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water surface profile under conditions of gradually varied flow; and (3) <br />Direct determination with varying numbers of measurements. <br />MANNING EQUATION, ASSUMING UNIFORM FLOW CONDITIONS <br />This approach can be used to determine the stage-discharge rela- <br />tionship for individual cross sections. The uniform flow assumption <br />allows the use of the measured hydraulic slope instead of the energy <br />slope, since by definition-, they are equal. In addition, this approach <br />assumes that flow variations caused by changes in channel configuration <br />are negligible. <br />Generally, the more uniform the channel, the more reliable the <br />results using this approach. As the channel becomes less uniform, <br />the reliability of the results deteriorates. <br />Under this approach, the Manning equation is solved for n at one <br />discharge, for which the following measurements must be made: (1) The <br />water surface elevation (stage) and the discharge at the measured flow; <br />(2) The hydraulic slope; and (3) The dimensions of the channel cross <br />section. <br />The cross-sectional area and hydraulic radius are determined by the <br />cross-sectional measurements and the stage. Manning's n may then be <br />computed for the cross section by equation 5: <br />Solving for n, <br />n = 1.486 R21SS31 A (8) <br />Manning's n is then assumed constant in subsequent calculations <br />where new stages are calculated for different discharges, using <br />equation S. <br />WATER SURFACE PROFILES UNDER VARIED FLOW CONDITIONS <br />In most cases, the assumption of uniform flow cannot be made, <br />either because of channel conditions or because of accuracy requirements <br />of the instream flow study. The computation of the water surface <br />profile is a means of more accurately determining the stage-discharge <br />relationship with little more effort than the-previous method. While <br />the computations are considerably more complex, there are several <br />computer programs available which are capable of rapid computation of <br />the water surface profile. Program names and descriptions may be found <br />in Appendix E, and may be used for this computation procedure. <br />The determination of the water surface profile requires essentially <br />the same kind of data as the previous approach. However, the computa- <br />tion procedure is much different. This approach determines the energy <br />losses between two cross sections under assumed conditions of depth and <br />r2