Understanding Open Channel Flow and Mannings Equation

 
1
 
CTC 261  Review
 
Hydraulic Devices
Orifices
Weirs
Sluice Gates
 
Siphons
Outlets for Detention Structures
 
2
 
This Week:
 
Open Channel Flow
Uniform Flow (Manning’s Equation)
Varied Flow
 
3
 
Objectives
 
Students should be able to:
Use Manning’s equation for uniform
flow calculations
Calculate Normal Depth by hand
Calculate Critical Depth by hand
Utilize Flowmaster software for open
channel flow problem-solving
 
4
 
Open Channel Flow
 
Open to the atmosphere
Creek/ditch/gutter/pipe flow
Uniform flow
-EGL/HGL/Channel Slope are
parallel
velocity/depth constant
Varied flow
-EGL/HGL/Channel Slope not
parallel
velocity/depth not constant
 
5
 
Uniform Flow in Open Channels
 
Water depth, flow area, Q and V distribution at
all sections throughout the entire channel reach
remains unchanged
 
The EGL, HGL and channel bottom lines are
parallel to each other
 
No acceleration or deceleration
 
6
 
Manning’s Equation
 
Irish Engineer
 
“On the Flow of Water in Open Channels and
Pipes” (1891)
 
More:
http://www.engineeringtoolbox.com/mannings-roughness-d_799.html
https://www.hydrologystudio.com/pulp-friction/
https://www.h2ometrics.com/manning-equation/
 
7
 
Manning’s Equation-English
Solve for Flow
 
Q=AV=(
1.486
/n)(A)(R
h
)
2/3
S
1/2
Where:
Q=flow rate (cfs)
A=wetted cross-sectional area (ft
2
)
R
h
=hydraulic radius=A/WP  (ft)
WP=wetted perimeter (ft)
S=slope (ft/ft)
n=friction coefficient (dimensionless)
 
 
 
 
 
8
 
Manning’s Equation-Metric
Solve for Flow
 
Q=AV=(
1
/n)(A)(R
h
)
2/3
S
1/2
Where:
Q=flow rate (cms)
A=wetted cross-sectional area (m
2
)
R
h
=hydraulic radius=A/WP  (m)
WP=wetted perimeter (m)
S=slope (m/m)
n=friction coefficient (dimensionless)
 
 
 
 
 
9
 
Manning’s Equation-English
Solve for Velocity
 
V=(
1.486
/n)(R
h
)
2/3
S
1/2
Where:
V=velocity (ft/sec)
A=wetted cross-sectional area (ft
2
)
R
h
=hydraulic radius=A/WP  (ft)
WP=wetted perimeter (ft)
S=slope (ft/ft)
n=friction coefficient (dimensionless)
 
 
 
 
 
10
 
Manning’s Equation-Metric
Solve for Velocity
 
V=(
1
/n)(R
h
)
2/3
S
1/2
Where:
V=flow rate (meters/sec)
A=wetted cross-sectional area (m
2
)
R
h
=hydraulic radius=A/WP  (m)
WP=wetted perimeter (m)
S=slope (m/m)
n=friction coefficient (dimensionless)
 
 
 
 
 
11
 
Manning’s Friction Coefficient
 
http://www.lmnoeng.com/manningn.htm
 
Typical values:
Concrete pipe:  n=.013
CMP pipe: n=.024
 
 
12
 
Triangular/Trapezoidal
Channels
 
Must use trigonometry to determine area
and wetted perimeters
 
13
 
Pipe Flow
 
Hydraulic radii and wetted perimeters are
easy to calculate if the pipe is flowing full
or half-full
 
If pipe flow is at some other depth, then
tables/figures/software are usually used
 
14
 
15
 
Example-Find Q
 
     Find the discharge of a rectangular
channel 5’ wide w/ a 5% grade,
flowing 1’ deep.  The channel has a
stone and weed bank (n=.035).
A=5 sf; WP=7’; R
h
=0.714 ft
S=.05
Q=38 cfs
 
16
 
Example-Find S
 
     A 3-m wide rectangular irrigation
channel carries a discharge of 25.3
cms @ a uniform depth of 1.2m.
Determine the slope of the channel if
Manning’s n=.022
A=3.6 sm; WP=5.4m; R
h
=0.667m
S=.041=4.1%
 
17
 
Friction loss
 
How would you use Manning’s equation
to estimate friction loss?
 
