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CHAPTER 2.RUNOFFPrincipal contributors:W. R. Gwinn, SEA hydraulic engineer (chapter coordinator)USDA/SEA Hydraulic Structures LaboratoryOklahoma State UniversityStillwater, Okla.K. G. Renard, SEA hydraulic engineer (chapter coordinator)USDA/SEA Southwest Watershed Research CenterTucson, Ariz.J. B. Burford, SEA hydraulic engineerUSDA/SEA Hydrologic Data LaboratoryBeltsville, Md.D. L. Chery, Jr., SEA hydraulic engineerUSDA/SEA Southwest Watershed Research CenterTucson, Ariz.L. L. Harrold, SEA hydraulic engineer (retired)USDA/SEA North Appalachian Experimental WatershedCoshocton, OhioH. N. Holtan, SEA hydraulic engineer (retired)USDA/SEA Hydrograph LaboratoryBeltsville, Md.C. W. Johnson, SEA hydraulic engineerUSDA/SEA Northwest Watershed Research CenterBoise, IdahoN. E. Minshall, SEA hydraulic engineer (retired)Agriculture Engineering DepartmentUniversity of WisconsinMadison, Wis.W. 0. Ree, SEA hydraulic engineer (retired)USDA/SEA Hydraulic Structures LaboratoryOklahoma State UniversityStillwater, Okla.R. R. School’, SEA hydraulic engineerUSDA/SEA Southern Great Plains Watershed Research CenterChickasha, Okla.P. Yates, SEA agricultural engineerUSDA/SEA Southeast Watershed Research CenterAthens, Ga.75

on of gaging station controlPrecalibrated devices for measuringrunoffWeirsFlumesExisting structuresHighway box culvertsSoil conservationInstallation of the HS, H, and HLflumesSubmergence effect on H flumesRating malformed flumes and weirsPreparation of rating tablesPondage correctionsNatural controlsOther factors in selecting gagingstation locationsInstrumentationWater stage recordStilling wellField observations and maintenanceInstrument and equipment notationand maintenanceNonrecording gagesRecorder chart notation andmaintenanceEquipment servicingStage recordersMiscellaneous gaging equipmentDischarge measurementSelecting the measuring stationGage datum maintenanceRunoff into farm ponds a reduction and processingAnalog chart record processingDigital punch tape processingDischarge measurement calculationMissing recordsEstimating recessionsHigh watermarksComparison with runoff or retentionfrom nearby watershedsEstimate of flow during ice periodsManual calculationsCalculations for pondage correctionsCheck method for total runoffComputer calculationsComputer check of digital recordUpdating the basic dataInstantaneous discharge valuesNumerical integration with noadjustment for pondingNumerical integration withadjustment for pondingNumerical integration withadjustment for pondage and rainon the pondAlternative method for dischargedeterminationFlow duration computationsRoutine for flow durations andvolumeMaximum (or minimum) volume forselection time intervalcomputationsSummary 194194200202203204204204205205205209210210212213

