Figure 19.33 Filter construction details (after Van Bendegom 1969)
that the thickness of the filter construction be increased at these places. Some examples of common constructional details are shown in Figure 19.33.
As we saw in Section 19.6.1, channels with a hydraulic gradient flatter than the land
sloperequire structures that dissipate surplus energy. Such a structure can be divided into four parts: 1) The part upstream of the (control) section, where flow is accelerated to critical flow; 2) The part in which water is conveyed to the anticipated lower elevation; 3) The part immediately downstream of section U (Figure 19.34), where energy is dissipated; 4) The channel reach that requires aconstruction to protect it against erosion. 780
basin length L g 4 -
Figure 19.34 Illustration of terminology for a straight drop structure
In the upstream part of the structure, the flow over the sill is controlled. The head, h,, versus discharge, Q,relationship of this control is a function of the sill height, pI, the longitudinal profile of the weir crest, the shape of the control section perpendicular to the flow, and the width of this control section, b. Each combination of these four properties yields one out of an infinite number of combinations of h, and Q (Bos 1989). Further, the channel upstream of the structure has a discharge capacitythat can be characterized by the water depth, y,, versus discharge, Q, relationship, written as
Q = KI Y,"
K, = a factor which varies with the shape and hydraulic properties of the channel u = the exponent to y,, varying between 1.7 for trapezoidal channel with wide bottom, to 2.3 for a narrow-bottomed channel
To avoid sedimentation upstream of the structure, the controlshould be dimensioned
so that the head-discharge curve of the structure coincides with the y, versus Q curve of the channel throughout the flow range with sediment transport (see Figure 19.35).
For a broad-crested weir sill with a rectangular control section perpendicular to the flow (Figure 19.34), the head-discharge relationship reads
2 2 Q = CdC , 3 L g b, h11.5
Cd =discharge coefficient (-) C , = approach velocity coefficient (-) b, = width of control section (m)
flow range with sediment transport
Figure 19.35 Matching of Q-y, and Q-h, curves for a structure with sediment transport
The product of the discharge- and the approach velocity coefficients may, for general design purposes, be taken as cdc, -N 1.O. For detailed informationon the head-discharge relationship of control structures, consult Bos 1989; and Bos, Replogle, and Clemmens 1984. We can dimension the conveyance and energy dissipation parts of the structure in relation to the following variables (Figure 19.34): H, = upstream sill-referenced energy head (m) AH = change in energy head across structure (m) Hd = downstream energy head (m) q = discharge per unitwidth of sill (m2/s) g = acceleration due to gravity, being 9.81 m/sz n = step height (m) yu = flow depth at section U (m) Yd = downstream flow depth relative to basin floor (m) y2 = flow depth in downstream channel (m) These variables can be combined to calculate H I and H,, after which we can make a first estimate of the drop height
(AH + Hd) - HI
Subsequently, we canestimate the flow velocity and depth at section U with
vu = J&Äz
and with the continuity equation, we calculate
9 y =u v u
The flow at section U can best be characterized by the dimensionless Froude number
VU Fr, = -
This Froude number classifies the flow phenomena at the downstream side of the structure and enables the selection of a...