Open Channel Flow Over a Permeable River Bed

ABSTRACT We have modelled an open channel flow through a porous media (River). In the model, we considered water as an incompressible fluid; the flow as steady and uniform; the system is assumed to be isothermal and the flow, also a laminar flow. We have solved the resulting equation using analytical method. By some mathematical operations, the momentum partial differential equation (PDE) was reduced to ordinary differential equation (ODE) and the resulting equations are solved analytically using the technique for solving linear equations with constant coefficients-method of variation of parameters. The analysis of the result was done and plotted on graph using MATLAB to show the effect of permeability on flow parameters such as velocity, pressure gradient and the height of the channel. Recommendations were made to control and manage the flow of rivers.

TABLE OF CONTENTS

Title page -------------------------------------------------------------------------- i

Certification page --------------------------------------------------------------- ii

Dedication ------------------------------------------------------------------------ iii

Acknowledgement-------------------------------------------------------------- iv

List of figures, tables and graphs -------------------------------------------- v

Abstract ---------------------------------------------------------------------------- vi

Table of Contents ----------------------------------------------------------------

vii-viii

Open Channel flow ------------------------------------------------------------- ix

CHAPTER ONE

1.1 Introduction -------------------------------------------------------------- 1-3

1.2 Aims and Objectives of the study ------------------------------------ 3-4

1.3 Scope of the study ------------------------------------------------------- 4

1.4 Relevance of the study -------------------------------------------------4

1.5 Limitations of the study ------------------------------------------------ 5

CHAPTER TWO

2.0 Literature Review --------------------------------------------------------- 6-

14

CHAPTER THREE

8

3.0 Theory of Channel flow

3.1 Properties of fluid ------------------------------------------------------- 15-

26

3.2 Types of flow in Channels (structure) ---------------------------------- 26-

27

3.2.1 Steady flow and unsteady flow -------------------------------------- 28-29

3.2.2 Uniform and Non-uniform (or varied flow) ---------------------- 29-30

3.2.3 Laminar flow and Turbulent flow ---------------------------------- 30-31

3.2.4 Subcritical flow, critical flow and supercritical flow ------------- 31-32

3.3 Volumetric flow rate ----------------------------------------------------- 32-

33

3.4 Permeability of fluid during flow -------------------------------------- 33-

35

CHAPTER FOUR

4.0 Model Equation in open channel flow over a permeable flow

4.1 Mass Conservation ----------------------------------------------------- 36-39

4.2 Conservation of Momentum ------------------------------------------ 39-41

4.3 Equation of an open channel flow through porous media with porosity f -

--------------------------------------------------------------------------------------- 41-

42

4.4 Method of solution of modelled equation ------------------------ 43-51

CHAPTER FIVE

9

5.0 Analysis and discussion of Results ---------------------------------- 52-58

5.1 Conclusion ---------------------------------------------------------------- 59

5.2 Recommendations ------------------------------------------------------60

REFERENCES ----------------------------------------------------------------------- 61-

62