18
 
Using Manning’s equation to
estimate pipe size
 
Size pipe for Q=39 cfs
Assume full flow
Assume concrete pipe on a 2% grade
Put R
h 
and A in terms of Dia.
Solve for D=2.15 ft = 25.8”
Choose a 27” or 30” RCP
Also see Appendix A of your book
 
 
Break
 
 
 
19
 
20
 
Normal Depth
 
Given Q, the depth at which the water
flows uniformly
 
Use Manning’s equation
Must solve by trial/error (depth is in area
term and in hydraulic radius term)
 
21
 
Normal Depth Example
 
Find normal depth in a 10.0-ft wide
concrete rectangular channel having a
slope of 0.015 ft/ft and carrying a flow of
400 cfs.
 
Assume n=0.013 (concrete)
 
22
 
Normal Depth Example
 
23
 
Stream Rating Curve
 
 
Plot of Q versus depth (or WSE)
 
Also called stage-discharge curve
 
24
 
Specific Energy
 
Energy above channel bottom
 
Depth of stream
Velocity head
 
25
 
Depth as a function of Specific
Energy
 
Rectangular channel
Width is 6’
Constant flow of 20 cfs
 
26
 
27
 
28
 
Critical Depth
 
Depth at which specific energy is at a
minimum
 
Other than critical depth, specific energy
can occur at 2 different depths
Subcritical (tranquil) flow     d > d
c
Supercritical (rapid) flow      d < d
c
 
29
 
Critical Velocity
 
 
Velocity at critical depth
 
30
 
Critical Slope
 
 
Slope that causes normal depth to
coincide w/ critical depth
 
31
 
Calculating Critical Depth
 
a
3
/T=Q
2
/g
A=cross-sectional area (sq ft or sq m)
T=top width of channel (ft/m)
Q=flow rate (cfs or cms)
g=gravitational constant (32.2/9.81)
 
Rectangular Channel—Solve Directly
Other Channel Shape-Solve via trial & error
 
Critical Depth
(Rectangular Channel)
 
Width of channel does not vary with depth;
therefore, critical depth (d
c
) can be solved for
directly:
d
c
=(Q
2
/(g*w
2
))
1/3
 
For all other channel shapes the top width
varies with depth and the critical depth must
be solved via trial and error (or via software
like flowmaster)
 
32
 
33
 
Froude Number
 
F=Vel/(g*D)
.5
F=Froude #
V=Velocity (fps or m/sec)
D=hydraulic depth=a/T (ft or m)
g=gravitational constant
F=1 (critical flow)
F<1 (subcritical; tranquil flow)
F>1 (supercritical; rapid flow)
 
34
 
Varied Flow
 
Rapidly Varied – depth and velocity change
rapidly over a short distance; can neglect
friction
hydraulic jump
 
Gradually varied – depth and velocity change
over a long distance; must account for
friction
backwater curves
 
35
 
Hydraulic Jump
 
Occurs when water goes from
supercritical to subcritical flow
Abrupt rise in the surface water
Increase in depth is always from below
the critical depth to above the critical
depth
 
36
 
Hydraulic Jump
 
Velocity and depth before jump (v
1
,y
1
)
Velocity and depth after jump (v
2
,y
2
)
Although not in your book, there are
various equations that relate these
variables. Specific energy lost in the
jump can also be calculated.
 
37
 
Hydraulic Jump
 
http://www.ce.utexas.edu/prof/hodges/classes/Hydraulics.html
 
http://krcproject.groups.et.byu.net/
 
http://www.lmnoeng.com/Channels/HydraulicJump.php
 
 
 
 
 
 
Circular hydraulic jumps 
http://www-math.mit.edu/~bush/jump.htm
 
38
 
Varied Flow
Slope Categories
 
 
M-mild slope
S-steep slope
C-critical slope
H-horizontal slope
A-adverse slope
 
39
 
Varied Flow
Zone Categories
 
Zone 1
Actual depth is greater than normal and critical
depth
Zone 2
Actual depth is between normal and critical depth
Zone 3
Actual depth is less than normal and critical depth
 
40
 
Water-Surface Profile
Classifications
 
H2, H3 (no H1)
M1, M2, M3
C1, C3 (no C2)
S1, S2, S3
A2, A3 (no A1)
 
Water Surface Profiles
http://www.fhwa.dot.gov/engineering/hydraulics/pubs/08090/04.cfm
 
41
 
Water Surface Profiles-Change in Slope
http://www.fhwa.dot.gov/engineering/hydraulics/pubs/08090/04.cfm
 
42
 
43
 
Backwater Profiles
 
Usually by computer methods
 HEC-RAS
Direct Step Method
Depth/Velocity known at some section (control
section)
Assume small change in depth
Standard Step Method
Depth and velocity known at control section
Assume a small change in channel length
Slide Note
Embed
Share

This review covers hydraulic devices such as orifices, weirs, sluice gates, siphons, and outlets for detention structures. It focuses on open channel flow, including uniform flow and varied flow, and explains how to use Mannings equation for calculations related to water depth, flow area, and velocity distribution. The content delves into the characteristics of uniform flow in open channels and provides information on how to solve for flow and velocity using Mannings equation in both English and Metric units.


