INFLUENCE OF CHANNEL BED SLOPE ON ENTROPY PARAMETER USED FOR DISCHARGE ESTIMATION

Abstract

River flow measurement is an essential practice in hydraulic engineering for water resources planning and management, water availability analysis, reservoir operation, flood forecasting, designing of hydraulic structures, etc. However, conventional methods of discharge measurement are costly, time-consuming, cumbersome, labour intensive, dangerous during high floods and rough weather. In the discharge estimation process, the velocity distribution with flow depth is generally required, for which traditional methods like Prandtl Von Karman universal velocity distribution law (a logarithmic law) and power laws are used. These laws are valid for wide open channels only, i.e., channels having longitudinal velocity variation with maximum velocity occurring at the free surface. These methods cannot be applied to all kinds of river reaches. Also considering the longitudinal limitations of traditional methods and errors associated with them, Chiu (1987) presented the probability approach for finding velocity distribution at a river section with the help of the principle of maximum entropy, which provides better results in numerous situations like sediment-laden flows. As stated in the literature, the entropy theory relies on a parameter called entropy parameter that, in turn, remains constant in different conditions of flow. Hence, it can be surmised as an intrinsic parameter. Value of entropy parameter is a fundamental measure of information about the characteristics of channel section such as changes in channel roughness, bed slope, and geometric shape. Experimental investigations on laboratory flume were conducted to collect precise data at different discharge rates through a channel cross-section at varying channel bed slopes to record corresponding velocity distribution data. Collected data was used to apply the concept of entropy theory for calculating the entropy parameter and discharge. Work was carried out on experimental flume HM 162 in the Watershed Hydrology lab of the Department of Hydrology, Indian Institute of Technology, Roorkee under controlled conditions, i.e., uniform and steady flow conditions. Final analysis of the collected data depicts that state equilibrium constant and entropy parameter (M) remains constant with varying channel bed slopes and discharge values. Results obtained based on analysis of collected data revealed that the twodimensional entropy model was a quick and accurate technique for estimation of mean crosssectional velocity and discharge.