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<br />e <br /> <br />COMPUTATION OF WATER-SURFACE PROFILES <br />IN OPEN CHANNELS <br /> <br />By Jacob Davidian <br /> <br />Abstract <br /> <br />The standard step-backwater method of computing <br />water-surface profiles is described in this chapter. The <br />hydraulic principles and assumptions are reviewed. and <br />the field data requirements are described. Certain special <br />cases of backwater curves and certain special field condi- <br />tions are discussed in detail. The technique is used to <br />establish or extend stage-discharge ratings; to define <br />areas which will be innundated by flood flows of a given <br />frequency; and to compute profiles through various <br />reaches, including multichannel flows. and past control <br />structures such as bridges, culverts. and road embank- <br />ments. A brief description of analysis of flood ways and <br />effects of encroachments is also presented. <br /> <br />Introduction <br /> <br />Water-surface profiles along stream chan- <br />nels can be computed quickly when electronic <br />computers are applied to the commonly used <br />step-backwater method. The method requires <br />the evaluation of the energy losses between any <br />two points on the water-surface profile. <br />Water-surface profile computations by the <br />step-backwater method are a major part of <br />most studies leading to the delineation of flood <br />plains in urban and suburban areas. Flood <br />plains must be delineated before they can be <br />properly zoned to reduce flood damages. <br />The method is also applied to flood way analy- <br />sis. Given a stream profile for a flood of a cer- <br />tain magnitude, a surcharge, or increase in <br />stage, is chosen for the entire profile, Then the <br />encroachments on the flood plains are deter- <br />mined by the step-backwater method such that <br />the total stream conveyance remains un- <br />changed, This application is useful in planning <br />and in flood-insurance studies. <br /> <br />e <br /> <br />The method is also used in establishing or <br />extending stage-discharge relations at gaging <br />stations or at other sites along a stream. This <br />information is valuable in the design of struc- <br />tures, <br />A survey of the geometry of the stream <br />channel along the reach for which the profiles <br />are needed produces the data required-princi- <br />pally, cross sections of the channel drawn to a <br />common datum at intervals along the reach and <br />the value of the roughness coefficient. From <br />these data, the water-surface profile for any <br />known or assumed discharge may be computed. <br />This manual describes the standard step- <br />backwater method of computing water-surface <br />profiles and the channel geometry data needed. <br />Certain sources of error and some special field <br />conditions are discussed in detail. Frequent <br />reference is made to computer program E431 <br />of the V.S, Geological Survey, Because compu- <br />ter programs are frequently changed, details <br />of that program are not discussed here. Pro- <br />gram E431 is described by Shearman (1976) in <br />detail, with respect to data handling and prep- <br />aration, computed results, error messages, <br />and assumptions. <br /> <br />Hydraulic Principles <br /> <br />Steady, uniform flow <br /> <br />Almost all open-channel flows are both un- <br />steady (depth at a point varies with time) and <br />nonuniform (depth changes from point to point <br />along a channel). Because these flows are diffi- <br />cult to analyze, a steady, uniform flow is fre- <br /> <br />1 <br />