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<br />e <br /> <br />Water cannot expand to completely fill the section between <br />the wingwalls in an abrupt expansion. The majority of the <br />flow will stay within an area whose boundaries are defined <br />by tanS = l/3Fr. As shown in figure IV-A-l, flaring the <br />wingwall more than l/3Fr--450 for example--provides unused <br />space which is not completely filled with water. <br /> <br />Design Procedure <br /> <br />l. Determine the flow conditions at the culvert outlet: <br />(Vo) and (Yo) (see chapter III) . <br /> <br />2. Calculate the Froude number (Fr) = Vo/lgyo at the culvert <br />outlet. <br /> <br />, <br /> <br />3. Find the optimum flare angle (S) using tanS = l/3Fr. <br />If the chosen wingwall flare (SW) is gre?ter than (S), <br />consider reducing Sw to S. <br /> <br />4. Use figure IV-A-4 for boxes and IV-A-5 for pipes to <br />find the average depth downstream. The ratio yA!yo <br />is obtained knowing the Froude number (Fr) and the desired <br />distance downstream (L) expressed in cul.ert diameters <br />(D) . <br /> <br />e <br /> <br />5. Use figure IV-A-2 for boxes and IV-A-3 for pipes to <br />find average velocity (VA). <br /> <br />6. Calculate the downstream width (W2) using: <br /> <br />W2 = Wo + 2LtanS <br />TanS = l/3Fr <br /> <br />IV-A-l <br />IV-A-Z <br /> <br />if SW>S <br /> <br />use Sw in equation IV-A-l. <br /> <br />7. If S was used in equation IV-A-l, calculate downstream <br />depth Y2 using W2 and VA. This depth will be larger <br />than YA since the flow prism is now laterally confined. <br /> <br />, <br /> <br />~ <br /> <br />If Sw was used, Y2=YA and the average flow width is <br />(WA)=Q/VAYA. If WA WZ, use W2 to calculate YZ=Q/VAWZ. <br /> <br />Example Problem <br /> <br />Given: <br /> <br />5 x 5 RCB <br />L = 200 ft. <br />80= O.OOZ ft/ft. <br /> <br />Q = 270 cfs <br />Q/BD3/2= 4.83 <br />dc= 4.5 <br /> <br />e <br /> <br />IV-A-4 <br />