DISTRIBUTION OF SHEAR STRESS IN SMOOTH RECTANGULAR OPEN CHANNEL
TAN SWEE YEN
Bachelor of Engineering with Honours (Civil Engineering)
2010
UNIVERSITI MALAYSIA SARAWAK
R13a BORANG PENGESAHAN STATUS TESIS
Judul: DISTRIBUTION OF SHEAR STRESS IN SMOOTH RECTANGULAR OPEN CHANNEL
SESI PENGAJIAN: 2009/2010
Saya TAN SWEE YEN (HURUF BESAR)
mengaku membenarkan tesis * ini disimpan di Pusat Khidmat Maklumat Akademik, Universiti Malaysia Sarawak dengan syarat-syarat kegunaan seperti berikut:
1. Tesis adalah hakmilik Universiti Malaysia Sarawak.
2. Pusat Khidmat Maklumat Akademik, Universiti Malaysia Sarawak dibenarkan membuat salinan untuk tujuan pengajian sahaja.
3. Membuat pendigitan untuk membangunkan Pangkalan Data Kandungan Tempatan.
4. Pusat Khidmat Maklumat Akademik, Universiti Malaysia Sarawak dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara institusi pengajian tinggi.
5. ** Sila tandakan ( ) di kotak yang berkenaan
SULIT (Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktub di dalam AKTA RAHSIA RASMI 1972).
TERHAD (Mengandungi maklumat TERHAD yang telah ditentukan oleh organisasi/
badan di mana penyelidikan dijalankan).
TIDAK TERHAD
Disahkan oleh
(TANDATANGAN PENULIS) (TANDATANGAN PENYELIA)
Alamat tetap: 1651 TMN RIVERVIEW,
LORONG 1D, JLN DAYA, BINTAWA MR. CHARLES BONG HIN JOO
Nama Penyelia 93450 KUCHING SARAWAK.
Tarikh: Tarikh:
CATATAN * Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah, Sarjana dan Sarjana Muda.
** Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu dikelaskan sebagai SULIT dan TERHAD.
The following Final Year Project:
Title: Distribution of Shear Stress in Smooth Rectangular Open Channel Author: Tan Swee Yen
Metric: 17418
has been read and certified by
____________________
Mr. Charles Bong Hin Joo Date
Supervisor
DISTRIBUTION OF SHEAR STRESS IN SMOOTH RECTANGULAR OPEN CHANNEL
TAN SWEE YEN
This project is submitted to Faculty of Engineering, University Malaysia Sarawak
in partial fulfillment of the requirements for the
Degree of Bachelor of Engineering with Honours.
(Civil Engineering) 2010
vi
TABLE OF CONTENTS
Page
Acknowledgement iii
Abstrak iv
Abstract v
Table of Contents vi
List of Tables x
List of Figures xi
List of Symbols xiv
List of Abbreviation xvi
Chapter 1 INTRODUCTION
1.1 General Overview 1
1.2 Significance Study on Determining the Shear Stress 2
1.3 Objective and Purpose 3
1.4 Scope of Study 3
1.5 Structure of Final Year Project Chapters Outline 3
1.5.1 Chapter 1: Introduction 4
1.5.2 Chapter 2: Literature Review 4
1.5.3 Chapter 3: Methodology 4
1.5.4 Chapter 4: Result, Analysis and Discussion 5 1.5.5 Chapter 5: Conclusion & Recommendation 5
vii Chapter 2 LITERATURE REVIEW
2.1 Introduction 6
2.2 Significance of Boundary Shear Stress 6
2.3 Distribution of Shear Stress in Smooth
Rectangular Open Channel 8
2.3.1 Velocity distribution 8
2.3.2 Secondary current 9
2.4 Review of Previous Research Work 11
2.4.1 Wall and bed shear forces in open channel 12 2.4.2 Shear stress ratio and width to depth of the channel 14 2.4.2.1 Relationship of Mean Shear Stress for Bed
and Wall Shear Stress 16
2.4.2.2Relationship of Bed and Wall Shear Stress Distribution to Depth and Hydraulic Radius
Mean Shear Stress 18
2.4.2.3 Relationship of Shear Stress Distribution for Open
Channel with Smooth Wall and Rough Bed 21
2.4.3 Research on Boundary Shear Stress 22
2.4.3.1 Relationship of Distribution of Boundary Shear
Stress to measured Velocity Field 24
2.4.3.2 Relationship of Distribution of Boundary Shear
Stress to Ray-Isovel 25
2.5 Method to determine shear stress distribution 27
2.5.1 Ray-Isovel Method 27
2.5.2 Einstein’s Hydraulic Radius Separation Method 38
viii
2.5.3 Method of wall shear stress calculation 30 2.6 Theoretical basic for boundary shear stress 34 2.6.1 First Approximation with non secondary
current consideration 31
2.6.2 Second Approximation with Correction Factors 31 2.6.3 Comparison of First and Second Approximation
Method to Experimental Result 32
