Uniform Open Channel Flow

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Uniform Open Channel Flow
Mannings Eqn for velocity or flow
where n Mannings roughness coefficient R
hydraulic radius A/P S channel slope Q
flow rate (cfs) v A
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Uniform Open Channel Flow Brays B.
Brays Bayou
Concrete Channel
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• Normal depth is function of flow rate, and
  geometry and slope. Can solve for flow rate if
  depth and geometry are known.
• Critical depth is used to characterize channel
  flows -- based on addressing specific energy
• E y Q2/2gA2 where Q/A q/y
• Take dE/dy (1 q2/gy3) 0.
• For a rectangular channel bottom width b,
• 1. Emin 3/2Yc for critical depth y yc
• yc/2 Vc2/2g
• yc (Q2/gb2)1/3

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In general for any channel, B top
width (Q2/g) (A3/B) at y yc Finally Fr
V/(gy)1/2 Froude No. Fr 1 for critical
flow Fr lt 1 for subcritical flow Fr gt 1 for
supercritical flow
Critical Flow in Open Channels
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Optimal Channels
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Non-uniform Flow
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Non-Uniform Open Channel Flow
With natural or man-made channels, the shape,
size, and slope may vary along the stream length,
x. In addition, velocity and flow rate may also
vary with x.
Thus,
Where H total energy head z elevation
head, ?v2/2g velocity head
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Replace terms for various values of S and So. Let
v q/y flow/unit width - solve for dy/dx
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Given the Fr number, we can solve for the slope
of the water surface - dy/dx
Note that the eqn blows up when Fr 1 or So S
where S total energy slope So bed slope,
dy/dx water surface slope
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Now apply Energy Eqn. for a reach of length L
This Eqn is the basis for the Standard Step
Method to compute water surface profiles in open
channels
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Backwater Profiles - Compute Numerically
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Routine Backwater Calculations

• Select Y1 (starting depth)
• Calculate A1 (cross sectional area)
• Calculate P1 (wetted perimeter)
• Calculate R1 A1/P1
• Calculate V1 Q1/A1
• Select Y2 (ending depth)
• Calculate A2
• Calculate P2
• Calculate R2 A2/P2
• Calculate V2 Q2/A2

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Backwater Calculations (contd)

• Prepare a table of values
• Calculate Vm (V1 V2) / 2
• Calculate Rm (R1 R2) / 2
• Calculate Mannings
• Calculate L ?X from first equation
• X ??Xi for each stream reach (SEE SPREADSHEET)

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Watershed Hydraulics
Bridge
D
QD
Tributary
Floodplain
C
QC
Main Stream
Bridge Section
B
QB
A
QA
Cross Sections
Cross Sections
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Brays Bayou-Typical Urban System

• Bridges cause unique problems in hydraulics
• Piers, low chords, and top of road is
  considered
• Expansion/contraction can cause hydraulic
  losses
• Several cross sections are needed for a bridge
• Critical in urban settings

288 Crossing
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The Floodplain
Top Width
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Floodplain Determination
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The Woodlands

• The Woodlands planners wanted to design the
  community to withstand a 100-year storm.
• In doing this, they would attempt to minimize any
  changes to the existing, undeveloped floodplain
  as development proceeded through time.

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HEC RAS Cross Section
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3-D Floodplain