77INTRODUCTIONThe objectives of a study influence selectionof a runoff measuring device. For example, if awater budget is studied in an area where runoffaccounts for only about 5 percent of the waterbudget, 95 percent of the funds should not bespent on measurement of runoff. More fundsshould be directed to other parts of the hydrologic cycle. If the objective of a study, on theother hand, is to measure the effect of landtreatment on the water supply derived from awatershed, a precalibrated runoff measuringdevice would be required. Less funds and timeshould be directed to other parts of the hydrologic cycle.This chapter provides guidance on selectingdevices for measuring runoff. It also providesguidance on types of recorders, field installationand maintenance of a station, and how toprocess data.INSTALLATIONSSelection of a device for measuring runoffdepends on such factors as the peak runoffrate; distribution of runoff volume by categories of flow rate; absence or presence ofsediment or woody trash, or both, in the flow;whether backwater submergence will affectflow through the device; icing conditions; foundation conditions; material availability; andeconomics.The term “runoff’ normally is used to distinguish surface flows from ground-water contributions to a streamflow. This distinction generally is derived through analysis of hydrographssince independent measurement is not feasible.The terms “runoff” and “streamflow” are usedinterchangeably here. They refer to all theflow, regardless of origin, that passes throughthe control at the point of measurement.Selection of Gaging Station ControlIn open channels, a control is a cross sectionor length of reach above which the water levelis a stable index of the discharge rate. Allsections have equal capacity to pass a flow. Innatural streams the control may shift from onepoint to another with changes in stage. For useas a runoff station, a control must be selected,altered, or constructed to provide a stable headdischarge relationship.Many conditions influence selection of a control for flow measurements. The ultimate objective is to provide a stable relationship betweenthe depth of water and the rate of flow. Sincethe rate of flow equals the product of averagevelocity and the cross-sectional area, controlsshould be selected for stability of cross sectionand such factors as slope; configuration; channel roughness; and absence of tailwater, whichaffects velocity.Quantitative evaluation of flow is easier ifthe flow passes from subcritical to supercriticalaround the control section. Precalibrated devices use this advantage. Natural controls thatmaintain critical flow at all stages are unusual.They are selected, therefore, to provide subcritical velocities at all depths since changes indepth are approximately equal to changes inspecific energy. Measurement of flow at criticaldepth should be avoided since it presents somany difficulties. This sometimes can be accomplished by converting to subcritical flowthrough impoundment or manipulation of thechannel gradient. The flow subsequently canpass through critical downstream of the pointof head measurement.For some purposes the control must be located so that gaged streamflow represents theentire flow from the watershed—none escapesbeneath or around the control. Cutoff wallsextending vertically in impervious strata and

78laterally in floodplains may be needed to prevent flow from bypassing the gaging station.Bypassing flow may be unimportant for somestudies and at some locations.Other considerations in selecting a controlinclude capacity needed for major flows; silt,ice, and debris content of expected flows; andstructural requirements such as footings andprotection against frost heaving. Controls areclassified herein as (1) precalibrated devices, (2)existing structures adapted to calibration, and(3) natural controls, such as cross sections orchannel reaches with suitable hydraulic characteristics for calibration. Procedures for eachclass will be given.A flow chart to assist in selecting a runoffmeasuring device is shown in figure 2.1. Although other criteria besides size may be usedin selection, the use of size is convenient. Thus,the primary key to the flow chart is the maximum discharge rate to be selected. The flowchart provides paths based on the absence orpresence of debris, type of flow in the approachchannel, whether ponding is allowed, whetherbackwater problems are anticipated, and, finally, the type of stream and flow characteristics (perennial streams have relatively long,constant requirements for measuring baseflow). Although a flow chart is a quick reference, the following material should be checkedcarefully to ensure selection of the best measuring device for the flow conditions encountered.Precalibrated Devices for MeasuringRunoffDevices for measuring runoff usually areselected to meet specific needs at each location.Runoff should be measured as accurately aspossible at low, medium, and high rates ofdischarge. Flow occurs on some watershedsonly as the result of occasional storms of highintensity. Other watersheds have continuousflow.Wherever possible, precalibrated devicesshould be used to gage the entire flow. Forlarge watersheds, precalibrated devices largeenough to gage high rates of flow may not befeasibla Instead, a precalibrated device may beneeded to measure low flows and current-metermeasurements may be needed to establish thehigh part of the stage-discharge relationship.WeirsA weir is a low dam or overflow structurebuilt across an open channel. It has a specificsize and shape with a unique free-flow, head.discharge relationship. The edge or surfaceover which the water flows is called the crest.Discharge rates are determined by measuringthe vertical distance from the crest to thewater surface in the pool upstream from thecrest. When the water level in the downstreamchannel is sufficiently below the crest to allowfree aeration of the nappe (the thin sheet ofwater falling over the crest), the flow is said tobe free. If the nappe is partially under water,the weir is said to be submerged and the headdischarge relationship may not be unique. Ifsubmergence is permitted, special head-discharge computations may be necessary andaccuracy of measuring the flow may be reduced. Do not install weirs for measuring runoffsites where concentrations of sediment exceedlow values.Many formulas and shapes and sizes of weirsare used to compute the discharge rate. Somecommonly used weirs will be described here.Sharp-Edged WeirsKindsvater and others (22) developed amethod for computing rates of flow over rectangular, sharp-edged weirs. Their method includes both suppressed and unsuppressed freedischarge weirs with correction factors for approach velocity. These factors change with theratio of crest length to approach channel widthand with the ratio of head-to-crest height abovethe bottom of the approach channel or weirbox.V-notched WeirsTriangular or V-notched weirs measure lowdischarges more accurately than horizontalweirs. The V-notch is usually a 900 openingwith the sides of. the notch inclined 45 with thevertical. The approach velocity can be neglectedif the minimum distance from the weir to thechannel banks is at least twice the head and ifthe minimum distance from the channel bottomto the crest is at least twice the head.

