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14 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS contraction. The discharge coefficient used in the computations is the net, or completely adjusted, coefficient listed as C ADJUSTED. It includes the adjustment for degree of con- traction, as well as the reduction to a maxi- mum value of O. 98 in the event that the var- ious adjustments result in a combination giv- ing a value for C in excess of 0.98. or im- possible values greater than 1.00. Results for both types 5 and 6 flow appear when high-head now occurs. Criteria given In Bodhaine (1968, p. 30) will be helpful in deciding which result to use. If supercritical flow occurs at the ap- proach section, the culvert is no longer the control, and a valid computation is not pos- sible. APPLICATION OF RESULTS The results in the printout enable the an- alyst to develop a graphical stage-discharge relation, or a family of curves if the tail- water elevation partially controls the re- lation. Often, results for type 3 now that is just submerging type I or 2 now will give head- water elevations a few hundredths of a foot lower than that for type 1 or 2. Use the critical-depth condition (type 1 or 2 now) or the high-head nows (type 5 or 6) as the limit- ing curvell such a slight anomaly exists. The transition from low- to high- head flow is made, using recommendations of Bodhaine (1968, p.47), as follows: For transition from type 1 to type 5 flow, use low-head results below a headwater- diameter ratio, (hI - z) I D, of I. 2 and high- head results above a ratio of 1.5. Draw a straight-line transition between the two points. For transition from type 2 to type 6 flow, use low-head results below a headwater- diameter ratio of 1. 25, high-head results above a ratio of 1. 75 and a straight line be- tw('en. For type 4 flow, the discharge is not re- lated to stage, but is a function of the differ- ential head between the approa~h section and the tailwater. Discharge is plotted.agajnst (h1 - h4). See Bodhaine (1968, fig. 31). Crest- stage gages are frequently installed upstreaIIl from a culvert so that the culvert acts as the control for the stage- discharge relation. At many sites, it is not" practical to install the gage at the approach section, or the peak gage heights recorded are not direct- ly representative of the average piezometric head in the approach section. Observations of peak gage heights and surveys to deter- mine elevations. of high- water marks at both ends of the approach section must be made to establish the relation between average ele- vations at the approach section and peak gage heights found in the crest- stage gage. THIS IS IMPORT ANT . SPECIAL CONDITIONS Milered Culverts Headwater elevations for pipe or pipe- arch culverts with mitered or step-mitered entrances cannot be computed directly be- cause lengths of the approach reach and cul- vert barrel vary with the headwater elevation. For a culvert with a mitered entrance. prepare three or more sets of data, depend- ing upon the size of culvert, using average values of Land L for several values of w d2' D. including a value of 1. O. Choose dis- charges that might be expected to now within that part of the culvert. Screen the output from all sets of data and select the combi- nation best suited to the conditions for the develop~ent of the stage-discharge relation. If the culvert has a step-miter, prepare data sets for the top of the vertical part just above the culvert invert. for one or more elevations along the mitered part. and for the lower and upper elevat~ons of the vertical part near the top of the culvert. Use average values of Land L, and select discharges w expected in each range. Choose the combi- nation of output from all data sets best suited to the conditions and develop the stage- dis- charge relation from it. The above procedures are satisfactory be- cause changes in Land L do not affect the discharge signific~tly. Culverts with 90' Wingwalls In culverts with 900 wingwalls. the proper