Tài liệu Open channel hydraulíc for engineers ppt

PREFACE The subject of Open Channel Hydraulics for Engineers, also called Applied Hydraulics, is a subject required not only for Hydraulic Engineering students but also for other enginee

CANTHO UNIVERSITY

MHO 5/6 project Civil and Mechanical Engineering

OPEN CHANNEL HYDRAULICS

FOR ENGINEERS

LECTURE NOTE

PREPARED BY

LE ANH TUAN

DELFT, 2003

To my wife Hoang Nga, my son Anh Tu and my daughter Hoang Ngan,

and all my closed friends

You are lovely rivers flowing in my dreams

LA Tuan

PREFACE

The subject of Open Channel Hydraulics for Engineers, also called Applied Hydraulics, is a subject required not only for Hydraulic Engineering students but also for other engineering fields involved, such as Construction Engineering, Transportation Engineering and Environmental Engineering It follows the previous subject named Fluid Mechanics The knowledge of open-channel hydraulics, which is essential to the design of many hydraulic structures, has made advances by leaps and bounds The practical importance of this topic in the water resources development together with the challenge posed by the variety and complexity of its problems, has created for a long time the need for more comprehensive and detailed treatment of this subject As a result, many excellent texts have been written, not only in English, but also in other languages The best of these texts have imposed a logical and coherent structure in the study of the subject, and created a tradition that present texts consciously follow

This lecture note is prepared as a reference document for the subject It emphasizes the dynamics of the open-channel flow, by attempting to provide a complete framework of the basic equations of motion of the fluid, which are used as building blocks for the treatment of many practical problems The structure of the document, with seven chapters totally, follows a logical sequence from a description and classification of Fluid Mechanics and Open Channel Flows, as reviewed in Chapter 1

A development of the basic equation of motion for uniform flow is encountered in Chapter 2 Coming to Chapter 3, the fruitful concepts of specific energy and hydraulic jumps are introduced and developed Chapter 4 presents a variety of non-uniform flows and applications of drawing water-surface profiles Spatially-varied flow, found

at spillways and weirs is considered in Chapter 5 Transitions and energy dissipators are discussed in Chapter 6 Finally, in Chapter 7, unsteady flow in open channels is introduced generally and an introduction to the method of characteristics is presented Writing on the subject matter of this lecture note, grateful use has been made of the authoritative texts and treatises on the subject by Ven Te Chow (1973), Henderson (1966), Sergio Montes (1998) and Hubert Chanson (1999), to which frequent references were made

Developing this lecture note is part of the activities within the MHO 5/6 project This document could not have been completed without the enthusiastic support and advices

of Professor Dr Henri L Fontijn, Head of the Fluid Mechanics Laboratory of the

Faculty of Civil Engineering & Geosciences (CiTG), Delft University of Technology

He spent numerous hours of his time reading and advising on the typed texts

Special acknowledgments are due to the faculty and staff members of CiTG, CICAT, Delft University of Technology and my colleagues at CanTho University, who encouraged me in many ways

Finally, I would like to thank all my family members and friends, whose help in loving support is most gratefully acknowledged