79CONTINUEDFIGURE 2.1.—Se ection guide for measuring runoff.

soCONTINUEDFIGURE 2.1.—Selection guide for measuring runoff.

81FIGURE 2.’ CONTINUEDflOURS 2.1.—Selection guide for measuring runoff.Broathcrested V-Notched WeirsSharp-crested V-notched weirs are difficult tomaintain if they are used to obtain dischargerecords for long periods. They may become dulldue to impact from ice or drift (11). Broadcrested V-notched weirs, over which ice anddebris pass without damage, are desirable formeasuring runoff over long periods. These arecalled triangular weirs.Triangular weirs with 2-to-i, 3-to-i, 5-to-i,and 10-to-i crests measure flows larger than1,000 ft3/s (7.9 lls). A 3-to-i triangular weirinstallation is shown in figure 2.2. The recorderfor water stages is located on a stilling well 10feet (3 m) upstream from the weii’. A reasonably straight channel that is level for 50 feet (i5m) above the weir is essential for accuracy. Thenotch must be 6 inches (15.2 cm) above thebottom of the channel.Cross-sectional dimensions are given in figure2.3. A weir of this size needs a substantialapron of concrete for about i2 feet (3.7 m)downstream from the weir, 2 feet (0.6i m) belowthe notch, and 20 feet (61 m) across the channel.A 3-foot (0.91 m) (plus) end cutoff wall also isneeded to prevent the weir from being undermined. The middle 10-foot (3 m) width of thisapron is level, and the two 5-foot (1.5 m) sidesare sloped slightly more than the weir crest.Calibration of these weirs, as given in table2.1, is affected by the approach velocity. Thecross-sectional area of the approach channel iOfeet (3 m) upstream from the weir at the pointof recording gage heights, is a measure of theapproach velocity. Table 2.1 supplies dischargefigures at each foot of head from 1 to 6 feet (0-3to 1.8 m) for several areas of cross section. Forexample, the discharge for a 3-to-i weir at 2foot (0.61 m) head and a section area of 40 ft2(3.7 m2) is 48.7 ft /s (380 cm /s). For an area of 62ft2 (5.76 m2) the discharge is 47.5 ft3/s (379cm /s).

82P N—Se 7 7FIGURE 2.2.—Installed triangular weir with 3-to-i side slopes, recorder shelter, and stilling well.The basic expression for discharge through aV-notch neglecting velocity of approach is:(2—1)Q CttanH2s cfs \/ tanHL50total angle of V-notch opening (for 900,tan 0/2 1.0);H head above the lowest point of the Vnotch (ft); andg gravitational acceleration (ft2/s).Most engineers consider the experimental workof Cone (11) very reliable. His formula for the900 V-notch weir is: —Qwhere 149 H2.1K(2—2)whereQ C discharge (ft /s);coefficient correcting for energy lossand contraction of the jet;2gC;Q discharge (ft3/s); andH head above lowest point of V-notch (ftO.Equation 2.2 can be generalized for values of 00between 60 and 90 by adding the tan term

