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Uniform Open Channel Flow

Uniform Open Channel Flow . Manning’s Eqn for velocity or flow. where n = Manning’s roughness coefficient R = hydraulic radius = A/P S = channel slope Q = flow rate (cfs) = v A. Uniform Open Channel Flow – Brays B. Brays Bayou. Concrete Channel.

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Uniform Open Channel Flow

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  1. Uniform Open Channel Flow Manning’s Eqn for velocity or flow where n = Manning’s 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. 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

  4. Critical Flow in Open Channels • 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 < 1 for subcritical flow • Fr > 1 for supercritical flow

  5. Optimal Channels

  6. Non-uniform Flow

  7. 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

  8. Replace terms for various values of S and So. Let v = q/y = flow/unit width - solve for dy/dx

  9. 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

  10. 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

  11. Backwater Profiles - Compute Numerically

  12. 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

  13. Backwater Calculations (cont’d) Prepare a table of values Calculate Vm = (V1 + V2) / 2 Calculate Rm = (R1 + R2) / 2 Calculate Manning’s Calculate L = ∆X from first equation X = ∑∆Xi for each stream reach (SEE SPREADSHEET)

  14. Watershed Hydraulics Bridge D QD Tributary Floodplain C QC Main Stream Bridge Section B QB A QA Cross Sections Cross Sections

  15. 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

  16. The Floodplain Top Width

  17. Floodplain Determination

  18. 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.

  19. HEC RAS Cross Section

  20. 3-D Floodplain

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