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. CONTENTS Preface umn ......................m________............__....__ ..m................. Abstract u.n..........__........................... Introduction ...nun ..................... Hydraulic principles .....__ ................ ..................... Steady, uniform flow m...................... Backwater curves .....mm................__...... ..n.m.m.m.m Transition curves .............. .........n..... ..nm................. Determination of normal depth ........n.................... Average profile in a long reach ........n Use of Ml and M2 curves ............m.m............... Use of S2 and S3 curves .................................... Local effects on profiles ....m... Convergence of backwater curves Special cases of backwater curves ......... Flows on very small slopes..m... Flows OD steep slopes ........................... ....nno................... Locus of critica1-depth .tages................. Control sections mm.n............................... Transitions between tranquil and rapid flows m...............m... Alternate depth. _........._ Energy equation .................m... Standard .tep method Subcritical flows .... Supercritical flows.... ................... Field data .......... Total reach length Locations of cross sections .. Individualsubreach lengths ......................... Weighted length of a subreach ......... Cross-section attributes ....................... 9 ........................ 12 12 15 15 16 16 17 18 19 20 20 Pa.. p... III 1 1 1 1 2 3 4 4 5 5 6 6 7 7 8 9 9 Field data -Continued Subdivisions of cross sections ................... 20 Velocity-head coefficient, a 23 Roughness coefficients .......................... 26 Special field conditions ..... ......................... 21 Verified reaches ......... .............................. ................. 27 Short reaches .................. 27 Crossing profiles .......... ............. 27 Transitions between inbank and overbank flow conditions. ................................ 28 Flow at tributaries ...m............. 29 Flow past islands ..mn.................... 30 Multichannel flows ............................ 82 Bridges ....................................... 34 Flow through culverts ............._......... 36 Road overflow at culverts ... ................. 36 Storage at culverts .. ................. ..... 37 Multiple-opening constrictions ......................... 37 Division into single-opening units .............m. 38 Two-bridge openings ................... ................. 39 Three or more bridges... 40 Alluvial channels .......................... 41 Use of step~backwater method for indirect discharge measurements .. ............................. Floodway analysis . ..... ..m............. Encroachment of cross sections ............_... VE R option .... VSA option ......... VHD option HOR option Selected references 43 44 44 46 ................. 46 47 47 48 FIGURES Sketch showing water-surface profiles on mild slopes .........m..... Sketch showing water-surface profiles on steep slopes Sketches showing backwater-curve transitions: 3. For mild slope to milder slope ........ 4. From small n to large n on mild slope. 5. For mild slope to steeper mild slope ....._... ................ 6. From large n to small n on mild slope .. 7. For mild slope to steep slope ._... 8. For steep slope to mild slope .................... Sketches showing: 9, Local effect of a bridge on an Ml or an M2 slope ..................... ................. 7 10. A family of Ml and M2 backwater curves ........................................... ..................._.......... ................. 8 11. Water-surface profiles involving critical- or supercritical-flow transitions .......................... ................... 10 12. Diagram illustrating determination of elevation of critical flow in a cross section for any discharge .... .... 11 1. 2. 3-8. 9-11. ;. PaRe 2 3 4 4 4 4 4 5 VII