83oreQ 2.49 tan(2—3)H2.4Sfor heads between 0.2 and 2.0 feet. The sameequation in metric units would be: 1.342 tan(24)Hm2 wheredischarge (cubic meters per second);andH,,, head above the lowest point in the Vnotch (meters).Likewise, this equation is accurate (1 percent)for 0 between 60 and 900 with heads between0.06 and 0.6 meter.For angles smaller than 60 , the experimentalresults reported by Lenz (24) should be used,The water-discharge equation without any correction for temperature is: (2.395 ) tan(2—5)H25 0.2475( DM9 ) The term 0.522 N/(3.281 H,/) always shouldhave a value equal to or less than 0.05.The stage-discharge relation is approximatedby use of the equations in figure 2.3. Wheneverpractical, make current-meter measurementstocheckthis calibration.Any largecuttingorfillingchangesin the approachcrosssectionmay require a revision of the calibration.Rating values for heads between 0.2 and 0.8foot may be obtained by [2.51 0.0066 tan[0.3292 0.5074/tan ]lo ioH]tan ;H2.3 whereQandH(2—7)discharge, cubic feet per second (ft3/s); s in Total angle of V notch (tanfig. 2.3); head above the point of zero flow on the V-notch, feet.This equation is based on full-scale tests withFor a water temperature of 70 :N 0.035 0.033 (tan 0.2475 tanE ’ 9 o.34o tan )negligible approach velocity. These tests wererun in the SEA hydraulic laboratory at Still-and 0.340 (tan )water, OkIa. Tan This formula is recommended for 0 anglesbetween 28 and 90 . The value of N/H alwaysshould be equal to or less than 0.09. If the weiris installed with complete contraction, the approach velocity will be low and can be neglectedin the head-discharge relationship.The value of discharge, Q, equation 2—5,expressed in cubic meters per second would be:varied between 2 and 10.The same equation for discharge in cubic meters per second for H,0 between 0.06 and 0.3meter is:c,,, 1.4795 0.003644 tan 0 0.1445tan—2 (0.18175 } Log,0 H,,,tan o0.28013\otan (2—8)(1.3220.522 N3.28P’ H,0 ) tanH 25whereH,,, head in meters;N 0.035 0.033 (tan )-0.8; and(2 )Dro BoxThe drop-box weir was modeled at Washington State University. Use of this weir to improve the accuracy of measuring water underheavy sediment load and varying conditions ofapproach was reported by Copp and Tinney

84TABLE2.1—Discharge values corresponding to various cross-sectional areas of the channel ofapproach 10 feet upstream from center of crest for triangular weir&2:1 TRIANGULAR WEIRS1-foot .040.045.050.060.070.080.02-foot 5.030.035.040.050.060.080.0110.0150.03-foot head4-foot head5-foot head6-foot 504503502501425388373360352345339334 589.088.888.688.488.288.088.088.088.03:1 TRIANGULAR 082.084.086.088.090.092.0

85TABLE 2.1 —Discharge values corresponding to various cross-sectional areas of the channel ofapproach 70 feet upstream from center of crest for triangular weirs’—Continued3:1 TRIANGULAR WEIRS—Con.1-foot head2-food head3-foot head4-foot head5-foot head6-foot schargeAreaDischargeAreaDischargeFtFtW5Ft’Ft 313471341133613311326132213105:1 TRIANGULAR 90200210220230

86TABLE 2.1 —Discharge values corresponding to vatious cross-sectional areas of the channel ofapproach 10 feet upstream from center of crest for triangular weirs1—Continued5:1 TRIANGULAR WEIRS—Con.1-foot head2-food head3-foot headAreaDischargeAreaDischargeAreaDischargeFt2Ft 018020022023223123022914017020030080.880.680.580 S250300400500228227226226‘4-foot head5-foot head6-foot headDischargeAreaDigchargeAreaDischargeFt 12751272127012701270AreaFtZ240Based on hydraulic laboratory tests made by the Soil Conservation Service at Cornell University, Ithaca, N.Y.S 2. 3. 5. or ICELEVATIONZ1?(18). Johnson, Copp, and Tinney (21) reported onfield experience with the drop-box weir in theReynolds Creek Experimental Watershed. Thisweir is shown in figure 2.4.The depth of the 1-to-i V-notch weir was usedto provide dimensionless proportion of the weir.The depth in the drop-box weir was 8 feet (2.4m) or 1 D. The following dimensionless equationof discharge is recommended: LXIi.67\/ ( )(2—9)coLTOP 96”,4or;VIEW6 1.67- / H4 Ii 2k” ‘1.t(6”g2 ”L(IJ SECTION(2—10),—— Rods spoced2’ on centersboth woysA-AFIGURE 2.3.—Shape of a standard cross section of atriangular weir with a 16-inch (40.6 cm) crest.whereQdischarge, (ft3/s);acceleration due to gravity (ft/s); head measured at gage 4 (fig. 2.3), feet;andD depth of 1-to-i V-section, feet.Equation 2—10 has a range of H4ID valuesbetween 0.25 and 0.7. Precalibration tests areunnecessary for flow within this range. FieldgH4