Chapter 3 METHODOLOGY
3.1 Introduction 35
3.2 Model Set-Up 35
3.3 Measurement Method 37
3.3.1 Velocity Measurement 38
3.3.2 Flow Depth Level Measurement 40
3.3.3 Local Velocity Distance Measurement 41
3.3.4 Thermometer 42
3.4 Experiment Parameter 43
3.5 Overview of Experiment Procedure 43
3.6 Method of Shear Stress Calculation 44
ix
Chapter 4 RESULTS, ANALYSIS AND DISCUSSIONS
4.1 Introduction 46
4.2 Open channel velocity distribution 46
4.3 Open channel shear stress distribution 58 4.3.1 Open channel wall shear stress distribution 58 4.3.2 Open channel bed shear stress distribution 62
Chapter 5 CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusion 69
5.2 Recommendation 71
REFERENCES 72
APPENDIX 75
x
LIST OF TABLES
Table Page
2.1 Experimental Channel Flow Condition 22
4.1 Condition of water dynamic viscosity for different
water temperature 61
xi
LIST OF FIGURES
Figure Page
2.1 Typical velocity profile 9
2.2 Velocity distribution and the effect of secondary
current in open channel 11
2.3 Percentage of wall shear stress vs B/H + 3 13
2.4 Percentage of wall shear stress vs B/ H 14
2.5 Open channel layout 15
2.6 Shear stress ratio to width to depth ratio of the channel 16 2.7 Relationship of wall and mean shear stress to the ratio
of B/y in smooth open channel 17
2.8 Relationship of bed and mean shear stress to the ratio
of B/y in smooth open channel. 28
2.9 Relationship based on dimensionless wall shear stress
using depth as a function of ratio B/y for smooth open channel 19 2.10 Relationship based on dimensionless bed shear stress
using depth as a function of ratio B/y for smooth open channel 20 2.11 Comparison of shear stress distribution for smooth channel
to rough channel based on using channel depth, y as a function
of B/y 21
2.12 Comparison result of measured and calculated boundary shear stress distribution for whole wetted perimeter of the
xii
channel 23
2.13 Experimental study of distribution boundary shear
stress and determine near-bank velocity 26
2.14 Cross section of ray-isovel orthogonal coordinate system 28 2.15 The separation of cross sectional area for bed shear stress,
and side wall shear stress, 29
2.16 Comparison of first and second approximation in term of
average bed shear stress to existing experiment data 32 2.17 Comparison of first and second approximation in term
of average side wall shear stress to existing experiment data 33 3.1 Flow channel in (UNIMAS) Hydraulics and Hydrology
Civil Laboratory 36
3.2 The side view of the flow channel 36
3.3 Flow channel bed slope level control adjustment. 37 3.4 Nixon Streamflo 430 current meter to measure velocity in
flow channel 39
3.5 Sensing probe attached to current meter to measure the speed
of water 39
3.6 Point gauge 40
3.7 Wire-mesh layout 41
3.8 Using thermometer to measure the water temperature 42 4.1 Average velocity distribution for 10.4cm depth of water 47 4.2 Average velocity distribution for 6.5cm depth of water 48
4.3 velocity distribution for 2.6cm depth of water 48
4.4 Velocity distribution in rectangular channel 50
xiii
4.5 Velocity distribution in natural channel 50
4.6 Velocity distribution contour for 10.4 cm water depth 52 4.7 Velocity distribution contour for 6.5 cm water depth 53 4.8 Velocity distribution contour for 2.6 cm water depth 54 4.9 Average velocity distribution for various water depths 56
4.10 Water velocity profile 57
4.11 Average wall shear stress distribution for various water depths 59 4.12 Velocity distribution contour for 10.4cm water depth 63 4.13 Velocity distribution contour for 6.5 cm water depth 64 4.14 Average bed shear stress for 10.4cm depth of water 65 4.15 Average bed shear stress for 6.5cm depth of water 66
xiv
LIST OF SYMBOLS
- density of operating fluid, water (kg/m³) - average bed shear stress
- average wall shear stress
- cross sectional area for bed shear stress - cross sectional area for wall shear stress - Static pressure (N/m²)
- Total pressure (N/m²)
