1. Design of Open Channels and Culverts CE453 Lecture 26
Ref: Chapter 17 of your text and HYDRAULIC DESIGN OF HIGHWAY CULVERTS, Hydraulic Design Series Number 5, Federal Highway Administration, Publication No. FHWA-NHI , September 2001; available at accessed March 18, 2006

2. Design of Open Channels

3. Longitudinal Slopes
Gradient longitudinal direction of highway to facilitate movement of water along roadway

4. Drains Along ROW Collect surface water
A Typical intercepting drain placed in the impervious zone

5. Drainage Channels (Ditches)
Design
Adequate capacity
Minimize hazard to traffic
Hydraulic efficiency
Ease of maintenance
Desirable design (for safety): flat slopes, broad bottom, and liberal rounding

6. Ditch Shape
Source: Fabriform1.com
Trapezoidal – generally preferred considering hydraulics, maintenance, and safety
V-shaped – less desirable from safety point of view and maintenance

7. Terms
Steady Flow: rate of discharge does not vary with time (Manning’s applies)
Uniform: channel properties are constant along length of channel
Slope
Roughness
Cross-section
Water surface is parallel to slope of channel
Non-uniform: properties vary

8. Terms Unsteady flow: rate of discharge varies with time Critical depth
a hydraulic control in design
depth of water where flow changes from tranquil to rapid/shooting
Critical velocity: velocity corresponding to critical depth
Critical slope: slope corresponding to critical depth

10. Flow Velocity Depends on lining type
Should be high enough to prevent deposit of transported material (sedimentation)
For most linings, problem if S < 1%
Should be low enough to prevent erosion (scour)
For most types of linings, problem if S > 5%

11. Use spillway or chute if Δelev is large

12. Rip Rap for drainage over high slope

13. Riprap (TN Design Manual)

14. Side Ditch/Open Channel Design-Basics
Find expected Q at point of interest (see previous lecture)
Select a cross section for the slope, and any erosion control needed
Manning’s formula used for design
Assume steady flow in a uniform channel

15. Manning’s Formula V = R2/3*S1/2 (metric) V = 1.486 R2/3*S1/2 n n
where:
V = mean velocity (m/sec or ft/sec)
R = hydraulic radius (m, ft) = area of the cross section of flow (m2, ft2) divided by wetted perimeter (m,f)
S = slope of channel
n = Manning’s roughness coefficient

17. Side Ditch/Open Channel Design-Basics
Q = VA
Q = discharge (ft3/sec, m3/sec)
A = area of flow cross section (ft2, m2)
FHWA has developed charts
to solve Manning’s equation
for different cross sections

18. Open Channel Example Runoff = 340 ft3/sec (Q) Slope = 1%
Manning’s # = 0.015
Determine necessary cross-section to handle estimated runoff
Use rectangular channel 6-feet wide

19. Open Channel Example Q = 1.486 R2/3*S1/2 n Hydraulic radius, R = a/P
a = area, P = wetted perimeter P

20. Open Channel Example Flow depth = d Area = 6 feet x d
Wetted perimeter = 6 + 2d
Flow depth (d)
6 feet

21. Example (continued) Q = 1.486 a R2/3*S1/2 n
340 ft3/sec = (6d) (6d)2/3 (0.01)1/2
(6 + 2d)
0.015
d  4 feet
Channel area needs to be at least 4’ x 6’

22. Example (continued) If you already know Q, simpler just to do
Find flow velocities.
V = R2/3*S1/2 n
with R = a/P = 6 ft x 4 ft = 1.714
2(4ft) + 6ft
so, V = 1.486(1.714)2/3 (0.01)1/2 = 14.2 ft/sec
0.015
If you already know Q, simpler just to do
V=Q/A = 340/24 = 14.2)

24. Example (continued) Find critical velocities.
From chart along critical curve, vc  13 ft/sec
Critical slope = 0.007
Find critical depth: yc = (q2/g)1/3
g = 32.2 ft/sec2
q = flow per foot of width
= 340 ft3/sec /6 feet = 56.67ft2/sec
yc = (56.672/32.2)1/3 = 4.64 feet > depth of 4’

25. Check lining for max depth of flow …

27. Rounded

28. A cut slope with ditch

29. A fill slope

30. Inlet or drain marker

31. Ditch treatment near a bridge
US 30 – should pier be protected?

32. A fill slope

33. Where’s the water going to end up?
Hidden Drain
Where’s the water going to end up?

36. Median drain

37. Design of Culverts
Source: Michigan Design Manual

38. Culvert Design - Basics
Top of culvert not used as pavement surface (unlike bridge), usually less than 20 foot span
> 20 feet use a bridge
Three locations
Bottom of Depression (no watercourse)
Natural stream intersection with roadway (Majority)
Locations where side ditch surface drainage must cross roadway

39. Hydrologic and Economic Considerations
Alignment and grade of culvert (wrt roadway) are important
Similar to open channel
Design flow rate based on storm with acceptable return period (frequency)

40. Culvert Design Steps
Obtain site data and roadway cross section at culvert crossing location (with approximation of stream elevation) – best is natural stream location and slope (may be expensive though)
Establish inlet/outlet elevations, length, and slope of culvert

42. Sometimes … you want a dam … why?

43. Culvert Design Steps
Determine allowable headwater depth (and probable tailwater depth) during design flood – control on design size – f(topography and nearby land use)
Select type and size of culvert
Examine need for energy dissipaters

44. Headwater Depth
Constriction due to culvert creates increase in depth of water just upstream
Allowable/desirable level of headwater upstream usually controls culvert size and inlet geometry
Allowable headwater depth depends on topography and land use in immediate vicinity

45. Inlet control Flow is controlled by headwater depth and inlet geometry
Usually occurs when slope of culvert is steep and outlet is not submerged
Supercritical, high v, low d
Most typical
Following methods ignore velocity head

46. Example:
Design ElevHW = (max)
Stream bed at inlet = 224.0
Drop = 6.5’
Peak Flow = 250cfs
5x5 box
HW/D = 1.41
HW = 1.41x5 = 7.1’
Need 7.1’, have 6.5’
Drop box 0.6’ below - OK

47. Outlet control
When flow is governed by combination of headwater depth, entrance geometry, tailwater elevation, and slope, roughness, and length of culvert
Subcritical flow
Frequently occur on flat slopes
Concept is to find the required HW depth to sustain Q flow
Tail water depth often not known (need a model), so may not be able to estimate for outlet control conditions

48. Example:
Design ElevHW = 230.5
Flow = 250cfs
5x5 box (D=5)
Stream at invert = 224
200’ culvert
Outlet invert = x200
= 220.0’ (note: = x200)
Given tail water depth = 6.5’
Check critical depth, dc = 4.3’
from fig
Depth to hydraulic grade line =
(dc+D)/2 = 4.7 < 6.5, use 6.5’

49. Head drop = 3.3’ (from chart) 220.0+6.5+3.3 = 229.8’<230.5 OK
Example (cont.)
Design ElevHW = 230.5
Flow = 250cfs
5x5 box
Outlet invert = 220.0’
Depth to hydraulic grade line = 6.5’
Head drop = 3.3’ (from chart)
= 229.8’<230.5 OK