2.5Section B-SUpstream ElevationSection c-c(Wok not Shown)Buttress0.1250C-SExtend to bankDrop-Box Weir DetailPlanFIGURE 2.4—-Dirnensions of the Salmon Creek weis of the Reynolds Creek Watershed, Idaho.Section D-DCenter Watt

88calibration tests are necessary for flows withH4ID values less than 0.25.Ratings above HID value of 0.7 have thefollowing limitations: Placement of the weir creates an approach angle (with the weir centerline) of 5 orless. The approach bed slope must be lessthan about 5 percent. Accuracy of the discharge rating mustbe within 5 percent.The formula for gage 1 for H4ID values between0.7 and 1.3 is:Q 1.73’ /g (H4)I.1D25(2—11) The formula for gage 2 for H5ID values between0.8” and 1.7 is:Q 1.20 / 1.20 J H5I9D06.(2—12)Periodic maintenance will be required to keepthe cage openings free from sediment and tokeep the box sidewall orifice from becomingblocked with debris.The estimated capacity of Salmon Creek was7,000 ft3/s (19.8 m Is). No model data werereported, however, in this range of discharge.The value of D can be determined for designingby using the maximum discharge in the following formula:D [QjO.46.8 ,/gThis equation was obtained using the capacityof Salmon Creek, which is 7,000 ft3ls (19.8 m3Is).The dimensions of the weir then may be determined using the Salmon Creek dimensions (fig.2.3) divided by 8 feet (2.4 m) and multiplied byDFlumesThere are many types of precalibratedflumes. Most flumes use the principle of mini-mum energy or critical depth. Critical-depthflumes fall into two categories: (1) Flumeswhere critical depth occurs in region of curvilinear flow and (2) flumes for which the lengthdimension is such that critical flow occurs in aregion where the flow lines are parallel ornearly parallel. Flumes that have little obstruction to the transport of these solids should beused to measure runoff where suspended andbedload solids are present in the flow. Whereflow contains heavy suspended or bedload solidsand velocity is reduced in the measuring section of the flume, material may deposit andinterfere with performance of the flow. If reduction in velocity and deposit of sediment occurbefore the flow enters the flume, the flume willperform correctly.Since HS flumes are designed to measurevery small flows with a high degree of accuracy,construct them in strict accordance with thedrawings and the following provisions. Theslanting opening must be bound by straightedges and have precisely the dimensions shownon the drawings. The opening must lie in aplane with an inclination of the exact degreeshown on the drawings. Prepare detailed drawings, using proportional dimensions shown infigure 2.5, with care taken to maintain thedimensional tolerance. Construction details aregiven with the discussion on H flumes.Use the discharge equations for HS flumes infigures 2.6 and 2.7. These equations contain thebasic dimensions that define the control sectionof the flume. Table 2.2 gives ratings for HSflumes of various sizes.H Flumes:Measure runoff from watersheds where themaximum runoff ranges from 0.3 to 30 ft3ls(0.009 to 0.85 m Is). An H flume 0.5 foot deepwill gage a maximum flow of 0.3 ft3/s (0.009 m31s). Table 2.3 gives ratings for H flumes ofvarious sizes. H-type flume dimensions andflow capacities are shown in figure 2.8. Tomeasure flows with the required accuracy, construct the flume in strict accordance with thedrawing and the following provisions of thesespecifications. The slanting opening must bebound by straight edges and have precisely thedimensions shown on the drawing.

