|Channel Design for Soil and Water Conservation|
Channel Design for Soil and Water Conservation
Proposed by Stillwater Outdoor Hydraulic Laboratory
Q -Rate of discharge or flow in cubic meters per second.
A - Cross-sectional area of the flow in square meters.
V - Velocity of flow (mean) in meters per second.
n - Coefficient of retardance used in flow formulas.
R - Hydraulic radius in meters. It is the cross-sectional area A divided by the wetted perimeter.
S - Slope of energy gradient in meters per meter. d - Depth of flow in meters.
D - Depth of channel in meters after freeboard is added.
t - Width of water surface when the water is at depth d.
z - Side slope- ratio of horizontal to vertical.
b - Bottom width of a trapezoidal channel in meters.
Character of Flow
Flow in conservation channels is turbulent. Turbulence exists when the direction and magnitude of the velocity at any point within a fluid varies irregularly with time. Considerable energy may be expended in this action.
The velocity V, as computed from Q/A or estimated from flow formulas, is the mean velocity of all components parallel to the axis of the channel. These velocity components in any vertical section range from a maximum near the surface to zero at the bed. With vegetation, the velocity distribution from surface to bed may be very nonuniform, increasingly so as the cover becomes taller, stiffer, and "bunchier."
In vegetation-lined channels, there are wide differences in velocity throughout a cross section. The water at the edges of the channel will be flowing through the vegetation at low velocities. In the deeper portions of the channel, where the vegetation has been bent over and submerged, resistance to flow will be less and velocities will be higher, the least resistance will be encountered where the flow is deepest. The velocity V, as ordinarily determined, is the mean for the entire cross section. It is apparent that channel shape affects velocity distribution. For the same mean velocity, the maximum velocity in the center of a triangular channel could be much higher than in a trapezoidal or parabolic channel. For this reason, a reduction in permissible velocities with triangular channels is desirable.
Flow in field channels lined with vegetation generally has a rough water surface. The more irregular the bed and vegetal growth and the higher the velocity, the greater is the surface roughness. The amount of aeration is also dependent upon these factors. A freeboard (vertical distance from the maximum water surface to the channel berm) allows for these conditions as well as for differences between estimated and actual discharge and capacity. Freeboards of 0.15 meter are commonly used for vegetation-lined channels.
The design of conservation channels will be based on a mean velocity determined from the Manning formula:
The Manning formula will apply to uniform flow in channels. In designing ordinary vegetation-lined channels, this condition of uniform flow can be assumed to exist. For some steep channels and all channels with artificial linings (example: concrete, sheet metal, wood), careful. Consideration must be given to (1) inlet and outlet design and their effect on the flow in the channel, (2) changes in grade and alignment, and (3) changes in cross-sectional shape.
Stability of Channels
Stability of Vegetation-Lined Channels
Vegetation protects the channel by reducing the velocity near the bed.
Dense stands of long-stemmed vegetations will produce deep mats, and velocities will be low in these vegetal zones. It follows a uniform; sod-forming vegetation having a dense, relatively deep root system will offer the greatest protection against scour. However, consideration must be given to the ability of vegetation to reassume its normal growing position and withstand and recover from excessive deposition. Bermuda grass possesses these properties and, as known by experience, is one of the best covers to use.
(a) Uniformity of cover is extremely important. The stability of a sparsely covered area is the stability of the entire channel.
(b) In construction, if practical, the topsoil should be preserved and replaced, particularly over the center portion of the channel where the flow will be deepest.
(c) Fertilization and proper soil preparation should be done on newly constructed channels to insure rapid growth.
(d) Maintenance by mowing or controlled grazing will help to assure continuance of the desired density and uniformity of cover.
(e) Timely repair of eroded areas and protection against damage by rodents cannot be stressed too highly.
(f) Control of deposition is the first. Consideration of the technician when designing the channel and selecting the cover. Bunchgrasses and open covers like alfalfa, kudzu, etc., offer less retardance to low-silting flows than sod covers. Keeping covers short will reduce deposition. Wide, flat trapezoidal channels will be the most difficult to maintain from the deposition standpoint. Parabolic and triangular sections are less subject to deposition. (Unless side slopes are 6:1. or flatter, triangular sections are generally not recommended because of the undesirable velocity distribution.)
