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<br />e <br /> <br />the water surface drops and the flow spreads out, the <br />potential energy stored as depth is converted to kinetic <br />energy or velocity. Therefore, the velocity leaving the <br />wingwall apron can be higher than the culvert outlet <br />velocity and must be considered in determining outlet <br />protection. The straight line transition may also be <br />. considered an abrupt transition if the tanS is greater than <br />l/3Fr. <br /> <br />e <br /> <br />B/2 <br /> <br /> <br />2.0 <br /> <br />ell <br />N <br />I- <br />et <br />z <br />o <br />i= <br />... <br />w <br />en <br />I <br />)(-- <br /> <br />ell <br />M <br />I- <br />et <br />z <br />o <br />I- <br />... <br />w <br />en <br />I <br />)(-- <br /> <br /> <br />W <br />B <br /> <br />1.0 2.0 <br />LIB <br /> <br />3.0 <br /> <br />4.0 <br /> <br />~ >0 = ~ ~ = <br />- - <br />> > <br /> <br />FIGURE IV.A.' DIMENSIONLESS WATER SURFACE <br />CONTOURS FROM REFERENCE IV-A-' <br /> <br />Desi~n Considerations <br /> <br />A reasonable estimate of transition end velocity can be <br />obtained by using the energy equation and assuming the losses <br />to be negligible. By neglecting friction losses, a higher <br />velocity than actually occurs is predicted making the error <br />on the conservative side. <br /> <br />. <br /> <br />~ <br /> <br />A more accurate way to determine apron end flow conditions <br />is that developed by Watts (IV-A-l). Watts' experimental <br />data have been converted to a family of curves relating <br />the Froude number (Fr) to the average depth--brink depth <br />ratio (YA/YO)' figures IV-.A-4 and 5 and Fr or Q/~ to <br />VAlVo figures IV-A-2 and 3. These curves were developed <br />for Fr from 1 to 2.5. This is the applicable Froude number <br />range for most abrupt outlet transitions. Normally, low <br />tailwater is encountered at the culvert outlet and flow <br />is supercritical on the outlet apron. <br /> <br />e <br /> <br />IV-A-3 <br />