891.05 0I.05D FRONT ELEVATIONSIDE ELEVATIONPROPORTIONS OF THE TYPEAPPROXIMATEDEPTH—0Feel0.40.60.8.0HS FLUMECAPACITIE CAPACITYC.f.s.0.0850.230.470.82FIGURE 2.5.—Dimensions, capacities, and constructiontolerances of the NB flume.Construction specifications for the H-typerate-measuring flumes are: Prepare detailed drawings, using the proportional dimensions shown in figure 2.8. Use only new materials of the best commercial quality in constructing H flume. Thesematerials must be free from defects. Use sheet metal of galvanized open-hearthiron or copper-bearing steel. Make all structural angles of high-gradestructural steel and galvanize them. Theseangles must be straight, and the surface of thelegs must be flat. Fabricate the flume by following the bestcommercial practice in all details of construction. Make all joints and seams watertight andstrong. Cut all plate edges straight and sharp. Donot warp the plates or distort them by cutting. Make the vertical sides of the flume fromone sheet. The bottom plate must not containmore than one joint, and no portion of this jointshould lie within 12 inches (30.5 cm) of theoutlet opening. Any necessary joint in thebottom plate must be transverse to the longitudinal axis of the flume and must be made sothat the joint is substantially flush. Make alldimensions for which tolerances are not indicated on the drawings within /4 inch (0.64 cm)of those given on the drawings. Form the slanting outlet opening so thatits dimensions are precisely those shown on thedrawing. The slopes on this drawing must berigidly adhered to. Edges of the opening mustbe straight and smooth. Clamp the plates rigidly in position andget the proper dimensions and slopes beforemaking the final connections. Make the sideplates perpendicular to the bottom of the flume.All cross sections of the flume mUst be symmetrical about the longitudinal axis. All platesmust be flat and show no appreciable warp,dent, or other distortion. No projections shouldoccur on the inside of the flume. All joints mustbe solid and watertight. Carry out all operations affecting the dimensions of the outlet opening and thestraightness of its edges. Follow good machineshop practices in all operations. The completedflume should not have deep tool marks, dents,or other blemishes. Before using, inspect the flume to confirmits compliance with the plans and specifications. Flumes 4.5 feet (1.37 m) deep can be constructed in the field if the proportional dimensions in figure 2.8 are used. The flow capacityof this flume is 84 ft3/s (2.35 m Is). Reinforcedconcrete floor resting on two reinforced concrete footings—one across the upper face of theflume and the other about 1 foot (30.5 cm) infrom the downstream edge—provides a substantial base for thaflume walls. These walls

,C0.080.04000.20.40.60.8Submergence d2/d1FIGURE 2.6.—Effect of submergence on the calibration of an H flume.1.0

913T T 3T 8 j4j8AATanUAZero HeadAElevation(c0 c Q v H Section A-Av2\2.5Lo io . )vtWtan (H a—2g1.33average velocity in cross section 10 feet(3.048 m) upstream from center of cresthead (water surface elevation zero head)10 feet (3.048 m) upstream from center ofcrest—T crest thickness (16 in or 0.4064m)Tan-;-Range i-C0C12220.750 1.6271.628-3.7163.717 0750.02002-0.013395550.750- 100.01017-0.12692-----FIGURE 2.7.—Discharge equations for triangular weirs.T 8

92may be either concrete or wood treated withpreservative. In either case, angle iron formsthe sloping edge of the flume. Sometimes thewood walls are lined with sheet metal. Thewood should be 2.inch (5 cm) shiplap or tongueand-grooved siding with watertight joints. H flumes using 1-on.8 sloping false floorare calibrated in table 2.3. Discharge equationsfor H flumes are listed in figure 2.6 and figure2.7. These equations contain the basic dimensions that define the control section of theflume.HL Flume:The HL flume was designed to handle flowrates up to 117 ft3/s (3.28 m3Is). As shown inTABLE 2.2 —Rating tables for HSflume&[Discharge in cubic feet per second)FLUME 0.4 FooT 1.630.8030FLUME 0.6 FooT 25.0

N. E. Minshall, SEA hydraulic engineer (retired) Agriculture Engineering Department University of Wisconsin Madison, Wis. W. 0. Ree, SEA hydraulic engineer (retired) USDA/SEA Hydraulic Structures Laboratory Oklahoma State University Stillwater, Okla. R. R. School', SEA hydraulic engineer USDA/SEA Southern Great Plains Watershed Research Center

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