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Chapter 2 Open Channel Hydraulic Theory 2-1. PhySical Hydraulic Elements Q, General, The physical hydraulic elements con- cerned in hydraulic design of channels consist of inven slope (5.,). cross-sectional area (A). wetted perimeter (Pl. and equivalent boundary sunace roughness (k). The hydraulic r:ulius (R) used in resistance fonnulae is the ratio NP. The invert slope of proposed channel im- provement is conlrOlled primarily by elevations of the ground along the alignment as determined by preliminary layout discussed in paragraph 1-6<1, A center-line prof1Ie between conlrOlling elevations along the proposed align- ment will indicale a preliminary channel slope. b, Channel cross secrion. (1) The proper channel cross section for a given re:lCh is the one that has adequate hydraulic capacity for a minimum cost of construction and maintenance. The economics must include the costs of right-of-way and structures such as bridges, In nual areas a trapezoidal cross section may be le:lSt costly. whereas in urban areas a rectangular cross section is often the least costly. (2) Plate 1 shows a sample cost compUl:ltion and related cost curve for a reach of curved rectangular con- crete channel. Similar procedures may be applied to compute the COSI for any type of cross section considered for design. Special types of concrete channel cross sec- tions are shown in Plate 2: the V -bottom channel and the modified trapezoidal channel. The latter has a small low-flow channel in the center. (a) In the V-bottom channel. low flows are concen- trated along the channel center line. This prevents moder- ate flow from meandering over the entire channel width. which would result in random deposition of material across the inven as in the case of a horizontll bottom. Deposition in the center of the V -bottom is removed by larger flows. Because the We:l1" caused by bed load is also concentrated ne:l1" the center line. maintenance cost is reduced. (b) In the modified trapezoidal cross section, vettical sidewalls reduce the top width. This design is desirable when the width of the right-of,way is limited. A small. l~w,flow channel in the center of the cross section pro- VIdes a flow way into which subdrninage can be emptied. In cold climates_ the low-flow channel reduces the inven area subjecled to the deleterious effects of freezing and EM 1110.2-1601 1 Jul 91 thawing. In some cases the low. flow channel may serve as a fishway, c. Roughness. The concept of surface roughness as the basic parameter in flow resistance (friction) is almost wuversally accepted. Absolute roughness is detennined fro,~ the physical dimensions of the wetted surface irregu- lan~es and IS nonnally of theoretical interest only. Eqwvalenl roughness is a 1ine:l1" dimension (effective roughness height) directly related to the bound:uy resis- tance of the channel (plate 3). The relations between roughness and the various coefficients for friction fonnu- Ia.: ~ adequately covered by Chow (1959, chap 8). Fnction fonnulae and their uses are discussed in paragraph 2-2. below. d, Composite roughness, Wllere there is material variation ~ roughness between various portions of the wetted penrneter such as might be found in nalIJr.ll chan- nels or channels with protected banks and natural inverts_ an equivalent or effective roughness or friction coefficient f~r eac~ st:lge considered should be detennined. Appen- dix C Illustrates a method for detennining a composite ~alue of k for each st:lge. Plates 4 and 5 give the rela- tion between k and Manning's n for flows in the rough flow zone shown in Plate 3. HDC sheets 631-4 and 631-4{1 also give a procedure for determining an effective Manning's n. e, Hydraulic efficiency. The problem of the most efficient cross section is treated by Brater and King (1976_ see pp 7-5 to 7-7) and Chow (1959. see paragraph 7-6). 2.2. Hydraulic DesIgn Aspects Q, General, This present:ltion assumes that the design engineer is fully acquainted with the hydraulic theories involved in unifonn and gradually varied flows, steady and unsteady flows. energy and momentum princi- ples. and other aspects such as friction related to hydraulic design nonnally covered in hydraulic texts and handbooks such as those by Brater and King (1976) and Chow (1959). The following is presented as guidance in the method of application of textbook material and to give additional infonnation not readily available in reference material. The use of k is emphasized herein because compul:ltional results are relatively insensitive to errors in assigned values of k. However. use of Manning's n has been retained in several procedures because of its wide accepl:lllce and simplicity of use. This applies panicularly to varied flow profiles. pulsating flow, and the design of free,surface hydraulic models. 2-1