(g) If possible, keep water diverted from the channel until vegetation is well established.
To serve in designing earth channels to be lined with vegetation, permissible velocities have been determined experimentally for many different covers. Prime factors determining permissible velocities are:
(a) Physical nature of vegetation (type and distribution of root growth and top growth and physical condition), (b) erodibility of soil, (c) uniformity of cover, and (d) bed slope.
Flow disturbances grow in severity with increase in bed slope. The ability of vegetation to provide adequate protection decreases with increase in slope.
Design of Bare and other Nonvegetal Channels
The application of the Manning formula to hard-surfaced channels of concrete, sheet metal, wood, etc., and to earth channels free of bottom vegetation is straightforward. For the former, n can usually be assumed as constant for a given type of lining irrespective of the slope and shape of channel and depth of flow. For earth channels with bank vegetation, the selection of n for the smaller channels must be based on the width of the water surface, since some bank vegetation partially submerged has a relatively greater retarding effect in narrow channels. Table 1 contains values of Manning's n for common hard-surfaced linings and various conditions of earth channels.
Design of Vegetation-Lined Channels
The various vegetations for which experimental n-VR relationships are available are classified in table 4 according to their degree of retardance, When a cover can be expected to be significantly shorter or much less dense than that described in the Mole, use the next lower degree of retardance in estimating capacity.
Above some minimum level of cover density, the tallness of the vegetation overshadows the effect of differences in density on retardance.
For these conditions, only limitations as to tallness and to density conditions need be considered. Except for very sparse coverage, table 5 may be used to judge the degree of retardance.
The design of vegetation-lined channels requires that n be compatible with the value of VR. To accomplish this easily, graphical solutions of the Manning formula that apply to the five degrees of retardance, A, B, C, D, and E are presented in figures 14 to 18. These apply to flow with the vegetation completely submerged or nearly so. For shallow flow through upright vegetation with no submergence, Manning's n ceases to be related to VR. Some results of low-flow studies have been reported in the Transactions of the American Geophysical Union (April 1946
To aid in channel design, graphical solutions of dimensions of trapezoidal (side slopes l:l, 1.5:1, 2:1, 2.5:l, 3:1, 4:1, 5:1, and 6:1), triangular, and parabolic channels are included in figures 2 to
Complete examples for using the graphical solutions are presented in subsequent sections.
The parabolic channel, offering distinct advantages for control Of scour and deposition, deserves explanation. Most natural channels tend to assume this shape. The parabolic channel is defined by d = k(t/2)2, where d is the depth, t the width at depth d, and k is a shape constant.
As soon as d and t have been determined for maximum flow (from fig. II), k is automatically evaluated (a fixed point on the pivot line in fig. 12). It remains constant for the parabolic channel in question. Other combinations of depth and width for that channel must give the same value of k.
To determine other values of t and d use the nomograph in figure 12. A specific parabolic channel will have only one intersection point on the pivot line. When this is located by a straight line through the d and t for maximum flow, it serves as a pivot point that allows width to be readily determined for any other depth. In the example illustrated on the nomograph, the maximum flow was at a depth of 0.59 meters and top width of 9.8 meters. A 0.15-m&w freeboard required a total depth of 0.74 meters. The top width at this depth is graphically determined to be 10.7 meters.
As an aid in judging the shape of the channel, a side-slope line is incorporated in the nomograph in figure 12. Extension of a line through a specific pivot point to this slope scale gives the approximate side slope at the depth being considered. In an initial design, a check of the side slope at maximum depth is recommended so as to assume that a steep, impractical shape is not being selected.
The triangular and, particularly, the trapezoidal cross sections will not maintain their shape as well as the parabolic under ordinary conditions of intermittent runoff. In fact, the trapezoidal and triangular sections tend to become parabolic in shape, due to the normal actions of channel flow, deposition, and bank erosion.
The parabolic cross section approximates the cross-sectional shape naturally assumed by many old channels. For conservation channels, this appears to be a very desirable, combining most of the strong points, with none of the undesirable characteristics of any other shape.