LE ANH TUAN

Delft University of Technology, the Netherlands, September 2003

CONTENTS

Preface iii

Contents iv

List of symbols vii

Chapter 1: INTRODUCTION 1

1.1 Review of fluid mechanics 1

1.1.1 Fluid mechanics 1

1.1.2 Hydrostatics 3

1.1.3 Continuity equation 4

1.1.4 Types of flow 4

1.1.5 Bernoulli’s equation 5

1.1.6 Euler’s equation 5

1.1.7 Flow through orifices, mouthpieces and pipes 5

1.1.8 Flow through open channel 6

1.2 Structure of the course 7

1.2.1 Objectives of the course 7

1.2.2 Historical note for the course 7

1.2.3 Structure of the course 8

1.3 Dimensional analysis 10

1.3.1 Fundamental dimensions 10

1.3.2 Dimensional homogeneity 11

1.3.3 Principles of Dimensional Homogeneity 12

1.3.4 Buckingham’s - theorem 14

1.3.5 Limitations of dimensional analysis 16

1.4 Similarity and models 16

1.4.1 Advantages of model analysis 16

1.4.2 Hydraulic similarity 17

1.4.3 Geometric similarity 17

1.4.4 Kinematic similarity 18

1.4.5 Dynamic similarity 18

1.4.6 Technique of hydraulic modelling 19

1.4.7 Developments in hydraulic model testing 20

1.4.8 Undistorted models 20

1.4.9 Comparison of an undistorted model and the prototype 21

1.4.10 Distorted models 22

1.4.11 Advantages and disadvantages of distorted models 23

1.4.12 Comparison of a distorted model and its prototype 23

Chapter 2: UNIFORM FLOW 25

2.1 Introduction 25

2.1.1 Definition 25

2.1.2 Momentum analysis 27

2.2 Basic equations in uniform open channel flow 28

2.2.1 Chezy’s formula 28

2.2.2 Manning’s formula 30

2.2.3 Discussion of factors affecting f and n 32

2.3 Most economical cross-section 32

2.3.1 Concept 32

2.3.2 Conditions for maximum discharge 32

2.3.3 Problems of uniform-flow computation 36

2.4 Channel with compound cross-section 38

2.5 Permissible velocity against erosion and sedimentation 40

Chapter 3: HYDRAULIC JUMP 46

3.1 Introduction 46

3.2 Specific energy 47

3.2.1 Specific energy 47

3.2.2 Critical depth and critical velocity 48

3.2.3 Types of flows 49

3.3 Depth of hydraulic jump 51

3.3.1 Concept 51

3.3.2 Water rise in hydraulic jump 51

3.3.3 Energy loss due to hydraulic jump 53

3.3.4 Hydraulic jump features 54

3.4 Types of hydraulic jump 55

3.4.1 Criterion for a critical state-of-flow 55

3.4.2 Types of hydraulic jump 58

3.5 Hydraulic jump formulas in terms of Froude-number 61

3.5.1 Momentum-transfer curve 61

3.5.2 Direct hydraulic jump 62

3.5.3 The initial depth and the sequent depth 62

3.5.4 Energy loss 64

3.5.5 Efficiency 66

3.5.6 Height of jump 66

3.5.7 Length of jump 66

3.6 Submerged hydraulic jump 67

3.6.1 Definition 67

3.6.2 Flow in submerged jump 68

Chapter 4: NON-UNIFORM FLOW 70

4.1 Introduction 70

4.1.1 General 70

4.1.2 Accelerated and Retarded flow 71

4.1.3 Equation of non-uniform flow 73

4.2 Gradually-varied steady flow 75

4.2.1 Backwater calculation concept 75

4.2.2 Equation of gradually-varied flow 75

4.3 Types of water surface profiles 77

4.3.1 Classification of flow profiles 77

4.3.2 Sketching flow profiles 79

4.3.3 Prismatic channel with a change in slope 82

4.3.4 Composite flow profiles with various controls 83

4.4 Drawing water surface profiles 84

4.4.1 Direct-step method 84

4.4.2 Direct numerical integration method 88

Chapter 5: SPILLWAYS 90

5.1 Introduction 90

5.2 General formula 91

5.3 Sharp-crested weir 93

5.3.1 Experiments on sharp-crested rectangular weirs 93

5.3.2 Other types of sharp-crested weirs used for flow measurement 96

5.4 The overflow spillway 98

5.4.1 The spillway crest 98

5.4.2 The spillway face 100

5.4.3 The spillway toe 101

5.5 Broad-crested weir 104

5.5.1 Introduction 104

5.5.2 Broad-crested weir discharge formula 105

5.5.3 Undular weir flow and discharge coefficients 105

Chapter 6: TRANSITIONS AND ENERGY DISSIPATORS 107

6.1 Introduction 107

6.2 Expansions and Contractions 108

6.2.1 The transition problem 108

6.2.2 Expansions and Contractions 108

6.3 Drop structures 114

6.3.1 Introduction 114

6.3.2 Free overfall 114

