**7. References**

258 Hydrodynamics – Natural Water Bodies

contains the distribution of f considering the experimental and the numerical data together. It was possible to adjust power laws between f and k/hc (k=scos), in the form f = a(k/hc)b. The values of the adjusted "a" and "b", and the limits of validity of the adjusted equations,

2

4

6

Pdf

(a) (b)

(11.31º51.13o) and the experimental results together (=45o). The total area covered by

a b k/hc Re R

[degrees] [-] [-] [-] [-] [-]

53.13 0.195 0.502 0.0798-0.485 8.0E6-1.2E8 0.97

45.00 0.146 0.355 0.0776-0.311 2.0E7-1.6E8 0.97

30.96 0.185 0.294 0.0942-0.377 2.0E7-1.6E8 0.96

In this chapter different aspects of the flows over stepped spillways were described, considering analytical, numerical and experimental points of view. The results show characteristics not usually found in the literature, and point to the need of more studies in

this field, considering the practical use of stepped chutes in hydraulic structures.

Fig. 19. Friction factor: (a) Probability distribution function for 11.31º51.13o and numerical results; (b) Probability distribution function considering the numerical

the bars is equal to 1.0 in both figures (R = correlation coefficient; Re = 4q/).

8

10

12

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 <sup>0</sup>

Experimental and numerical results

f

together with the geometrical information, are given in Table 2.

Numerical results

<sup>0</sup> 0.02 0.04 0.06 0.08 0.1 0.12 0.14 <sup>0</sup>

f

Table 2. Coefficients for f = a(k/hc)b and other details.

5

**5. Conclusions** 

10

Pdf

15


Stepped Spillways: Theoretical, Experimental and Numerical Studies 261

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**13** 

*Brazil* 

Rafael Manica

**Sediment Gravity Flows:** 

**Study Based on Experimental Simulations** 

*Instituto de Pesquisas Hidráulicas - Universidade Federal do Rio Grande do Sul* 

Gravity (or density currents) currents are a general class of flows (also known as stratified flows) in which flow takes place because of relatively small differences in density between two flows (Middleton, 1993). Gravity currents that are driven by gravity acting on dispersed sediment in the flow were called *sediment gravity flows* (Middleton & Hampton, 1973). Sediment gravity flows may occur in both subaerial (e.g. avalanches, pyroclastic flows and so on) and subaqueous ambients (e.g. bottom currents, turbidity currents, debris flow – see Simpson, 1997) and may flow above, below or inside the ambient fluid. The distinction regarding sediment gravity flows and open-channel flows is due to the order of magnitude of the density difference between the fluids. Sediment gravity flow are generally of the same order of magnitude, whilst open-channel flow the difference in density between the flow

The interest in these types of flows are mainly due to four factors: (i) phenomenon comprehension highlighting the origin, transport and deposition processes; (ii) their great magnitude and unpredictability (potential environmental hazards); (iii) the lack of monitoring these events in nature and; (iv) because of their economic significance, since

Despite the great progress addressing theoretical and analytical evaluation of these phenomena, particularly on the origin, transport and deposition of this class of flow, even today, they are not completely comprehended. Generally, the complexity of the phenomenon can be expressed by: (i) interaction between the flow and the bed morphology; (ii) the quantity and the composition of sediment transported and (iii) the complex mixing processes. As a consequence, the origin and the hydrodynamics properties of these flows are less understood than open-channel flows (Baas et al., 2004). Simple definitions, such as volumetric concentrations of sediments, its composition and size distribution of solid particles in the mixture as well as the sediment-support mechanisms are difficult to measure

Kneller & Buckee (2000) commented that difficulties in understanding the dynamics of suspended sediment are extremely complex by virtue of turbulence. In that case, the phenomenon is: non-linear; non-uniform (variation in space) and unsteady (variation in time). If the flow contains large loads of sediments and/or cohesive sediments in suspension this complexity increases even more. Besides the variation of density with time and space (open boundary conditions), the mechanical properties (rheology) of the suspensions

some deposits generated by such currents are prospective reserves of hydrocarbon.

(e.g. rivers) and the ambient air is much higher than that.

in nature which is also an indicative of such complexity.

**1. Introduction** 

