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.

Site factors for gaging

1. stable control - bedrock, non-erosive channel, man-made structure

2. locate gage a short distance above control3. want minimal backwater or tidal influence4. straight reach above gage for 4-5 channel widths5. No local inflows or outflows- groundwater or flood bypasses6. must be accessible at all times7. securely mounted structure8. stable confining banks9. good to have a benchmark nearby for datum10. good to have an auxillary stage nearby- staff gage

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

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 MeterRotations make clicking

sound in headphones

If current strong may need weight

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Velocity Profile

0.6 depth

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0.8

0.2

If stream is deep, take average of measurements at 0.2 and 0.8

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

Water surface

Tape measure- horizontal location of measures taken from tape

Velocity measured 0.6d from water surface (0.4d from bottom)

Record x value (tape distance), y value (total depth at measurementsite, and velocity at 0.6d

Measurement represents mid-section of a polygon

Velocity – Area method of discharge measurement

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.

Mid-point method of calculating discharge (Q)Location of depth and velocity measurements

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) U Mass, Boston

Float method in action

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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

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

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

How else might we estimate streamflow?

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Fixed Gauging Stations - Weirs

Stable cross section with simple geometryrating curve – just measure stage

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Nonrecording gauges

Staff Gauge

Estimating Peak Flow

Debris Line

Crest Gauges - Cork

How do we measure the stage?

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Continuous Measurement - Water Level Recorders

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The Stage of a Stream

Float moves up / down with water surfaceU Mass, Boston

Measure discharge at different flows

How can we relate stage to discharge?

Rating Curve – relates stage to discharge Empirical relationship from observations

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.

Rating curve

Fit a mathematical equation

We can do this is Excel

Very often it is a power equation (log-log)

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Resistance Equations

Manning’s Equation Equation 7.2

2132 SRn

49.1v

Manning’s Equation• In 1889 Irish Engineer, Robert Manning

presented the formula:

2132 SRn

49.1v

• 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.

Equation 7.2

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

Parameters for Manning’s equation

Wetted perimeter = p area of stream in contact with bottom and sides

Water surface

Cross sectional area = A

R = hydraulic radius = A/p

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.

Mid-point method of calculating discharge (Q)Location of depth and velocity measurements

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

Sluggish reaches, weedy, deep pools 0.05 0.07 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 0.03 0.04 0.05

Bottom: cobbles with large boulders 0.04 0.05 0.07

Table 7.1 Manning’s n Roughness Coefficient

http://manningsn.sdsu.edu/barnes013_24.html

http://manningsn.sdsu.edu/barnes101_41.html

MountainStream-Bottom with cobbles and large boulders

Plains stream- full stage, no rifts or deep pools

http://manningsn.sdsu.edu/barnes020_27.html

Channel Conditions Values Material Involved Earth n0 0.025

Rock Cut 0.025 Fine Gravel 0.024 Coarse Gravel 0.027 Degree of irregularity Smooth n1 0.000 Minor 0.005 Moderate 0.010 Severe 0.020 Variations of Channel Cross

Section Gradual n2 0.000

Alternating Occasionally 0.005 Alternating Frequently 0.010-0.015 Relative Effect of Obstructions Negligible n3 0.000 Minor 0.010-0.015 Appreciable 0.020-0.030 Severe 0.040-0.060 Vegetation Low n4 0.005-0.010 Medium 0.010-0.025 High 0.025-0.050 Very High 0.050-0.100 Degree of Meandering Minor m5 1.000 Appreciable 1.150 Severe 1.300

Table 7.2. Values for the computation of the roughness coefficient (Chow, 1959)

n = (n0 + n1 + n2 + n3 + n4 ) m5 Equation 7.12