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CHANNEL CURVES, SUPERELEVATION, Sheet 660-1

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HYDRAULIC DESIGN CRITERIA
SHEETS 660-1
CHANNEL CURVES
SUPERELEVATION

1. Purpose.

Flows in curved channels result in increases in depth along the outside channel walls with corresponding decreases along the inside walls. The difference in the water-surface elevations between the channel center line and the outside wall is called the flow superelevation. This rise in water surface is a function of the channel shape, velocity, width, and radius of curvature. Chart 660-1 presents a graphical means of estimating superelevation for various combinations of channel velocities, widths, and radii of curvature.
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2. Design Controls. 

Channel capacity (wall heights) should be based on the maximum expected resistance (friction) factor. The curve geometry and flow superelevation should be based on the minimum expected resistance factor. This design combination should result in economically conservative design for all flows.

3. Design Equations. 

The transverse rise in water surface of flow in a channel bend can be adequately described for both tranquil and rapid flow using an equation adapted from the centrifugal force equations.


where

¥Äy = the rise (superelevation plus surface disturbances) in water surface between the channel center line and ther outsiede wall, (ft)

C = a coefficient depending upon flow Froude number, channel shape, and curve geometry

V = average channel velocity, (fps)

W = straight channel water-surface width, (ft)

g = acceleration of gravity, (ft/sec^2)

r = radius of curvature at center line, (ft)

The following tabulation relates the coefficient C with flow conditions, channel shape, and curve geometry. These relations are also shown by the sketches in Chart 660-1.

4. Curve Design

a. Tranquil flow. 
The required increase in the outer wall height in a channel curve over that of the straight channel for both rectangular and trapezoidal channels is obtained from Chart 660-1 using a C value of 0.5. The inner wall height should remain that of the straight channel. The unbalanced flow condition in the curve causes helicoidal flow that can result in undesirable scour and deposition in and downstream from the curve. Tests by Shukryl indicate that helicoidal flow can be minimized if the curve radius is greater than three times the channel width.

b. Rapid flow.
Rapid flow in a simple circular curve results in a transverse rise in the water surface approximately twice that occurring with tranquil flow. This increase results from surface disturbances generated by changes in direction. These disturbances persist for many channel widths downstream of the curve. Superelevation for rapid flow can be estimated from Chart 660-1 using the appropriate C values given in the tabulation above or in the chart. A detailed analysis of the cross waves generated in simple curves is given by Ippen.(2)

The criterion for minimum radius of a simple curve, based on structures built by the Los Angeles District, is:


with y equal to the flow depth for the minimum expected friction factor (Chart 631). This criterion is recommended for rapid flow curves with or without invert banking. A similar criterion for maximum allowable superelevation for acceptable flow conditions in rectangular channels is

¥Äy_max = 0.09W


c. Invert banking.
Invert banking maintains flow stability in curved channels and when used with spiral transitions results in minimum total rise in water surface between the channel center line and outside wall. It is limited to channels of rectangular cross sections. The invert is usually banked by rotating the bottom about the channel center line. The invert along the inside wall is depressed by ¥Äy below the center-line elevation with a corresponding rise along the outside wall. The banking upstream and downstream from the curve should be accomplished linearly in accordance with the spiral transition lengths determined from equation 3 of Sheets 660-2 to660-2/4. Wall heights on both sides of banked curves are usually designed to be the sane as the wall height of the straight channel. Banking of trapezoidal channels is not practicable. Such channels should be designed wherever possible to have long radius curves resulting in minimum superelevation.

5. References.

(1) Shukry, A., ¡°Flow around bends in an open flume.¡± Transactions American Society of Civil Engineers, vol 115, paper 2411(1950), PP 751-779.

(2) Ippen, A. T., ¡°Channel transitions and controls,¡± Engineering Hydraulic, H. Rouse, ed. John Wiley & Sons, Inc., New York, N. Y., 1950, pp 496-588.
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USACE, Hydraulic Design Criteria, SHEET 660-1, CHANNEL CURVES, SUPERELEVATION



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