we will now move on to study rating curves for natural channels
DESCRIPTION
We will now move on to study rating curves for natural channels. Overbank. Gh - e. Channel Control. Section Control. Discharge. The relation between stage and discharge in a natural channel can also be assumed to be a power function. - PowerPoint PPT PresentationTRANSCRIPT
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We will now move on to study rating curves for natural channels
SectionControl
ChannelControl
Overbank
Gh
- e
Discharge
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The relation between stage and discharge in a natural channel can also be assumed to be a power function
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Here is the power function that is often used to relate discharge and head under section control
Q = a(GH-e)b
where:a = coefficientb = slope of the relation(b is almost always greater than 2)
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Here is the equation that is often used to relate discharge and head under channel control
Manning’s equation:Q = 1.486 A R 2/3 S 1/2 n
Where:A = cross section areaR = hydraulic radius (area/wetted perimeter)S = energy slopen = Manning’s “n” (roughness coefficient)
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Manning equation can be reduced to a simple power function
Q = 1.486 A R 2/3 S 1/2 n Can be reduced to:
Q = C d1.67 = C (GH-e)1.67
Click here if you want to see how this is done.
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Just to be sure we all know how to use exponents and how to compute basic hydraulic parameters we will go through a brief math primer
Q = 2.5 x 20 x 2 1.50 =
Weir equation: Q = CBH 3/2
whereC = 2.5, B = Top width = 20 ftH = Average depth of flow = 2 ft
141 ft3/s
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Math Primer (cont)
Manning equation:Q = 1.486 AR 2/3 S 1/2
nwhere:
n = roughness coefficient = 0.05A = cross sectional area = 500 ft2
R = Hydraulic Radius (area / wetted perimeter) = 4.5 ftS = Energy slope (assume to be same as water surface
slope = 0.002 ft/ft
Q = 1.486 x 500 x 4.5 .667 x 0.0021/2 = 0.05
1812 ft3/s
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Math Primer (cont).
Compute area for gh = 10 ft
Area for main channel =
0 ft
10 ft
5 ft
(10 x 100) – ((5 x 100)/2) = 750 ft2
Area for overflow = (5 x 100) = 500 ft2
TOTAL AREA = 1250 ft2
100 ft0 ft 200 ft
Sand bar
Overflow
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Math Primer (cont.)
Compute WP, and R for gh = 12 ft
WP for main channel =
2 ft
12 ft
7 ft
10 + 100 + 5 = 115 ftWP for overflow = 100 + 5 = 105 ft
TOTAL WP = 220 ft
R = A / WP = (1000 + 500) / 220 = 6.82 ft
100 ft0 ft 200 ft
Overflow
Note: WP does not increase on main channel left bank above gh of 5 ft. There is no boundary friction there.
1000 ft2500 ft2
Main Channel
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Rating curve slopes can provide insights to control conditions
<21
>21
SectionControl
ChannelControl
Overbank
Gh
- e
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1
10
1 10 100Discharge
Gag
e H
eigh
tHere is how to measure rating curve slopes
<2 (usually 1.3 to 1.8)
>2
1
1
Measure down one unit then measure horizontal distance to rating using same unit of measure slope. Rating mustbe straight line and scales cannot be distorted!
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San Francisquito Creek
0.01
0.1
1
10
100
0.1 1 10 100 1000 10000Discharge, in cfs
Gag
e H
eigh
t - o
ffset
An example of a rating and controls
PZF = 0.07
G.H. = 5.4
G.H. = 6.25
Click here to see video of control at high flow (1.2 MB file)
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Artificial controls can also have compound shapes
Artificial section control
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Multiple offsets can be used to straighten different parts of ratings
• Use of multiple offsets makes sense for many ratings• GRSAT making working with multiple offsets easy!
Offset = 3
Offset = 1
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You must smooth the transition between rating segments when multiple offsets are used!
Click on the photo below to view an animation of changing controls
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It is often necessary to extend ratings to stages above or below where measurements have been made
??
?
?
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Ratings can be extended to low stages by:
1. Using arithmetic-scale graph and the PZF as a guide.
2. Using knowledge of the control
3. Using hydraulic equations
Point of zero flow
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Ratings can be extended to high stages by:
1. Plotting techniques• Use straight line, knowledge of
control.2. Slope-conveyance3. Step-backwater model4. Areal comparison of peak runoff rates5. Flood routing
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• Rule of Thumb -- Do NOT extend beyond twice the highest measured discharge (this may be a direct or indirect measurement)
Here is a rule of thumb to keep in mind when extending ratings
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1
10
100
10 100 1000
Discharge
Stag
e
?
?
The wrong offset can increase uncertainty when extending ratings
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10 100 1000
Discharge
Stag
e 2015
6
Straight lineextension
You can be much more certain of how to extending the rating when the correct offset is used!
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ChannelControl
Overbank
Gag
e he
ight
Rating extensions must consider channel geometry
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When to Draw a New Rating?
• When measurements indicate a significant, consistent, and permanent departure from the current rating, especially on the upper end.
• When the shape of the shift diagrams departs significantly from the shape of the rating.