- local roughness height of the boundary - length measurement from the boundary
- perimeter length along the boundary between the two rays - short distance velocity
- Density of manometer fluid, paraffin (kg/m³) - bed shear stress
- mean shear value - wall shear stress
a - directional normal to the channel wall B - channel width
b - flow depth
d - mean width of cobles at elevation z g - Acceleration due to gravity (g = 9.81 m/s²) h - flow depth
xv
k - coefficient of pitot tube (assumed to be unity) L - length between boundary to the surface of the ray ld - dummy integration variable along ray
Rh - Hydraulic radius of the channel S - channel slope
S0 - Slope of the channel
T - interim variable where t=exp (- h/b) v - velocity of water (m/s)
y - coordinate of lateral direction y - water depth
z - coordinate that is perpendicular to flow direction x and lateral direction y
γ - unit weight of water (N/m³)
Δh - Difference in levels on manometer (m) Ө - angle of channel slope
- mean shear stress - mass density of water
n - normal vector pointing outside of control volume
xvi
LIST OF ABBREVIATION
ASCE - American Society of Civil Engineer
ii
To my beloved parents & friends
iii
ACKNOWLEDGEMENT
I would like to express my sincere appreciation to my project supervisor, Mr. Charles Bong Hin Joo for his guidance and advices throughout the Final Year Project.
Without his support and interest, this thesis would not have been the same as presented here.
I would like to thank the personnel incharge of Civil Engineering hydrology Laboratory, Mr. Ruizani for providing the necessary laboratory equipments for my research.
Lastly, I wish to thank those who have assisted me either direct or indirectly throughout the entire progress of my Final Year Project. Thank you.
iv ABSTRAK
Kajian tentang pengedaran daya rintangan ricih air merupakan salah satu elemen yang penting dalam kebanyakan bidang hidraulik kejuruteraan. Pengetahuan tentang pengedaran daya rintangan ricih air dapat membantu jurutera memahami struktur aliran air mekanik. Selain itu, pengedaran daya geseran air juga amat penting dalam proses pengangkutan mendapan terutamanya mendapan yang berlaku di sungai.
Tujuan utama kajian ini adalah untuk memahami pengedaran daya geseran air dalam saluran terbuka. Secara kesuluruhan, experimen ini dijalankan di Makmal Civil Hidraulik. Selain itu, formula Stokes (1845) akan digunakan untuk pengiraan daya geseran untuk dinding saluran terbuka. Formula yang sama akan diaplikasikan untuk daya geseran pada katil saluran terbuka. Di samping itu, keputusan experimen akan dibandingkan dengan teori yang sedia ada. Secara kesuluruhannya, didapati bahawa daya rintangan ricih air bergantung kepada jarak dari dinding saluran terbuka.
Peningkatan nilai daya rintangan ricih menyebabkan kelajuan air di dalam saluran terbuka berkurangan.
v ABSTRACT
The study of shear stress distribution is an important element in most hydraulic design field. A knowledge of the shear stress distribution helps in understanding of the mechanics flows and also solving certain problems such as sediment transportation and design of stable channels. The objective of this research is to study the distribution of the shear stress in smooth rectangular open channel. All the experimental work was conducted using the available open channel in Civil Engineering Hydrology Laboratory. The Stokes (1845) local wall shear stress formula will be use to determine the distribution of the shear stress in the open channel. Similar equation used for determining the local wall shear stress will be use to study the bed shear stress. Based on the result obtained, the results from this method are compared with theoretical statements in literature review. The results show that the increment of shear stress depends on the position of local velocity from the solid boundary of the open channel. This shows that higher shear stress results in reduction of local velocity.
