How do we measure how much
water is in a stream?
• Volumetric measurements– Work on very low flows, collect a known
volume of water for a known period of time
Volume/time is discharge or Q
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Cross-section/velocity measurements
Dilution gaging with salt or dye
Artificial controls like weirs
Empirical equations, e.g. Manning’s eqn.
Site factors for gaging
1. stable control - bedrock, non-erosive channel, man-made
structure
2. locate gage a short distance above control
3. want minimal backwater or tidal influence
4. straight reach above gage for 4-5 channel widths
5. No local inflows or outflows- groundwater or flood
bypasses
6. must be accessible at all times
7. securely mounted structure
8. stable confining banks
9. good to have a benchmark nearby for datum
10. good to have an auxillary stage nearby- staff gage
Other considerations
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Few eddies or areas of zero velocity
Few instream obstacles
Relatively consistent cross-section profile
Velocity and depth do not exceed
instrument capabilities or personnel height
Velocity – Area Method
of discharge measurement
By measuring the cross-sectional area of the stream and the
Average stream velocity, you can compute discharge
Q = VA units are L3/t (volume / time)
Where Q is discharge
V is velocity
A is cross-sectional area
Pygmy Meter
Rotations make clicking
sound in headphones
If current strong
may need weight
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Velocity Profile
0.2
0.6 depth
0.8
If stream is deep, take average of measurements at 0.2 and 0.8
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Velocity Distribution In A Channel
Depth-averaged velocity is above
the bed at about 0.4 times the depth
Photo from Black Hills State University
How many subsections?
• Subsections should be at least 0.3 feet or
~0.1 m wide
• Each subsection should have 10% or less of
total discharge
• Number of subsections should be doable
in a reasonable amount of time
Velocity – Area method of discharge
measurement
Tape measure- horizontal location of measures taken from tape
Water surface
Measurement represents mid-section of a polygon
Velocity measured 0.6d from water surface (0.4d from bottom)
Record x value (tape distance), y value (total depth at measurement
site, and velocity at 0.6d
Mid-point method of calculating discharge (Q)
Location of depth and velocity measurements
Area included
Area not included
Key Assumption: Over estimation (area included) = Under estimation (area not included),
therefore cross-section area is simply the sum of all the sections (rectangles), which is much
easier than taking the integral! However, the hypotenuse of each over-under estimation
triangle can be used to calculate the wetted perimeter.
Equation for computing subsection
discharge - qi
Equation for computing q in each subsection
X = distance of each velocity point along tape
Y = depth of flow where velocity is measured
V = velocity
Q = total discharge = sum of qis
Float method of discharge
measurement
• Gives good estimates when no equipment is
available
• Use something that floats that you can
retrieve or is biodegradable if you can’t
retrieve it
– E.g. oranges, dried orange peels, tennis balls
Float method of velocity measurement
Three people are needed to run the float test. One should be positioned
upstream and the other downstream a known distance apart, one in the
middle to record data.
The upstream person releases the f loat and starts the clock and the
downstream person catches the float and signals to stop the clock. The
recorder writes down the time of travel of the float.
Velocity is the distance traveled divided by the time it takes to travel that
distance.
You should conduct at least 3 float tests and take an average velocity.
With an estimate of cross-sectional area, discharge can be computed as
Q = VA where V is average velocity
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Float Method
surface velocity = distance / time
average velocity = (0.8*surface velocity)
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Float method in action
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Dilution gaging method
• Use a chemical tracer, dye or salt
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–
–
–
–
Exotic to stream
Stable
Non-toxic
Cheap
Detectable
• Do mass balance on concentrations
upstream and downstream
Constant injection method
• Inject at known rate for some time period
• Do mass balance
• CTQT = CTd (Q + QT)
– CT is concentration of tracer upstream
– QT rate of input of tracer upstream
– CTd is equilibrium concentration of tracer downstream
• Q = QT (CT - CTd )
CTd
How else might we estimate streamflow?
Stream Stage- elevation
The stage of a stream is the elevation
of the water surface above a datum.
The most commonly used datum is mean sea level.
Gages are used to measure the stage of streams.
Types of gages:
- recording
- non-recording
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Fixed Gauging Stations - Weirs
Stable cross section with simple geometry
rating curve – just measure stage
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How do we measure the stage?
