ABSTRACT

This project is all about comparative study of different dispersion coefficient models. The geometry method of determining the parameters were gotten from different dimension. A flow channel was constructed in a drainage system of both meandering and straight channel. The straight channel that was constructed in the drainage, which has a depth, length, width. While the meandering channel has three meander.

CHAPTER ONE
1.0          INTRODUCTION
1.1          Background of study

Accidental spills are major threats to urban meandering streams and longitudinal rivers. The Ontario Ministry of the Environment’s Spill Action Centre (SAC) documented 1030 spills to water courses during the year 2008(Ministry of Environment, 2008). Contaminant spills in streams may occur for different reasons such as chemical transport accidents which occur while moving chemicals too close to streams, illegal dumping of contaminants, and sudden increases in untreated wastewater discharges (bypass) into a stream (Chin, 2013).To more accurately simulate the travel time and the break-through curves of spilled contaminants, it is vital to predict longitudinal dispersion coefficients for different reaches of the stream during a range of flow conditions. The longitudinal dispersion coefficient (E) is known to depend on the bed material roughness(friction term), the aspect ratio (width-to-depth ratio), and the Froude number, which reflects the effect of the longitudinal slope (Disley et al., 2015).Some theoretical and empirical models that have been widely considered, include those by Elder (1959), Fisher (1968, 1975),Mc Quivery and Keefer (1974), Liu (1977), Fisher et al. (1979),Iwasa and Aya (1991), Seo and Cheong (1998), Kashefipour and Falconer (2002) and Disley et al. (2015). Although these models include the same key input variables, their predictions of longitudinal dispersion vary significantly. Moreover, all of the models have shortcomings with respect to the inadequate representation of natural data and the presence of large prediction errors. Compared with natural stream measurements, all of the models yielded significant errors in prediction of the longitudinal dispersion coefficient. Therefore, a simpler and more reliable approach is required to predict longitudinal dispersion coefficient in urban streams.

River pollution has received much attention in recent years. Dispersion coefficient is a fundamental parameter in hydraulic modeling of river pollution, for it is a measure of the intensity of the mixing of pollutants in natural streams and is therefore, of great interest to river managers, environmental engineers, institutional researchers, among others, who are involved in river water pollution control.

More than 30 years ago Fischer ~1967! Developed a theory for determination of the longitudinal dispersion coefficient from cross-sectional data and the transverse mixing coefficient. However, predicted longitudinal dispersion coefficients often deviate from observed ones by orders of magnitude. The deviation is attributed mainly to the inability to account for meandering and other non-uniform conditions of the river. The overall objective of this paper is to develop a simple yet reliable method of estimating the longitudinal dispersion coefficient in single-channel natural streams, including straight and meandering ones.

1.2          OBJECTIVE OF THE STUDY

This research is intended to compare already developed models for the longitudinal dispersion coefficient of natural rivers and meandering streams, from most recent   developed models that have already been developed. Comparing the recent models and drawing a best line of fitness from the models. The specific objectives are therefore to:

• To compare the different models of equations and know which one is best to determine the longitudinal dispersion in natural rivers and meandering streams.
• To understand the concepts of longitudinal dispersion in natural rivers and meandering stream.
• To understand the prediction and the time frame of longitudinal dispersion in natural rivers and meandering stream.
• To know those parameters that improved the above models.

1.3          SCOPE OF STUDY

The extent of work to be carried out in this research understands what longitudinal dispersion coefficient in straight rivers and meandering natural stream is all about. This is all about comparing the recent developed models in determining longitudinal dispersion coefficient in straight rivers and natural meandering stream. Comparing the recent world developed models of equation and understanding each of them their consideration that they both considered to derive their equation. Testing of the recent models was also carried out in the research. The practical was conducted in Bori and data was collected and tested with the recent models of equations.

1.4          STATEMENT OF PROBLEM

In recent years longitudinal dispersion of natural rivers and meandering stream has been a vital problem to both economical control and aquatic natural resources in rivers and streams. The bacterial in the water in both straight rivers and meandering stream has affected the life span of mankind through the pollution of water. It has also affected the agricultural sectors in different country world-wide.  The release of waste in the rivers causes contamination of water environment in straight rivers and meandering stream channels. The width to depth ratio (W/H), and stream bed roughness factor (U/U*), are key parameters for calculating the dispersion coefficient in natural streams.

1.5          LIMITATION OF THE STUDY

The basic assumptions of this analysis limit the application of the best line of fitness of the longitudinal dispersion coefficient equation for straight uniform rivers and meandering streams. The differences between observed and predicted dispersion coefficients are mainly attributed to the effects of dead zones, bends, secondary currents, and other irregular features that are not explicitly involved.

Moreover, the majority of streams are uniform enough for an approximate analysis (Fischer et al. 1979).Therefore, the regents equations can be used practically for natural rivers that approximately satisfy flow conditions with relative high accuracy. Furthermore, Fischer’s triple integral expression of the longitudinal dispersion coefficient, on which is based, is valid only after the initial convective-dominated period or after a distance downstream from the source where the balance between advection and diffusion is reached.