resist erosion
• Dynamic case
• entrainment and transport of boundary materials
  does not preclude stable channel configuration

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So you want to learn dynamic methods?
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Static Methods

• Permissible velocity
• vavg lt vmax permissible
• Permissible tractive force (shear stress)
• to lt tc

(HEC 15, FHWA)
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Tractive Force
Shields equation

• Grain motion is driven by shear stress, t
• Units of force/unit area psf, psi, Pa
• Critical shear stress, tc
• Shear stress needed to entrain a grain of a given
  size
• Shields number or
• dimensionless shear stress t

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Shields diagram
(Wilcock, 2006)
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Other Tractive Force Methods

• Lane Method
• uses d75
• Regime Method
• empirical relations developed by British
  engineers for design of irrigation canals in
  India
• sand-bed channels
• HEC-RAS Stable Channel Functions

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Filter Design

• A transitional layer of gravel/small stone placed
  between native soil and sized stone
• Filter
• prevents migration of fines
• distributes weight of placed stone
• Evaluate filter reqmt.
• upper placed stone
• lower native soil
• If filter is needed, subscripts refer to
  filter/soil comparisons when selecting filter
  gradation
• Filter thickness
• max thickness max grain size
• min thickness 6 in.

(HEC 11 and 15, FHWA)
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Tool XS Calculator
(Wilcock, 2006)
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What it does
(Wilcock, 2006)
Input Surveyed Station and elevation
data Surveyed water surface slope Stage Grain
size of interest Dimensionless critical shear
t Either n or measured Q Output Either n
or calculated Q Hydraulic characteristics (A, w,
d, R) Bed shear stress t Critical shear stress
for specified grain size tc
https//jshare.johnshopkins.edu/pwilcoc1/public_ht
ml/Skamania20Short20Course.htm
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Tool Estimating critical discharge
(Wilcock, 2004)
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How does it work??
(1)
Start with our old friends continuity, momentum
, flow resistance, and add hyd. geometry
(2)
(3)
(4)
Substitute (2), (3), and (4) into (1)
Simplify
Substitute Shields eqn. for t
Calculate Qc, critical discharge
(Wilcock, 2004)
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Tool Riprap Calculator
http//www.engr.colostate.edu/pierre/ce_old/class
es/