Designation: D5130 − 95 (Reapproved 2014)Standard Test Method forOpen-Channel Flow Measurement of Water Indirectly bySlope-Area Method1This standard is issued under the fixed designation D5130; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers the computation of discharge(the volume rate of flow) of water in open channels or streamsusing representative cross-sectional characteristics, the water-surface slope, and coefficient of channel roughness as input togradually-varied flow computations.2,31.2 This test method produces an indirect measurement ofthe maximum discharge for one flow event, usually a specificflood. The computed discharge may be used to help define thehigh-water segment of a stage-discharge relation.1.3 The values stated in inch-pound units are to be regardedas standard. The values given in parentheses are mathematicalconversions to SI units that are provided for information onlyand are not considered standard.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:4D1129 Terminology Relating to WaterD2777 Practice for Determination of Precision and Bias ofApplicable Test Methods of Committee D19 on WaterD3858 Test Method for Open-Channel Flow Measurementof Water by Velocity-Area Method2.2 ISO Standards:5ISO 748 Liquid Flow Measurements in Open Channels—Velocity-Area MethodISO 1070 Liquid Flow Measurements in Open Channels—Slope-Area Method3. Terminology3.1 Definitions—For definitions of terms used in this testmethod, refer to Terminology D1129.3.2 Definitions of Terms Specific to This Standard:3.2.1 Several of the following terms are illustrated in Fig. 1:3.2.2 alpha (α)—a velocity-head coefficient that representsthe ratio of the true velocity head to the velocity headcomputed on the basis of the mean velocity. It is assumed equalto 1.0 if the cross section is not subdivided. For subdividedsections, α is computed as follows:α 5(Ski3Ai2DKT3AT2where:K and A = the conveyance and area of the subsectionindicated by the subscript i, andKTand AT= the conveyance and area of the entire crosssection.3.2.3 conveyance (K)—a measure of the carrying capacity ofa channel and has dimensions of cubic feet per second or cubicmetres per second. Conveyance is computed as follows:K 51.486nAR2/3where:n = the Manning roughness coefficient,A = the cross-section area, ft2(m2), andR = the hydraulic radius, ft (m).NOTE 1—1.486 = 1.00 SI unit.3.2.4 cross sections (numbered consecutively in downstreamorder)—representative of a reach of channel and are positioned1This test method is under the jurisdiction of ASTM Committee D19 on Waterand is the direct responsibility of Subcommittee D19.07 on Sediments,Geomorphology, and Open-Channel Flow.Current edition approved Jan. 1, 2014. Published March 2014. Originallyapproved in 1990. Last previous edition approved in 2008 as D5130 – 95 (2008).DOI: 10.1520/D5130-95R14.2This test method is similar to methods developed by the U.S. GeologicalSurvey and described in Refs (1-3).33The boldface numbers in parentheses refer to a list of references at the end ofthis standard.4For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.5Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http://www.ansi.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1as nearly as possible at right angles to the direction of flow.They must be defined by coordinates of horizontal distance andground elevation. Sufficient ground points must be obtained sothat straight-line connection of the coordinates will adequatelydescribe the cross-section geometry. If major breaks in thehigh-water profile are evident, cross sections should be locatedat the breaks.3.2.5 cross-section area (A)—the area of the water belowthe high-water surface elevations that are computed by assum-ing a straight-line interpolation between elevations on eachbank. The area is computed as the summation of the productsof mean depth multiplied by the width between stations of thecross section.3.2.6 friction loss (hf)—the loss due to boundary friction inthe reach and is equivalent to the following:∆ h1∆hv2 k~∆hv!where:∆h = the fall in the reach,∆hv= the upstream velocity head minus the downstreamvelocity head,(k∆hv) = the energy loss due to acceleration or decelerationand to eddies in a contracting or expanding reach,where k is a coefficient for energy losses.All of the equations presented in this standard are based onthe assumption that k is zero for contracting reaches and 0.5 forexpanding reaches.3.2.7 fall (∆h)—the drop in the water-surface computed asthe difference in the average water-surface elevation at adja-cent cross sections.3.2.8 friction slope (Sf)—the energy loss divided by thelength of the reach or:Sf5hfLthat becomes:Sf5∆h1∆hvLwhen ∆hvis negative (for a contracting reach),or:Sf5∆h1∆hv2Lwhen ∆ hvis positive (for an expanding reach).3.2.9 Froude number (F)—an index to the state of flow inthe channel. In a prismatic channel, the flow is tranquil orsubcritical if the Froude number is less than 1.0 and is rapid orsupercritical if it is greater than 1.0. The Froude number iscomputed as follows:F 5V=gdmwhere:V = the mean velocity in ft/s (m/s),dm= the average depth in the cross section in feet, andg = the acceleration of gravity in ft/s/s (m/s/s).3.2.10 high-water marks—the evidence of the highest stagereached by a flood. Debris, stains, foam lines, and scour marksare common types of high-water marks. Water-surface slopesare determined by the elevations of these marks.3.2.11 hydraulic radius (R)—defined as the area of a crosssection or subsection divided by the corresponding wettedperimeter.3.2.12 roughness coeffıcient (n)—or Manning’s n is used inthe Manning equation. Roughness coefficient or Manning’s n isa measure of the resistance to flow in a channel. The factorsthat influence the magnitude of the resistance to flow includethe character of the bed material, cross section irregularities,depth of flow, vegetation, and alignment of the channel. Areasonable evaluation of the resistance to flow in a channeldepends on the experience of the person selecting the coeffi-cient and reference to texts and reports that contain values forsimilar stream and flow conditions (1 and 2). (See 9.3.)3.2.13 velocity head (hv)—computed as follows:hv5αV22gwhere:α = the velocity-head coefficient,V = the mean velocity in the cross section in ft/s (m/s), andg = the acceleration of gravity in ft/s/s (m/s/s).3.2.14 wetted perimeter (WP)—the total length of theboundary between the channel bed and the water for a crosssection. It is computed as the sum of the hypotenuse of theright triangle defined by the distance between adjacent stationsof the cross section and the difference in bed elevations.4. Summary of Test Method4.1 The slope-area method is used to indirectly determinethe discharge through a reach of channel, usually after a flood,FIG. 1 Definition Sketch of a Slope-Area ReachD5130 − 95 (2014)2using evidence left by the event and the physical characteristicsof the channel reach. A field survey is made to determinedistances between and elevations of high-water marks and todefine cross sections of the stream. These data are used tocompute the fall in the water surface between sections andselected properties of the sections. This information is usedalong with Manning’s n in the Manning equation to computethe discharge, Q. The Manning equation in terms of discharge,Q, is as follows:Q 51.486nAR2/3Sf½or Q 5 KSf½The symbols on the right sides of the equations are definedin Section 3.5. Significance and Use5.1 This test method is particularly useful for determiningthe discharge when it cannot be measured directly by sometype of current meter to obtain velocities and with soundingweights to determine the cross section.5.2 Even under optimum conditions, the personnel availablecannot cover all points of interest during a major flood. Fieldpersonnel cannot always obtain reliable results by directmethods if the stage is rising or falling very rapidly, if flowingice or debris interferes with depth or velocity measurements.5.3 Under the worst conditions, access roads are blocked,cableways and bridges may be washed out, and knowledge ofthe flood frequently comes too late to obtain direct measure-ments of flow. Therefore, some type of indirect measurement isnecessary. The slope-area method is a commonly used method.6. Apparatus6.1 The equipment generally used for a “transit-stadia”survey is recommended. An engineer’s transit, a self-levelinglevel with azimuth circle, newer equipment using electroniccircuitry, or other advanced surveying instruments may beused. Standard level rods, a telescoping, 25-ft (7.6 m) level rod,rod levels, hand levels, steel and metallic tapes, tag lines (smallwires with markers fixed at known spacings), vividly coloredflagging, survey stakes, a camera (preferably stereo) with colorfilm, light meter, and ample note paper are necessary items.6.2 Additional equipment that may expedite a survey in-clude axes, shovels, a portable drafting machine, a boat withoars and motor, hip boots, waders, rain gear, nails, soundingequipment, two-way radios, ladder, and rope.6.3 Safety equipment should include life jackets, first aidkit, drinking water, and pocket knives.7. Sampling7.1 Sampling as defined in Terminology D1129 is notapplicable in this test method.8. Calibration8.1 The surveying instruments, levels and transits, etc.,should have their adjustment checked before each use andpossibly daily