SOME ASPECTS OF FLOW IN STABLE ALLUVIAL CHANNELS

Abstract

For hydraulic engineers responsible for the develop ment of irrigation facilities and their maintenancej the hydraulics of stable channels carved in loose alluvial material assumes great importance. The major problem in the design of such channels is to determine the width, depth and slope for given values of discharge and? bed material load and size. The main objective of the investigation is to study the various aspects of the problem of design of stable channels in alluvial material, in particular, 1. t6 evolve a method (i) for determining the width? depth and area and (ii) for predicting the shape of a selfformed stable channel, the relations being dimensionally homogone ousV 2. to develop a resistance relationship for predicting the bed slope necessary for a stable channel} 3. to study the role of sediment concentration in shaping the entire channel*, and if. to investigate and if possible provide a physical basis for stable channel design by using the principles of maximum sediment transport and/or minimum energy loss of flow. For the purpose of investigation, a large^data of stable channels from India, Pakistan, U.S.A. and Egypt have been used. A limited number of experiments have also been performed in the laboratory under controlled conditions to -11- determine the effect of the sediment concentration on the channel dimensions and slope. Experiments conducted in a sand tray indicated that the width is insensitive to the sediment concentration, the depth is slightly dependent and the slope is fairly strongly dependent on the concentration. A study based on the principles of maximum sediment transport rate and minimum energy loss of flow as the cri teria of adjustments in stable channel has been carried out by using different sediment transport and resistance relations by taking width, depth and slope as variables for given discharge Q, sediment load Qm and sediment sized. Though the former has yielded unrealistic results, the latter provides certain results. In some cases the grain shear stress is related directly to critical tractive stress of the size of the bed material. In certain other cases, the relation for width in terms of power of discharge agrees fairly well with the existing relations e.g. Lacey's and others. Further, in these cases, it is also found that the sediment concent ration does not affect the width and depth significantly, but has appreciable influence on the slope. Instead of taking slope as a variable, if it is taken as constant, it is shown that the principle of maximum sedi ment transport rate also yields tangible results which are exactly the same as obtained by the principle of minimum energy loss earlier. -111- I'ihen these results are applied to field data, deviations are noticed in the computed and actual para meters. The field data have been analyzed based on the principles of dimensional analysis so as to evolve a procedure for finding cross-sectional dimensions. Of all the parameters considered, including the sediment concen tration, Q/(d2J(AYs/P)d) defined as Qnd and g1/2d3/2/ v defined as d. are the important parameters for defining the water surface width W « and depth D. Here AY is diff- S 3 erence in specific weights of sediment and water, and P and v are mass density and kinematic viscosity of water respectively. Area A is found to be dependent on Qnd only. Equations for VJ , D and A have been presented. These give better prediction than that by the existing equations of Lacey, Simons and Chitale. Only two equations are required for the design for the known shape or side slope. Equations for W_ and A,being more accurate^ are S3 recommended for use in the design. Analysis for shapes of stable channels showed that the method based on the similarity hypothesis gives better prediction of shape than either the existing methods or Fourier analysis method developed herein. According to the similarity method the x and y coordinates of the channel are related by the equation y/3^ = f(x/x^) ,in which x3/d and yx/d are f-L(Qnd) and f2(Qnds d*)•Here yx =A/Wg -IVand the distance x from the bank where y - y-, is defined as x-j. For slope a premise is made that a sediment trans port law can also be used as resistance law for known value of Qm. On the basis of this, an equation for slope is developed in terms 0, Fd and y,/d >where 0- QT/(vigJ (AYs/p)d^) and Fd = U / JTAYg/P)d. When sediment load is not known an equation for determining the slope is also evolved in terms of F, and y-»/d. The prediction of slope by this equation is found to be bettor than the existing equation. The sediment carrying capacity of such a stable channel can be computed by the earlier equation using the slope as obtained from the latter