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<br />Zo + Yo + V02/2g = z2 + Y2 + V22/2g + Hf <br />Hf = 0 and Zo = z2 <br />3.4 + (l5.88) 2/64.4 = Y2 + (lO.8/Y2) 2/64.4 <br />3.4 + 3.92 = Y2 + l.8l/Y2 <br />7.32 = Y2 + 1.8l/Y22 <br /> <br />e <br /> <br />Y2 = 0.516 feet, which is 41% lower than first solution <br />V2 = lO.8/0.516 = 20.9 fps lO%, which is higher than <br />first solution <br /> <br />2. Another depth approximation can be obtained if <br />W2 is based on S where tan S = l/3Fr <br /> <br />. <br /> <br />W2 = Wo + 2L tan l2.41 <br />= 5 + 20(.22) = 9.4 feet <br />A2 = 9.4Y2, V2 = 270/9.4Y2 = 28.7/Y2 <br />7.32 = Y2 + l2.8/Y22 <br /> <br />Y2 = 1.48 feet, which is 68% higher than first solution <br />V2 = 28.7/l.48 = 19.4, which is 2% higher than first <br />solution <br /> <br />DESIGN OF SUBCRITICAL FLOW TRANSITIONS <br /> <br />Subcritical flow can be transitioned into and out of highway <br />structures without causing adverse effect if subcritical <br />flow is maintained throughout the structure. The flow cannot <br />approach or pass through critical depth (Yc)' The range of <br />depths to avoid is .9yc to l.lyc. In this range, slight <br />changes in specific energy are reflected in large changes <br />in depth, i.e., wave problems develop. <br /> <br />e: <br /> <br />The straight line or wedge transition should be used if <br />conservation of flow energy is required; such as in irriga- <br />tion canal structures which traverses the highway. Warped <br />and cylindrical transitions are more efficient, but the <br />additional construction cost can only be justified for <br />structures where backwater is critical. <br /> <br />Design Considerations <br /> <br />Figure IV-A-6 illustrates the design problem. Starting <br />upstream of section (l) where some backwater exists due <br />to the culvert, the flow is transitioned from a canal into <br />then out of the highway culvert. The flare angle (SW) <br />should be l2.50, (4.5 to 1 or flatter) (VI-A-3). This criteria <br />provides a gradually varied transition which can be analyzed <br />using the energy equation. <br /> <br />, <br /> <br />~ <br /> <br />As the flow transitions into the culvert the water surface <br />approaches Yc. To minimize waves, y should be equal to <br />or greater than l.lyc. In the culvert, the depth will <br /> <br />IV-A-6 <br /> <br />e' <br />