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

4. For a rectangular channel bottom width b,
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. 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

7. Optimal Channels

8. Non-uniform Flow

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
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 (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)

18. Watershed Hydraulics 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. 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