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<br />5. COMPUTATION PROCEDURE <br /> <br />The unknown water surface elevation at a cross section is determined <br />by an iterative solution of equations (1) and (2). The computational <br />procedure is as follows: <br /> <br />1. Assume a water surface elevation at the upstream cross <br />section (or downstream cross section if a supercritical <br />profile is being calculated). <br /> <br />2. <br /> <br />Based on the assumed water surface elevation, determine <br />the corresponding total conveyance and velocity head. <br /> <br />With values from step 2, compute Sf and solve equation (2) <br />for he' <br /> <br />3. <br /> <br />4. <br /> <br />With values from steps 2 and 3. solve equation (1) for WS2, <br /> <br />5. <br /> <br />Compare the computed value of WS2 with the values assumed <br />in step 1; repeat steps 1 througn 5 until the values agree <br />to within .01 feet (or .01 meters). <br /> <br />Criteria used to assume water surface elevations in the iterative <br />procedure varies from trial to trial. Generally the first trial is <br />based on projecting the previous cross section's water surface elevation <br />on the average of the friction slopes from the previous two cross sections. <br />The second trial is an arithmetic average of the computed and assumed <br />elevations from the first trial. The third and subsequent trials are <br />generally based on a "secant" method of projecting the rate of change <br />of the difference between computed and assumed elevations for the previous <br />two trials to zero. The change from one trial to the next is constrained <br />to a maximum of !50% of the assumed depth from the previous trial. <br /> <br />Once a 'balanced' water surface elevation has been obtained for a <br />cross section, checks are made to ascertain that the elevation is on <br />the 'right' side of the critical water surface elevation (e.g., above <br />the critical elevation if a subcritical profile is being calculated). <br />If the balanced elevation is on the 'wrong' side of the critical water <br />surface elevation. critical depth is assumed for the cross section and <br />a message to that effect is printed by the program. The program user <br />should be aware of critical depth assumptions and determine the reasons <br />for their occurrence, because in many cases they result from reach <br />lengths being too long or from misrepresentation of the effective flow <br />areas of cross sections. <br /> <br />7 <br />