1. UH-Downtown
White Oak
Buffalo

2. Brays Bayou
Concrete Channel under a bridge
June 9, 2001

3. Uniform Open Channel Flow
Uniform flow - Manning’s Eqn in a prismatic channel - Q, V, y, A, P, B, S and roughness are all constant
Critical flow - Specific Energy Eqn (Froude No.)
Non-uniform flow - gradually varied flow (steady flow) - determination of floodplains
Unsteady and Non-uniform flow - flood waves

4. Critical Flow in Open Channels
In general for any channel shape, B = top width
Critical Flow ---- Q2/g = (A3/B) (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
Critical Flow in Open Channels

6. 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. Non-uniform flow can be best approximated using a numerical method called the Standard Step Method.

7. Non-Uniform Computations
Typically start at downstream end with known water level - yo.
Proceed upstream with calculations using new water levels as they
are computed.
The limits of calculation range between normal and critical depths.
In the case of mild slopes, calculations start downstream.
In the case of steep slopes, calculations start upstream.
Calc. Q
Mild Slope

8. Non-Uniform Open Channel Flow
Let’s evaluate H, total energy, as a function of x.
Take derivative,
Where H = total energy head
z = elevation head,
v2/2g = velocity head

9. Replace terms for various values of S and So
Replace terms for various values of S and So. Let v = q/y = flow/unit width - solve for dy/dx, the slope of the water surface

10. Given the Froude number, we can simplify and solve for dy/dx as a fcn of measurable parameters
*Note that the eqn blows up when Fr = 1 and goes to
   zero if So = S, the case of uniform OCF.
where S = total energy slope
So = bed slope,
dy/dx = water surface slope

11. Now apply Energy Eqn. for a reach of length L
This Eqn is the basis for the Standard Step Method Solve for L = Dx to compute water surface profiles as function of y1 and y2, v1 and v2, and S and S0

12. ALL POSSIBLE PROFILES

13. Mild Slopes where --- Yn > Yc
Uniform Depth
Mild Slopes where --- Yn > Yc

14. Numerical Solver – select y value and
break into small steps and solve for Dx x

15. Backwater Profiles - Compute Numerically
y y2 y1

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 (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 SPREADSHEETS)
Energy Slope Approx.

18. 100 Year Floodplain Bridge D QD Floodplain C QC Bridge Section B QB A
Tributary
Floodplain C QC
Main Stream
Bridge Section B QB A QA
Cross Sections
Cross Sections

19. Floodplain Determination

20. The Floodplain
Top Width

21. 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.

22. HEC RAS (River Analysis System, 1995)
HEC RAS is a computer model designed for cross sections
in natural rivers. It solves the governing equations for the
standard step method, generally in a downstream to upstream
direction.
It can also handle the presence of bridges, culverts, and
variable roughness, flow rate, depth, and velocity.

23. HEC - RAS
Orientation - looking downstream

25. BRIDGES

26. BRIDGES

27. BRIDGES

28. River
Multiple Cross Sections

29. HEC RAS (River Analysis System, 2016)

30. HEC RAS Bridge CS

31. HEC RAS Input Window

32. XS A
XS B
XS C
Laser Beam
GIS LIDAR TECHNOLOGY
LIDAR DATA

33. Current Brays Bayou Watershed 100-yr Floodplain

34. 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
288 Bridge causes a 2 ft
288 Crossing