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<br />THEORETICAL BASIS FOR PROFILE CALCULATION <br /> <br />1 . GENERAL <br /> <br />This section describes methodology used in HEC-2 for the calcula- <br />tion of water surface profiles. Topics discussed include equations used <br />for basic profile calculation, cross section subdivision for determining <br />conveyance and velocity distribution, friction loss evaluation, iterative <br />procedure for solving the basic equations and critical depth determination. <br />Computational methodology for calculating flow through bridges is presented <br />in Appendix IV. Methodology used by HEC-2 to determine and evaluate flood <br />plain encroachments is contained in Appendix II. <br /> <br />2. <br /> <br />EQUATIONS FOR BASIC PROFILE CALCULATION <br /> <br />(the <br />tion <br /> <br />The following two equations are solved by an iterative procedure <br />standard step method) to calculate an unknown water surface eleva- <br />at a cross section: <br /> <br />WS2 + <br /> <br />2 <br />[J.2V2 <br />2g <br /> <br />= WSl + <br /> <br />2 <br />[J.l Vl <br />2g <br /> <br />+ h <br />e <br /> <br />(1) <br /> <br />he = L Sf + C <br /> <br />2 <br />[J.2V2 <br />2g <br /> <br />2 <br />[J.l Vl <br />2g <br /> <br />(2) <br /> <br />where: <br /> <br />WS1, WS2 <br /> <br />= water surface elevations at ends of reach <br />(see Figure 1) <br /> <br />= mean velocities (total discharge f total flow area) <br />at ends of reach <br /> <br />Vl, V2 <br /> <br />[J.l' [J.2 <br /> <br />= velocity coefficients for flow at ends of reach <br /> <br />g <br /> <br />= acceleration of gravity <br />= energy head loss <br /> <br />he <br /> <br />L <br />Sf <br />C <br /> <br />= discharge-weighted reach length <br /> <br />= representative friction slope for reach <br /> <br />= expansion or contraction loss coefficient <br /> <br />3 <br />