when in continuous use or after some occurrencethat may have affected the adjustment.8.2 The standard check is the “two-peg” or“ double-peg”test. If the error is over 0.03 ft in 100 ft (0.9 cm in 30.5 m), theinstrument should be adjusted. The two-peg test and how toadjust the instrument are described in many surveying text-books and in instructions provided by the manufacturer. Referto manufacturer’s manual for the electronic instruments.8.3 If the “reciprocal leveling” technique is used in thesurvey, it is the equivalent of the two-peg test between each ofthe two successive hubs.8.4 Sectional and telescoping level rods should be checkedvisually at frequent intervals to be sure sections are notseparated. A proper fit at each joint can be quickly checked bymeasurements across the joint with a steel tape.8.5 All field notes of the transit-stadia survey should bechecked before proceeding with the computations.9. Procedure9.1 Selection of a reach of channel is the first and probablythe most important step to obtain reliable results. Ideal reachesrarely exist; so the various elements in a reach must beevaluated and compromises made so that the best reachavailable is selected (3). Selection soon after the flood event isrecommended because livestock, humans, heavy rain, and banksloughing can destroy high-water marks.9.1.1 Good high-water marks are essential for good results.At times a reach with poor quality marks must be used becauseof other complicating factors such as inflow, proximity to agaging station, etc. List high-water marks in a format such asshown in Fig. 2.9.1.2 The nearer the reach to a uniform channel the better.Marked changes in channel shape should be avoided becauseof uncertainties regarding the value of the expansion/contraction loss coefficient (k) and the friction losses in thereach. Changes in channel conveyance should be fairly uni-form from section to section to be consistent with the assump-tion that the mean conveyance is equal to the geometric meanof the conveyances at the end sections.9.1.3 A reach with flow confined to a roughly trapezoidalchannel is desirable because roughness coefficients have beendetermined for such shapes. However, compound channels,those with overbank flow, for example, can be used if they areproperly subdivided into subareas that are approximatelytrapezoidal.9.1.4 A straight reach that contracts is preferred, but bothconditions seldom exist in the same reach. Whether or not areach is contracting or expanding depends solely upon thedifference in velocity head (∆hv) between sections. The reachis contracting if the difference in the velocity head is negative.The reach is expanding if the velocity-head difference ispositive.9.1.5 Cross sections are assumed to be carrying water inaccordance with the conveyance for each part of the section.Therefore, the channel for some distance upstream should besimilar to that of the reach. Then the discharge will bedistributed in relation to depths, roughness, and shape. If theupstream section is located too close to a sharp bend, a bridgethat constricts the width, or a natural constriction, slack water,D5130 − 95 (2014)3or even an eddy may occupy part of the section; and the sectionwill not be effective in carrying water downstream in propor-tion to the computed conveyance.9.1.6 Channels in mountainous areas may be very rough andsteep and may have free fall over riffles and boulders. TheManning equation is not applicable when free fall exists.However, free fall may or may not be indicated by thehigh-water profiles or by inspection of the reach. Crosssections can be located to eliminate any part of a reach inwhich free fall is indicated. If the reach includes stretches inwhich free fall might have occurred, the computed dischargesare not reliable.9.1.7 The reach should be long enough to develop a fall thatis well beyond the range of error in the surveying method, inalternative interpretations of the high-water profile, or inuncertainties related to the computation of the velocity head.One suggested criteria is that the fall in the reach should be 0.5ft (0.15 m) or greater than the velocity head in the reach, orboth.9.2 Cross sections represent the geometry of a reach ofchannel. For example: section 2 should be typical of the reachfrom halfway upstream to section 1 to halfway downstream tosection 3. A minimum of three cross sections is highlyrecommended.9.2.1 Locate cross sections at major breaks in the high-waterprofiles. To do so, the high-water marks should be plotted inthe field, and a profile for each bank drawn before sections arelocated and surveyed. Several high-water marks near the endsof the sections are desirable to define the high-water ele