1. 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
Cross-section/velocity measurements
Dilution gaging with salt or dye
Artificial controls like weirs
Empirical equations, e.g. Manning’s eqn.

2. 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

3. Other considerations 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

4. of discharge measurement
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

5. Rotations make clicking
Pygmy Meter
Rotations make clicking
sound in headphones
If current strong
may need weight
U Mass, Boston

6. 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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7. Velocity Distribution In A Channel
Depth-averaged velocity is above the bed at about 0.4 times the depth

8. Photo from Black Hills State University

9. 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

10. 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

11. 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.

12. 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

13. 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

14. 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
U Mass, Boston

15. Float Method surface velocity = distance / time
average velocity = (0.8*surface velocity)
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16. Float method in action
U Mass, Boston

17. Dilution gaging method
Use a chemical tracer, dye or salt
Exotic to stream
Stable
Non-toxic
Cheap
Detectable
Do mass balance on concentrations upstream and downstream

18. 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

19. Stream Stage- elevation
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
U Mass, Boston

20. Fixed Gauging Stations - Weirs
Stable cross section with simple geometry
rating curve – just measure stage
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21. How do we measure the stage?
Nonrecording gauges
Staff Gauge
Estimating Peak Flow
Debris Line
Crest Gauges - Cork
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22. Continuous Measurement - Water Level Recorders
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23. The Stage of a Stream Float moves up / down with water surface
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24. 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.

25. Rating curve We can do this is Excel Very often it is a power
equation (log-log)
Fit a mathematical equation
U Mass, Boston

26. Resistance Equations
Manning’s Equation
Equation 7.2

27. Manning’s Equation
In 1889 Irish Engineer, Robert Manning presented the formula:
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.

28. Discharge from Manning’s equation
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

29. 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

30. 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.

31. 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
0.045
0.05
Same as above, lower stages and more stones
0.06
Sluggish reaches, weedy, deep pools
0.07
Very weedy reaches, deep pools, or floodways
0.075
0.1
0.15
with heavy stand of timber and underbrush
Mountain streams, no vegetation in channel, banks steep, trees & brush along banks submerged at high stages
Bottom: gravels, cobbles, and few boulders
0.04
Bottom: cobbles with large boulders

33. Mountain
Stream-
Bottom with
cobbles and
large boulders

34. Plains stream-
full stage, no rifts
or deep pools

35. n = (n0 + n1 + n2 + n3 + n4 ) m5 Equation 7.12
Table 7.2. Values for the computation of the roughness coefficient (Chow, 1959)
n = (n0 + n1 + n2 + n3 + n4 ) m5 Equation 7.12