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 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 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

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

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

Velocity Profile 0.2 0.6 depth 0.8 If stream is deep, take average of measurements at 0.2 and 0.8 U Mass, Boston

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 U Mass, Boston

Float Method surface velocity = distance / time average velocity = (0.8*surface velocity) U Mass, Boston

Float method in action U Mass, Boston

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 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

Fixed Gauging Stations - Weirs Stable cross section with simple geometry rating curve – just measure stage U Mass Boston

How do we measure the stage? Nonrecording gauges Staff Gauge Estimating Peak Flow Debris Line Crest Gauges - Cork U Mass, Boston

Continuous Measurement - Water Level Recorders U Mass, Boston

The Stage of a Stream Float moves up / down with water surface U Mass, Boston

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.

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

Resistance Equations Manning’s Equation Equation 7.2

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.

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 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 0.045 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

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

Mountain Stream- Bottom with cobbles and large boulders http://manningsn.sdsu.edu/barnes101_41.html

Plains stream- full stage, no rifts or deep pools http://manningsn.sdsu.edu/barnes020_27.html

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