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EM 1110-2-1601 1 Jul 91 nature of curvilinear flow, the amount of channel alignment curvatUre should be kept to a minimum consistent with other design requirements. (2) The required amount of superelevation is usually small for the channel size and curvature commonly used in the design of tranquil-flow channels. The main problem in channels designed for rapid now is standing waves generated in simple curves. These waves not only affect the curved flow region but exist over long distances downslream. The total rise in water surface for rapid flow has been found experimentally to be about twice that for lranquil now. (3) Generally, the most economical design for rapid flow in a curved channel results when wave effects are re- duced as much as practical and wall heights are kept to a minimum. Channel design for rapid now usually involves low rates of channel curvature. the use of spiral aransi- tions with circular curves, and consideration of invert banking. b. Superelevazion. The equation for the aransverse water-surface slope around a curve can be obtained by balancing outward centrifugal and gravitational forces (Woodward and Posey 1941), If concentric now is assumed where the mean velocity OCCW"S around the curve, the following equation is obtained toy = C v2w gr (2-31) where toy" rise in water swface between a theoretical level water swface at the center line and outside water- surface elevation (superelevation) C = coefficient (see Table 2-4) v = mean channel velocity W = channel width at elevation of center-line water surface g = accelerations of gravity r = radius of channel center-line curvature 2-12 Use of the coefficient C in Equation 2-31 allows compu- tation of the tolal rise in water surface due to supereleValion and standing waves for the conditions listed in Table 2-4. If the tolal rise in water surface (superelevation plus surface disturbances) is less than 0.5 ft. the normally determined channel freeboard (para_ graph 2-6 below) should be adequate. No special lre:ll- ment such as increased wall heights or invert banking and spiral lransitions is required. Table 2-4 Supereievation Formula Coetficienta i,,;nannel Flaw Type CIllSS Section Type of Curve Value of C Tranqu~ Tranquil Rapid Rapid Rapid Rapid Rapid Rectangular Trapezoidal Rectangular Trapezoidal Rectangular Tapezoidal Rectangular Simple CiraJlar Simple CiraJlar Simple Circular Simple CiraJlar Sj>iraI Transitions Spiral Transitions Sj>iral Bank.od 0.5 0.5 1.0 1.0 0.5 1.0 0.5 (I) Tranql1i1 flow. The amount of superelevation in aranql1i1 flow around curves is small for the normal chan- nel size and curvature used in design. No special lre:ll- ment of curves such as spirals or banking is usually necessary. Increasing the wall height on the outside of the curve to contain the superelevation is usually the most economical remedial me:lSure. Wall heights should be increased by toy over the full length of curvature. Wall heights on the inside of the channel curve should be held to the straight channel height because of wave action on the inside of curves. (2) Rapid flow. The disturbances caused by rapid flow in simple curves not only affect the tlow in the curve. but persist for many channel widths downstream. The cross waves generated at the beginning of a simple curve may be reinforced by other cross waves generated farther downsa-eam. This could happen at the end of the curve or within another curve, provided the upslrea/ll and downStre:lm waves are in phase. Wall heights should be inCre:lSCd by the amount of superelevation, not only in the simple curve. but for a considerable distance downstream. A detailed analysis of standing waves in simple curves is given in Ippen (1950). Rapid-flow conditions are improved in curves by the provision of spiral aransition curves with or without a banked invert. by dividing walls to reduce the channel width. or by invert sills located in the curve. Both the dividing wall and sill lre:llments require structures in the flow; these structures create debris problems and. therefore. are not generally used.