Uploaded on Sep 12, 2024 | 1 Views


Download Presentation

Please find below an Image/Link to download the presentation.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.

E N D

Presentation Transcript


  1. CTC 261 Review Hydraulic Devices Orifices Weirs Sluice Gates Siphons Outlets for Detention Structures 1

  2. This Week: Open Channel Flow Uniform Flow (Manning s Equation) Varied Flow 2

  3. Objectives Students should be able to: Use Manning s equation for uniform flow calculations Calculate Normal Depth by hand Calculate Critical Depth by hand Utilize Flowmaster software for open channel flow problem-solving 3

  4. Open Channel Flow Open to the atmosphere Creek/ditch/gutter/pipe flow Uniform flow-EGL/HGL/Channel Slope are parallel velocity/depth constant Varied flow-EGL/HGL/Channel Slope not parallel velocity/depth not constant 4

  5. Uniform Flow in Open Channels Water depth, flow area, Q and V distribution at all sections throughout the entire channel reach remains unchanged The EGL, HGL and channel bottom lines are parallel to each other No acceleration or deceleration 5

  6. Mannings Equation Irish Engineer On the Flow of Water in Open Channels and Pipes (1891) More: http://www.engineeringtoolbox.com/mannings-roughness-d_799.html https://www.hydrologystudio.com/pulp-friction/ https://www.h2ometrics.com/manning-equation/ 6

  7. Mannings Equation-English Solve for Flow Q=AV=(1.486/n)(A)(Rh)2/3S1/2 Where: Q=flow rate (cfs) A=wetted cross-sectional area (ft2) Rh=hydraulic radius=A/WP (ft) WP=wetted perimeter (ft) S=slope (ft/ft) n=friction coefficient (dimensionless) 7

  8. Mannings Equation-Metric Solve for Flow Q=AV=(1/n)(A)(Rh)2/3S1/2 Where: Q=flow rate (cms) A=wetted cross-sectional area (m2) Rh=hydraulic radius=A/WP (m) WP=wetted perimeter (m) S=slope (m/m) n=friction coefficient (dimensionless) 8

  9. Mannings Equation-English Solve for Velocity V=(1.486/n)(Rh)2/3S1/2 Where: V=velocity (ft/sec) A=wetted cross-sectional area (ft2) Rh=hydraulic radius=A/WP (ft) WP=wetted perimeter (ft) S=slope (ft/ft) n=friction coefficient (dimensionless) 9

  10. Mannings Equation-Metric Solve for Velocity V=(1/n)(Rh)2/3S1/2 Where: V=flow rate (meters/sec) A=wetted cross-sectional area (m2) Rh=hydraulic radius=A/WP (m) WP=wetted perimeter (m) S=slope (m/m) n=friction coefficient (dimensionless) 10

  11. Mannings Friction Coefficient http://www.lmnoeng.com/manningn.htm Typical values: Concrete pipe: n=.013 CMP pipe: n=.024 11

  12. Triangular/Trapezoidal Channels Must use trigonometry to determine area and wetted perimeters 12

  13. Pipe Flow Hydraulic radii and wetted perimeters are easy to calculate if the pipe is flowing full or half-full If pipe flow is at some other depth, then tables/figures/software are usually used 13

  14. 14

  15. Example-Find Q Find the discharge of a rectangular channel 5 wide w/ a 5% grade, flowing 1 deep. The channel has a stone and weed bank (n=.035). A=5 sf; WP=7 ; Rh=0.714 ft S=.05 Q=38 cfs 15

  16. Example-Find S A 3-m wide rectangular irrigation channel carries a discharge of 25.3 cms @ a uniform depth of 1.2m. Determine the slope of the channel if Manning s n=.022 A=3.6 sm; WP=5.4m; Rh=0.667m S=.041=4.1% 16

  17. Friction loss How would you use Manning s equation to estimate friction loss? 17

  18. Using Mannings equation to estimate pipe size Size pipe for Q=39 cfs Assume full flow Assume concrete pipe on a 2% grade Put Rh and A in terms of Dia. Solve for D=2.15 ft = 25.8 Choose a 27 or 30 RCP Also see Appendix A of your book 18

  19. Break 19

  20. Normal Depth Given Q, the depth at which the water flows uniformly Use Manning s equation Must solve by trial/error (depth is in area term and in hydraulic radius term) 20

  21. Normal Depth Example Find normal depth in a 10.0-ft wide concrete rectangular channel having a slope of 0.015 ft/ft and carrying a flow of 400 cfs. Assume n=0.013 (concrete) 21

