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AUTOMATIC COMPUTATION OF STAGE-DISCHARGE RELATIONS AT CULVERTS 15 ~ choice of culvert length may be a problem. A recommended solution is to run- the entire problem with L measured along the invert to the toe of the wingwall, and again with L measured along the top of the culvert to the headwall. If the computed results are signi- ficantly different, there will be a basis pro- vided for reasonable interpolation between the two stage- discharge relations, or a basis for selection of lengths for different ranges of discharge in future runs. Unusual Culvert Entrances The coefficient of discharge for the com- mercial flared opening described in figure 8 in Bodhaine (1968) is 0.95 for flow types I, 2, and 3 for all diameters of pipe and all values of (hl - z)t D. The properties of these flared end sections are shown in figure 8 in Bodhaine (1968). For- culvert entrances of unusual shape. estimate the discharge coefficient on the basis of known values for the more common shapes (reentrant, sharp, 45- degree wing- walls). For the six types of flow discussed in this manual, this entrance coefficient can usually be estimated with sufficient accuracy. In high-head flow the entrance shape is very important because it may mean the difference between a culvert flowing full or partly full. Remember that the effect of side contrac- tion becomes negligible for flow types <4, 5, and 6 and that vertical contraction is very important. Culverts with Fillets Box culverts sometimes have corner fillets - - a condition for which no provision is made on the data- input form. There are no set criteria for handling this situation; there- fore, trial solutions may be necessary. As a first step, assume no fillets in the top corners. Compute an effective width (b in columns 24- 29 of card 9) by dividing the cross- sectional area by D. The solution using this b will probably be most applicable for types 1, 2,. and 3 flows involving small discharges. Another trial solution can be performed using an effective b ha,sed on fillets in all corners. This solutioIl would be more appli- cable for the larger discharges of types 4, 5, and 6 flows. If the fillets are small relative to the cross- sectional area of the barrel. these two trials should not differ much. If they do differ, a probable stage-discharge relation can be interpolated between the two solutions obtained.. Multiple Culverts Computations are sometimes required for two or more culverts that share a common approach cross section. The culverts might be identical. but located far enough apart so that the space between them cannot be con- sidered to be a web, or they may be culverts of quite different geometry, slope, and rough- ness. The procedure recommended is to treat the culverts independently, assigning a part of the approach cross section to each. If the approach cross section has a large, trapezoidal shape, it may be partitioned in proportion to the gross area of each culvert. See the method described by Matthai (1967, fig. 34 and p. 44). If the approach cross section is irregular, with a main- channel section and overbank subsections. plot the cumulative area (for stage represented by W ) as shown by max Matthai (1967, fig. 30), and divide this in proportion to the gross culvert areas to de- termine the stationing of subdivision of the approach cross section. Should these procedures result in individ- ual approach sections that are so far dis- placed from their designated culverts that the flow pattern would seem to be unnaturally tortuous, the divisions should be readjusted somewhat to conform more with the natural geometry of the ponded regions upstream from the culverts. The stage-discharge re- lation is more affected by the approach sec- tion for the low-head flows than for the high- head flows. This fact should help influence the choice of appropriate boundaries. If the culverts are relatively close togeth- er, or if the_ approach cross section is nec- essarily subdivided at points that do not (;oin- cide with natural geometric boundaries such as between a deep, natural channel and an adjacent nood plain of higher elevation, then it is recommended that the vertical division lines in the approach cross section not have