1
CHAPTER 1
INTRODUCTION
1.1 General Overview
The studies of the distribution of shear stress in smooth rectangular open channel have been conducted widely around the world. Numerous research and experiments have been carried out to improve understanding of the distribution of the shear stress in open channel. The term “shear stress” in hydraulics context can be defined as a flowing liquids subjected by a drag force to its boundary. In other words, it can be described as the force applied by the flowing liquid attempt to drag the channel surface downstream with it (Chen and Cotton, 1986).
The study of the shear stress is vital element which can be apply in most hydraulics design field that can be used to solved hydraulics problem. For example, further studies of distribution of shear stress enable hydraulics engineer to improve their hydraulic structure design such as storm water drainage channel and also to have better understanding on channel erosion problem.
One of the important studies of shear stress conducted by Lundgren and Jonsson (1964) on analytical study of boundary shear stress in straight channel has contributed to the study of bank erosion. Furthermore, their researched have been
2
carried out and improved by Houjou et al. (1990) to calculate the boundary shear stress in open channel flow.
1.2 Significance Study on Determining the Shear Stress
The distribution of shear stress studies gave important impact in hydraulic structure design, research on sediment transportation and also in the study of velocity distribution. According to Guo and Julien (2005), it is essential to separate the bed shear stress and wall shear stress to study open channel flows. From the knowledge of the shear stress separation, the application of wall shear stress knowledge can be adapted to solve channel migration and erosion problem. For example, the development of wall shear stress equation enables the hydraulic engineers to determine the amount of shear stress applied to the channel wall according to the velocity of the liquid flow. From these data, engineers are able to predict the shear force effect and designed a hydraulic structure such as hydraulically stable storm water drainage channel that can collect and convey the storm water without causing erosion problem.
3 1.3 Objective and Purpose
The following is the aim of the study:
i. To study the distribution of shear stress in a smooth rectangular open channel for the condition of uniform flow.
ii. To determine the distribution of wall shear stress and bed shear stress using Stokes (1845) local shear stress formula.
1.4 Scope of Study
The study of distribution of shear stress in smooth rectangular open channel is only limited to uniform flow. During the study, experimental result is conducted in order to obtain the required data for analysis purposes. Then the experimental result is used with Stokes (1845) local shear stress method in order to calculate the shear stress. All the experimental work will be conducted in Civil Engineering Hydrology Laboratory, Universiti Malaysia Sarawak.
1.5 Structure of Final Year Project Chapters Outline
The shear stress distribution in smooth rectangular open channel report consists of five main chapters which are the introduction, literature review, methodology, result, analysis and discussion, and conclusion and recommendation
4 1.5.1 Chapter 1: Introduction
The introduction chapter consists of general idea about this study which covers the important of shear stress to solved hydraulics engineering structure design problem, aim and objectives of the study and also the scope and limitations of the study.
1.5.2 Chapter 2: Literature Review
This chapter describes several aspects such as study on previous researched done by others that related with this study. Besides that, other aspect such as mathematical formula and graphs relationship on distribution shear stress also presented in this chapter. The purpose of literature review is to shows the researched done by others and gain better understanding for the purpose of this study.
1.5.3 Chapter 3: Methodology
In this chapter, explanations about the method use to conduct the experiments are presented. All details regarding the required instruments, experiment set-up and methods to obtain the experimental data are presented clearly according to steps.
5
1.5.4 Chapter 4: Result, Analysis and Discussion
Experimental results will be analyse in this chapter. Based on experimental data, the data is analysed and are presented in the forms of tables and graphs. The discussion covers criteria such as the possible parameters or variables that influence the outcome of the experimental result.
1.5.5 Chapter 5: Conclusion & Recommendation
This chapter covers the conclusions of the overall study and the recommendations. Recommendations on the improvement works for this study in the future are also included.
Hence, further understanding on shear stress distribution will be conducted in the following literature review. From the literature review, the aim of this study is to get the idea of previous research done by others and conduct an experiment to determine the shear stress distribution in open channel.