Nonrecording gauges
Staff Gauge
Estimating Peak Flow
Debris Line
Crest Gauges - Cork
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Continuous Measurement - Water Level Recorders
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The Stage of a Stream
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Float moves up / down with water surface
How can we relate stage to discharge?
Rating Curve – relates stage to discharge
Empirical
relationship
from
observations
Measure
discharge
at different
flows
USGS
Rating curves usually have a break point, which is around the stage at which the river
spreads out of it's banks, or it could be at a lower stage if the river bed cross section
changes dramatically. Above that stage, the river does not rise as fast, given that other
conditions remain constant. This is illustrated by a change in slope in the rating curve.
On this figure the break point appears to be around 6-7 feet.
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Rating curve
We can do this is Excel
Very often it is a power
equation (log-log)
Fit a mathematical equation
Resistance Equations
Manning’s Equation
1.49 2 3 1 2
v
R S
n
Equation 7.2
Manning’s Equation
• In 1889 Irish Engineer, Robert Manning
presented the formula:
1.49 2 3 1 2
v
R S
n
Equation 7.2
• v is the flow velocity (ft/s)
• n is known as Manning’s n and is a coefficient of roughness
• R is the hydraulic radius (a/P) where P is the wetted perimeter (ft)
• S is the channel bed slope as a fraction
• 1.49 is a unit conversion factor. Approximated as 1.5 in the book.
Use 1.0 if SI (metric) units are used.
Discharge from Manning’s equation
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Q = vA equation 7.1
v =(1.5/n) R2/3 S1/2 (equation 7.2)
R= A/P, hydraulic radius (equation 7.3)
A = width x depth
P= wetted perimeter
S = water slope (ft/ft)
N = Manning’s roughness coefficient
Parameters for Manning’s equation
Water surface
Cross sectional area = A
Wetted perimeter = p area of stream in contact with
bottom and sides
R = hydraulic radius = A/p
Mid-point method of calculating discharge (Q)
Location of depth and velocity measurements
Area included
Area not included
Key Assumption: Over estimation (area included) = Under estimation (area not included),
therefore cross-section area is simply the sum of all the sections (rectangles), which is much
easier than taking the integral! However, the hypotenuse of each over-under estimation
triangle can be used to calculate the wetted perimeter.
Table 7.1 Manning’s n Roughness Coefficient
Type of Channel and Description
Minimum Normal
Maximum
Streams on a plain
Clean, straight, full stage, no rifts or deep pools
0.025
0.03
0.033
Clean, winding, some pools, shoals, weeds &
stones
0.033
0.045
0.05
Same as above, lower stages and more stones
0.045
0.05
0.06
0.05
0.07
0.07
0.075
0.1
0.15
Bottom: gravels, cobbles, and few boulders
0.03
0.04
0.05
Bottom: cobbles with large boulders
0.04
0.05
0.07
Sluggish reaches, weedy, deep pools
Very weedy reaches, deep pools, or floodways
with heavy stand of timber and underbrush
Mountain streams, no vegetation in channel,
banks steep, trees & brush along banks
submerged at high stages
http://manningsn.sdsu.edu/barnes013_24.html
Mountain
StreamBottom with
cobbles and
large boulders
http://manningsn.sdsu.edu/barnes101_41.html
Plains streamfull stage, no rifts
or deep pools
http://manningsn.sdsu.edu/barnes020_27.html
Table 7.2. Values for the computation of the roughness coefficient (Chow, 1959)
Channel Conditions
Material Involved
Degree of irregularity
Variations of Channel Cross
Section
Relative Effect of Obstructions
Vegetation
Degree of Meandering
Earth
Values
n0
0.025
Rock Cut
0.025
Fine Gravel
0.024
Coarse Gravel
0.027
Smooth
n1
0.000
Minor
0.005
Moderate
0.010
Severe
0.020
Gradual
n2
0.000
Alternating Occasionally
0.005
Alternating Frequently
0.010-0.015
Negligible
n3
0.000
Minor
0.010-0.015
Appreciable
0.020-0.030
Severe
0.040-0.060
Low
n4
0.005-0.010
Medium
0.010-0.025
High
0.025-0.050
Very High
0.050-0.100
Minor
m5
1.000
Appreciable
1.150
Severe
1.300
n = (n0 + n1 + n2 + n3 + n4 ) m5
Equation 7.12