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<br />FIGURES <br /> <br />1. Flow lines for typical normal crossing _ __ _ __ __ __ __ __ __ __ __ _ __ _ __ __ 3 <br />2, Normal crossing: Wingwall abutments_ _ _ __ _ __ __ _ __ _ __ _ __ _ __ _ __ __ 4 <br />3, Norm'll crossing: Spillthrough abutments____ ____ __ ____ __ ____ __ ___ 7 <br />4, Types of flow encountered______________________________________ 8 <br />5, Aid for estimating a,__ __ __ _ __ __ __ _ __ __ _ __ _ _ __ __ _ __ __ __ __ __ __ _ __ 11 <br />6, Backwater coefficient base curves (subcritical flow)________________ 14 <br />7, Incremental backwater coefficient for piers__ _ _ _ _ __ __ _ _ _ _ _ _ _ __ _ _ _ _ _ 15 <br />8, Incremental backwater coefficient for eccentricity __ _ __ __ _ _ __ _ _ _ _ _ _ _ 16 <br />9, Skewed crossing8__ _ _ ___ _ __ __ __ __ __ __ __ __ __ __ _ __ _____ __ __ _ _ _ __ _ 17 <br />10, Incremental backwater coefficient for skew ____ __ __ __ __ _ __ _ __ _ __ __ _ 18 <br />11. Ratio of projected to normal length of bridge for equivalent backwater <br />(skewed crossings)__ __ _ ___ __ _ _ _ _ ___ ___ __ _ _ _ __ __ ____ _ __ _ _ _ _ ___ 19 <br />12, Differential waterlevel ratio base curves___ __ __ __ __ _ ____ _ __ _ __ _ __ _ 21 <br />13, Distance to maximum backwater __ __ _ __ _ __ _ __ _ __ _ __ __ _ _ _ _ _ _ _ __ __ 25 <br />14, Backwater multiplication factor for dual parallel bridges____________ Z7 <br />15, Differential level multiplication factor for dual parallel bridges_ _ _ _ _ _ 28 <br />16. Backwater with abnormal stage-discharge condition__ __ _ __ , __ __ __ __ 32 <br />17, Effect of scour on bridge backwater______________________________ 36 <br />18, Scour at wingwall abutment and single circular piers (model)________ 37 <br />19. Cross section of scour at upstream side of bridge (model) __ __ _ __ __ __ 38 <br />20, Correction factor for backwater with scour ____ _ __ __ _ __ __ _ ____ __ __ _ 39 <br />21. Discharge coefficients for upstream girderin flow (case 1)___________ 42 <br />22, Discharge coefficient for all girders in flow (case II) __ __ __ __ _ __ _ __ __ 43 <br />23, Buoyant and horizontal forces moved these 80-foot spans downstream_ 45 <br />24, Di8charge coefficients for flow over roadway embankments__ _ ,_ _ _ _ _ _ 46 <br />25, Missouri River Bridge on route 1-70_____________________________ 47 <br />26, Nottoway River Bridge on Virginia Route 40_____________________ 48 <br />27, Flow concentration along upstream side of embankments at Big <br />Nichols Creek__ __ _ _ __ _ ____ _ _ ____ _ __ _ ___ _ __ __ _ _ _ _ __ _ __ _ __ __ __ 51 <br />28, Extent of scour measured after the flood at Big Nichols Creek_____ __ 52 <br />29, Model of a spur dike___________________________________________ 52 <br />30, Chart for determining length of spur dikes_ _ __ _ _ __ _ _ _ __ _ _ _ _ __ _ __ _ _ 54 <br />31. Spur dikes on model of Tarbela Bridge, Indus River, West Pakistan_ _ 55 <br />32, Spur dike on 450 skewed bridge over Susquehanna River, Nanticoke, <br /> <br />Pa______________________________________________,__________ 55 <br />33, Plan and cross section of spur dike_ __ __ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ __ __ _ __ __ 56 <br />34, Tentative backwater coefficient curve for type II flow _ _ _ _ _ _ _ _ _ _ _ _ _ _ 57 <br />35, Status of U ,S. Geological Survey nationwide flood frequency project- _ 60 <br />36. Example 1: Plan and cross section of normal crossing______________ 66 <br />37. Example 3: Plan of skewed crossing____________________________~ 70 <br />38, Examples 1-3: Conveyance and area at section L_________________ 71 <br />39, Example 4: Cross section of eccentric river crossing__ __ __ _ __ _ _ __ _ __ 72 <br />40, Example 4: Stage-discharge curve for river at bridge site__ __ __ _____ 72 <br />41. Example 4: Area and velocity head coefficient__ __ ____ __ __ ____ ____ 74 <br />42, Example 4: Conveyance at section L_____ __ __ __ __ __ __ __ __ __ _____ 74 <br /> <br />vii <br />