UUNNIIVVEERRSSIITTII MMAALLAAYYSSIIAA PPAAHHAANNGG

BBOORRAANNGG PPEENNGGEESSAAHHAANN SSTTAATTUUSS TTEESSIISS♦♦♦♦

JUDUL : INVESTIGATING THE EFFECT OF GAS FLOW RATE ON THE DRAG REDUCTION PERFORMANCE IN

GAS OIL – SOLID GAS FLOW SYSTEM

SESI PENGAJIAN : 2011/2012

Saya NOR ` AQILAH BINTI NORAHZAN

(HURUF BESAR) mengaku membenarkan tesis (PSM/Sarjana/Doktor Falsafah)* ini disimpan di Perpustakaan

Universiti Malaysia Pahang dengan syarat-syarat kegunaan seperti berikut :

1. Tesis adalah hakmilik Universiti Malaysia Pahang

2. Perpustakaan Universiti Malaysia Pahang dibenarkan membuat salinan untuk tujuan

pengajian sahaja.

3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara

institusi pengajian tinggi.

4. **Sila tandakan ( √ )

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 : NO. 38 TAMAN SRI BATIK, Associate Prof Dr. Hayder A. Abdul Bari

TELUK MURUH, LUMUT, Nama Penyelia

32200 LUMUT, PERAK

Tarikh : 19 JANUARY 2012 Tarikh: 19 JANUARY 2012

CATATAN : * Potong yang tidak berkenaan.

** Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak

berkuasa/organisasiberkenaan dengan menyatakan sekali sebab dan tempoh

tesis ini perlu dikelaskan sebagai SULIT atau TERHAD.

♦ Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana

secara penyelidikan, atau disertasi bagi pengajian secara kerja kursus dan

penyelidikan, atau Lapuran Projek Sarjana Muda (PSM).

INVESTIGATING THE EFFECT OF GAS FLOW RATE ON THE DRAG

REDUCTION PERFORMANCE IN GAS OIL- SOLID GAS FLOW SYSTEM

NOR`AQILAH BINTI NORAHZAN

A thesis submitted in fulfillment

of the requirements for the award of the Degree of

Bachelor of Chemical Engineering (Gas Technology)

Faculty of Chemical & Natural Resources Engineering

UNIVERSITI MALAYSIA PAHANG

JANUARY 2012

iii

SUPERVISOR`S DECLARATION

“I hereby declare that I have read this thesis and in my opinion this thesis has fulfilled

the qualities and requirements for the award of Degree of Bachelor of Chemical

Engineering (Gas Technology)”

Signature : …………………………………….

Name of Supervisor : Associate Prof. Dr. Hayder A. Abdul Bari

Position :

Date : 19 January 2012

iv

STUDENT`S DECLARATION

I declare that this thesis entitled “Investigating the effect of gas flow rate on the drag

reduction performance in gas oil- solid gas flow system” is the result of my own

research except as cited in references. The thesis has not been accepted for any degree

and is not concurrently submitted in candidature of any other degree.”

Signature :

Name : Nor ’ Aqilah Binti Norahzan

ID Number : KC08034

Date : 19 January 2012

v

To my beloved Mum and Dad for always being there for me,

and my wonderful supervisor, Associate Prof. Dr. Hayder A. Abdul Bari who never

stops believing in me.

vi

ACKNOWLEDGMENT

First and foremost, I would like to express my warmest appreciation to my

dedicated supervisor, Associate Prof. Dr. Hayder A. Abdul Bari for his continuous

enthusiasm, encouragement, words of wisdom, excellent advice and great concern

towards my work. Within the course of my research, he has given a steady and excellent

supervision and created a very friendly environment which made the research enjoyable.

My sincere appreciation also extends to all my colleagues and others who have

contributed towards my understanding and thoughts, and provided assistance at various

occasions. To all the people who are not listed but surely enrich my life while doing this

research, thank you. The experiences and knowledge I gained throughout the process of

completing this research project would prove invaluable to better equip me for the

challenges which lie ahead.

