Determine the dimensions of a reinforced concrete box culvert that is to be placed under a roadway, and the gradual transition needed for a 15-ft wide rectangular flood control channel at a slope of 0.0001 ft. Transition structures are used to transition flow from an open channel to a culvert and then transition flow from the downstream of the culvert back to the channel. Gradual transitions are used when the flow is subcritical throughout the culvert. Refer to Figure P16.2.13. The culvert has a length of 150 ft and is to convey a design discharge of 135 cfs. Use a Manningâ€™s n of 0.02. Straight line transitions are to be used so the expansion and contraction coefficients,Ce andCc, are respectively, 0.5 and 0.3. Assume that section 1 defines the flood-control channel just before the contraction upstream of the culvert and section 4 defines the flood-control channel after the expansion downstream of the culvert. Sections 2 and 3 are located at the upstream and downstream ends of the culvert. The headloss in the contraction is CcÃ°V2 2 =2g

Â V2 1 =2gÃž and the headloss in the expansion is CeÃ°V2 3 =2g

Â V2 4 =2gÃž. The transition lengths (LT) are specified using a 4.5:1 flare so that LT Â¼ 4:5Ã°W4

Â W3Ãž=2 and LT Â¼ 4:5Ã°W1

Â W2Ãž=2, where W is the widths at the respective sections. Choose y3

Â 1:1yc to have a subcritical depth. One important aspect of the culvert and transition design is to make sure that the backwater effect Ã°y1

Â y4Ãž does not exceed a preferred or required amount (freeboard). For the purposes of this problem, that amount is 1 ft.