6.3.3 The head of the overfall 116

6.3.4 The base of the overfall 118

6.3.5 The drop structure 119

6.4 Stilling basins 121

6.4.1 Concept of stilling basin 121

6.4.2 Simple stilling basin design for canals 121

6.4.3 Specially designed stilling basins 124

6.5 Other types of energy dissipators 128

6.5.1 Stepped spillways 128

6.5.2 Bucket-type and Ski-Jump 129

Chapter 7: UNSTEADY FLOW 130

7.1 Introduction 130

7.2 The equations of motion 131

7.2.1 Derivation of Saint-Venant equations 131

7.2.2 The equations of motion 131

7.3 Solutions to the unsteady-flow equations 135

7.3.1 Characteristic differential equations 135

7.3.2 Initial condition 138

7.3.3 The simple-wave problem 140

7.3.4 Numerical solution of the characteristic differential equations 143

7.4 Positive and negative waves; Surge formation 145

REFERENCES 147

LIST OF SYMBOLS

A cross-sectional area [m2]

b (average) width of channel [m]

B open-channel free surface width [m]

C Chezy coefficient [m½s-1

]

Cc contraction coefficient

Cd discharge coefficient

c natural wave speed [m/s]

cf friction coefficient

D (circular) pipe diameter [m]; hydraulic depth [m]

E mean specific-energy head [m]

F force [N]; momentum transfer per unit width [Nm-1]

f friction coefficient according to Darcy-Weisbach

g gravity constant [m/s2]

H local total energy-head [m]

height of water above crest of weir

HD design head, (i.e head over spillway crest) [m]

h flow depth, measured perpendicular to channel bed [m]

hc critical water depth [m]

he equilibrium flow depth [m]

hn normal depth at which flow is uniform [m]; hn = he

ho observed water depth [m]

ib slope of channel bed

ic slope of critical-depth line

ie slope of energy grade line

if friction slope

io observed slope; bed slope

e

i arithmetic mean slope of the energy grade line

L length (of channel, or pipe or weir) [m]

Lb length of stilling basin [m]

Lcrest crest length in flow direction [m]

n resistance coefficient in flow, called Manning's constant [m-1/3s]

P wetted perimeter [m]; weir height [m]

Pe equilibrium wetted perimeter [m]

p pressure [Pa]

q discharge per meter width [m2/s]

Q total volume discharge [m3/s]

R hydraulic radius [m]

s flow direction; coordinate along stream line

S (bed) slope; slope of energy gradient line

V depth-averaged or mean flow velocity [m/s]

Vo approach velocity to weir [m/s]

W channel bottom width [m]; top width of flow area [m]; water weight in

channel over a length L [N]

x Cartesian coordinate [m]

y Cartesian coordinate [m]

z Cartesian coordinate [m]; altitude or elevation,

measured positive upwards [m]

zb change of bottom elevation between two cross-sections [m]

zcrest spillway crest elevation [m]

zo reference elevation [m]; bed elevation [m]

Greek symbols

 velocity distribution coefficient; angle (of slope)

 deflection angle

h change in flow depth [m]

E change in specific-energy head [m]

H energy-head loss, i.e change in total energy-head [m]

L length [m]

p pressure difference [Pa]

s small distance along the flow direction [m]

V change in flow velocity [m/s]

zo change in bed elevation [m]

 specific weight [N/m3]

 dynamic viscosity [Pa.s]

 kinematic viscosity [m2/s]

 channel slope; angle of channel bed relative to horizontal

 density [kg/m3]

 surface tension [N/m]

 shear stress [Pa]

o mean longitudinal shear stress acting over perimeter [Pa]

Subcripts

c critical flow conditions

conj conjugate flow property

des design flow conditions

e equilibrium flow

i characteristics of section {i} (in numerical integration process);

running index

r ratio of prototype to model characteristics; roller

1 upstream flow conditions

2 downstream flow conditions

Abbreviations

LHS left-hand side of equation

sp.gr specific gravity

sp.wt specific weight (N/m3)

SI International System of Units (Syst ème International d'unités)

SAF Saint Anthony Falls Hydraulics Laboratory

SIA Swiss Society of Engineers

RHS right-hand side of equation

USBR United States Bureau of Reclamation