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<br />e <br /> <br />. <br /> <br />. <br /> <br />e <br /> <br />. <br /> <br />, <br /> <br />e <br /> <br />Chapter 2 <br />Open Channel Hydraulic Theory <br /> <br />2-1. Physical Hydraulic Elements <br /> <br />a. General. The physical hydraulic elements con. <br />cerned in hydraulic design of channels consist of invert <br />slope (Sol. cross-sectional area (A). wetted perimeter (P). <br />and equivalent boundary surface roughness (k). The <br />hydraulic radius (R) used in resistance fonnulae is the <br />ratio AlP. The invert slope of proposed channel im- <br />provement is controlled primarily by elevations of the <br />ground along the alignment as detennined by preliminary <br />layout discussed in paragraph 1-6<1. A center-line profIle <br />between controlling elevations along the proposed align- <br />ment will indicate a preliminary channel slope. <br /> <br />b. Channel cross section. <br /> <br />(I) The proper channel cross section for a given <br />re?"h IS the one that has adequate hydraulic capacity for a <br />milllmum cost of construction and maintenance. The <br />economics must include the costs of right-of-way and <br />structures such as bridges. In rural areas a trapezoidal <br />cross section may be least costly. whereas in UIban areas <br />a rectangular crosS section is often the least costly. <br /> <br />(2) Plate II shows a sample cost computation and <br />related cost curve for a reach of curved rectangular con- <br />crete channeL Similar procedures may be applied to <br />compute the cost for any type of cross section considered <br />for design. Special types of concrete channel cross sec- <br />tions are shown in Plate 2: the V -bottom channel and the <br />modified trapezoidal channeL The latter has a small <br />low-flow channel in the center. <br /> <br />(a) In the V-bottom channel, low flows are concen. <br />trated along the channel center line. This prevents moder- <br />ate flow from meandering over the entire channel width <br />which would result in random deposition of materiai <br />across the invert as in the case of a horizontal bottom. <br />Deposition in the center of the V -bottom is removed by <br />larger flows. Because the wear caused by bed load is <br />also concentrated near the center line, maintenance cost is <br />reduced, <br /> <br />(b) In the modified trapezoidal cross section vertical <br />sidewalls reduce the top width, This design is desirable <br />when the width of the right-of-way is limited. A small. <br /> <br />Plates mentioned in this and succeeding chapters are <br />included in Appendix B as Plates B-1, B-2, etc. <br /> <br />EM 1110-2-1601 <br />1 Jul 91 <br /> <br />low-flow channel in the center of the cross section pro- <br />VIdes a flow way into which subdrainage can be emptied. <br />In cold climates, the low-flow channel reduces the invert <br />area subjected to the deleterious effects of freezing and <br />thawing. In some cases the low.flow channel may serve <br />as a fishway. <br /> <br />c. Roughness. The concept of surface roughness as <br />the basic parameter in flow resistance (friction) is almost <br />universally accepted. Absolute roughness is detennined <br />from the physical dimensions of the wetted surface irregu- <br />larities and is nonnally of theoretical interest only. <br />Equivalent roughness is a linear dimension (effective <br />roughness height) directly related to the boundary resis- <br />tance of the channel (plate 3). The relations between <br />roughness and the various coefficients for friction fonnu- <br />130 are adequately covered by Chow (1959. chap 8). <br />Friction fonnulae and their uses are discussed in <br />paragraph 2-2, below. <br /> <br />d. Composite roughness. Where there is material <br />variation in roughness between various portions of the <br />wetted perimeter such as might be found in natural chan- <br />nels or channels with protected banks and natural inverts <br />an equivalent or effective roughness or friction coefficient <br />for each stage considered should be detennined. Appen- <br />dix C illustrates a method for detennining a composite <br />value of k for each stage. Plates 4 and 5 give the rela. <br />tion between k and Manning's n for flows in the rough <br />flow zone shown in Plate 3. HOC sheets 631-4 and <br />631-4/1 also give a procedure for detennining an effective <br />Manning's n. <br /> <br />e. Hydraulic efficiency. The problem of the most <br />efficient cross section is treated by Brater and King <br />(1976, see pp 7-5 to 7-7) and Chow (1959. see <br />paragraph 7-6). <br /> <br />2-2. Hydraulic Design Aspects <br /> <br />a. General. This presentation assumes that the <br />design engineer is fully acquainted with the hydraulic <br />theories involved in unifonn and gradually varied flows, <br />steady and unsteady flows, energy and momentum princi. <br />pies, and other aspects such as friction related to <br />hydraulic design nonnally covered in hydraulic texts and <br />handbooks such as those by Brater and King (1976) and <br />Chow (1959). The following is presented as guidance in <br />the method of application of textbook material and to give <br />additional infonnation not readily available in reference <br />material. The use of k is emphasized herein because <br />computational results are relatively insensitive to errors in <br />assigned values of k. However, use of Manning's n <br /> <br />2-1 <br />