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Uniform Open Channel Flow

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Normal depth is function of flow rate, and geometry and slope. Can solve for flow rate if depth and ... Piers, low chords, and top of road is considered ... – PowerPoint PPT presentation

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Title: Uniform Open Channel Flow


1
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
2
Uniform Open Channel Flow Brays B.
Brays Bayou
Concrete Channel
3
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4
  • 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

5
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
6
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7
Optimal Channels
8
Non-uniform Flow
9
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10
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11
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
12
Replace terms for various values of S and So. Let
v q/y flow/unit width - solve for dy/dx
13
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
14
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
15
Backwater Profiles - Compute Numerically
16
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

17
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)

18
Watershed Hydraulics
Bridge
D
QD
Tributary
Floodplain
C
QC
Main Stream
Bridge Section
B
QB
A
QA
Cross Sections
Cross Sections
19
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
20
The Floodplain
Top Width
21
Floodplain Determination
22
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.

23
HEC RAS Cross Section
24
3-D Floodplain
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