Flow of Fluids under the Influence of different Forces with Pollution and Mass Transfer

Abstract

The thesis is mainly concerned with some problems of pollutants of water and remediation of pollution by aeration, which is very important in our life. This thesis consists of seven chapters. In chapter (1), deals with the concept of pollution of water with definitions, and background and water sources of the River Nile. We present the pollutants discharging into the River Nile, and review of water quality models and some methods of treatment. Also we introduce equations describe the pollutant concentration. Finally, we review some reported works in pollution of water, solute transport and ground water. In chapter (2), there are many problems related to the pollution of water in Rosetta Branch of the River Nile, especially downstream El Rahawy Drain. As an example, in summer 2012 many tons of fish were found floating on the water. At the same time, thousands of people suffered from different diseases due to the water pollution in that area. Here comes the importance of this study to know the impact of this pollution and how we can predict the size of the problem at the reasonable time as well the procedure to control pollutants in this important ecosystem. We solve the equations of conservation of mass, momentum and constituent concentration by using Duflow model and we got the results: 1. In general, sections at which the values (levels) of H small correspond to the sections for which discharge (Q) is small and vice versa. 2. At constant time t, Q decreases as x increases, hence, Q x   < 0 . At constant x, H increases as t increases, hence H t   > 0. This result confirms equation (1.1). Summary II 3. At El Rahawy Drain, for t = 31 hours, the difference between the measured and simulated values of Dissolved Oxygen (DO) is small . Numerical studies show that for 0  t  23 h, this difference is large. 4. In general, the behavior of (DO) is opposite to the behavior of Biological Oxygen Demand ( BOD). Many solutions have been proposed to solve this disasterous problem in this important ecosystem. This study can be applied to any polluted area in any river from source to sink. In chapter (3), we present simple analytical solutions for the unsteady advection dispersion equations describing the pollutant concentration C(x,t) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions x 0and x  0and the origin at x = 0. The variation of C(x,t) with the time t  0 (the steady state case ) is taken into account in our study. The special case for which the dispersion coefficient D= 0 is studied in detail. The parameters controlling the pollutant concentration along the river are determined In chapter (4), simple analytical solution is presented for unsteady equation representing the concentration of the dissolved oxygen Y(x, t) along the river at any time t . The solution is obtained by using Laplace transformation technique. Adjoin solution techniques are used as boundary conditions to solve the equation. The variation of Y(x, t) with time t  0 (the steady state case) and with the parameters of the flow is taken into consideration in our study. It is shown that Y(x, t) increases as t increases, keeping the other parameters constant, but Y(x, t) decreases as the added pollutant rate along the river q increases. The adjoin solution techniques used in this work are effective and accurate for solving the equation representing the concentration of the dissolved oxygen Y(x, t) when arbitrary initial and boundary conditions are required. The details are demonstrated in graphs. Summary III In