  22. Normal Depth Example Assumed D (ft) 2.00 Area (sqft) 20 Peri. (ft) 14 Rh (ft) 1.43 Rh^.66 Q (cfs) 1.27 356 3.00 30 16 1.88 1.52 640 2.15 21.5 14.3 1.50 1.31 396 22

  23. Stream Rating Curve Plot of Q versus depth (or WSE) Also called stage-discharge curve 23

  24. Specific Energy Energy above channel bottom Depth of stream Velocity head 24

  25. Depth as a function of Specific Energy Rectangular channel Width is 6 Constant flow of 20 cfs 25

  26. Specific Energy Start Depth Depth Increment Flow Rect Channel Width g Critical Depth D+v^2/2g 0.2 ft 0.2 ft 20 cfs 6 ft 32.2 ft/sec^2 0.70 ft Depth 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 Area 1.20 2.40 3.60 4.80 6.00 7.20 8.40 9.60 10.80 12.00 13.20 14.40 15.60 16.80 18.00 Velocity 16.67 8.33 5.56 4.17 3.33 2.78 2.38 2.08 1.85 1.67 1.52 1.39 1.28 1.19 1.11 Specific Energy 4.51 1.48 1.08 1.07 1.17 1.32 1.49 1.67 1.85 2.04 2.24 2.43 2.63 2.82 3.02 26

  27. Specific Energy Curve 3.5 3.0 Channel Depth (ft) 2.5 2.0 1.5 1.0 0.5 0.0 0.0 1.0 2.0 3.0 4.0 5.0 Specific Energy (ft) 27

  28. Critical Depth Depth at which specific energy is at a minimum Other than critical depth, specific energy can occur at 2 different depths Subcritical (tranquil) flow d > dc Supercritical (rapid) flow d < dc 28

  29. Critical Velocity Velocity at critical depth 29

  30. Critical Slope Slope that causes normal depth to coincide w/ critical depth 30

  31. Calculating Critical Depth a3/T=Q2/g A=cross-sectional area (sq ft or sq m) T=top width of channel (ft/m) Q=flow rate (cfs or cms) g=gravitational constant (32.2/9.81) Rectangular Channel Solve Directly Other Channel Shape-Solve via trial & error 31

  32. Critical Depth (Rectangular Channel) Width of channel does not vary with depth; therefore, critical depth (dc) can be solved for directly: dc=(Q2/(g*w2))1/3 For all other channel shapes the top width varies with depth and the critical depth must be solved via trial and error (or via software like flowmaster) 32

  33. Froude Number F=Vel/(g*D).5 F=Froude # V=Velocity (fps or m/sec) D=hydraulic depth=a/T (ft or m) g=gravitational constant F=1 (critical flow) F<1 (subcritical; tranquil flow) F>1 (supercritical; rapid flow) 33

  34. Varied Flow Rapidly Varied depth and velocity change rapidly over a short distance; can neglect friction hydraulic jump Gradually varied depth and velocity change over a long distance; must account for friction backwater curves 34

  35. Hydraulic Jump Occurs when water goes from supercritical to subcritical flow Abrupt rise in the surface water Increase in depth is always from below the critical depth to above the critical depth 35

  36. Hydraulic Jump Velocity and depth before jump (v1,y1) Velocity and depth after jump (v2,y2) Although not in your book, there are various equations that relate these variables. Specific energy lost in the jump can also be calculated. 36

  37. Hydraulic Jump http://www.ce.utexas.edu/prof/hodges/classes/Hydraulics.html http://krcproject.groups.et.byu.net/ http://www.lmnoeng.com/Channels/HydraulicJump.php Circular hydraulic jumps http://www-math.mit.edu/~bush/jump.htm 37

  38. Varied Flow Slope Categories M-mild slope S-steep slope C-critical slope H-horizontal slope A-adverse slope 38

  39. Varied Flow Zone Categories Zone 1 Actual depth is greater than normal and critical depth Zone 2 Actual depth is between normal and critical depth Zone 3 Actual depth is less than normal and critical depth 39

  40. Water-Surface Profile Classifications H2, H3 (no H1) M1, M2, M3 C1, C3 (no C2) S1, S2, S3 A2, A3 (no A1) 40

  41. Water Surface Profiles http://www.fhwa.dot.gov/engineering/hydraulics/pubs/08090/04.cfm 41

  42. Water Surface Profiles-Change in Slope http://www.fhwa.dot.gov/engineering/hydraulics/pubs/08090/04.cfm 42

  43. Backwater Profiles Usually by computer methods HEC-RAS Direct Step Method Depth/Velocity known at some section (control section) Assume small change in depth Standard Step Method Depth and velocity known at control section Assume a small change in channel length 43

Related


More Related Content

giItT1WQy@!-/#giItT1WQy@!-/#giItT1WQy@!-/#giItT1WQy@!-/#