Last but definitely not the least I am grateful to all my family members,

especially Mum and Dad. I can never thank you enough for your love, and for

supporting me throughout my studies in University Malaysia Pahang (UMP).

vii

ABSTRACT

Phenomenon on drag reduction in gas-liquid system has to be emphasized in the past

decade because of the importance in academic and industry. Drag has long been

identified as the main reason for the loss of energy in fluid transmission like pipelines

and other similar transportation channels. The main contributor to this drag is the

turbulence of the flow as well as friction against the pipe walls, which will results in

more pumping power consumption, increasing in production rates, pipelines capabilities

and faster transportation. In this study, injection of gas into the pipe flow as a drag

reducing agent was investigated. The experimental procedure also investigates the

effects of liquid flow rate, powder addition concentration and particle size of suspended

solid. The gas that used to inject in the pipelines is an air gas. Particular attention was

focused to the influence on the pressure drop due to the injection of air gas into the

horizontal 1.5 inch or 0.0381 meter pipe flow. The experimental results showed that the

drag reduction is more superior towards bigger particle sizes, higher in liquid flow rate

of diesel concentration and increasing the solid addition concentration. Percentage of

drags reduction increases by increasing the particle size. The maximum percentage of

drag reduction in the 630 µm particle size with 300ppm solid addition concentration for

9.5 m³/h liquid flow rate is 61.43 %.

viii

ABSTRAK

Fenomena pada pengurangan seretan di dalam sistem gas-cecair telah diberi penekanan

dalam dekad yang lalu kerana kepentingan dalam akademik dan industri. Seret telah

lama dikenal pasti sebagai sebab utama untuk kehilangan tenaga dalam penghantaran

bendalir seperti saluran paip dan lain-lain saluran pengangkutan yang serupa.

Penyumbang utama kepada seretan ini adalah pergolakan aliran serta geseran terhadap

dinding paip, yang akan menyebabkan penggunaan kuasa yang lebih mengepam,

meningkatkan kadar pengeluaran, keupayaan saluran paip dan pengangkutan yang lebih

cepat. Dalam kajian ini, suntikan gas ke dalam aliran paip sebagai satu ejen

mengurangkan seretan disiasat. Prosedur eksperimen juga menyiasat kesan kadar aliran

cecair, serbuk kepekatan Selain itu, saiz zarah pepejal terampai dan tambahan dalam

kepekatan diesel. Gas yang digunakan untuk menyuntik di saluran paip gas udara.

Perhatian khusus tertumpu kepada pengaruh kepada kejatuhan tekanan akibat suntikan

gas udara ke dalam inci mendatar 1.5 atau 0.0381 meter paip aliran. Keputusan

eksperimen menunjukkan bahawa pengurangan daya seret lebih ke arah saiz zarah yang

lebih besar, lebih tinggi dalam kadar aliran cecair kepekatan diesel dan meningkatkan

kepekatan tambahan yang kukuh. Peratusan drags kenaikan pengurangan dengan

meningkatkan saiz zarah. Peratusan maksimum pengurangan heret dalam saiz 630 µm

zarah dengan kepekatan tambahan 300ppm kukuh untuk 9.5 m³ / h kadar aliran cecair

adalah 61.43%.

ix

TABLE OF CONTENT

PAGE

SUPERVISOR`S DECLARATION iii

STUDENT`S DECLARATION iv

DEDICATION v

ACKNOWLEDGEMENT vi

ABSTRACT vii

ABSTRAK viii

TABLE OF CONTENTS ix

LIST OF TABLES xii

LIST OF FIGURS xiv

LIST OF ABBREVIATIONS xvi

LIST OF APPENDIX xvii

CHAPTER 1 INTRODUCTION

1.1 Background of Research 1

1.2 Problem Statement 5

1.3 Objectives of Study 5

1.4 Scope of Study 6

1.5 Rationale and Significant 6

CHAPTER 2 LITERATURE REVIEW

2.0 Introduction 7

2.1 Types of Fluid Flows 7

2.1.1 Laminar Flow 9

2.1.2 Turbulence Flow 10

2.2 Pressure Drop due to Friction 11

2.2.1 Principle & Theory 13

2.3 Drag Reduction 15

x

2.3.1 Mechanism of Drag Reduction 17

2.4 Drag Reduction Agents 18

2.4.1 Polymeric Drag Reduction Agent 18

2.4.2 Surfactant Drag Reduction Agent 20

2.4.3 Fiber Drag reduction agent 21

2.5 Two phase flow drag reduction 22

CHAPTER 3 METHODOLOGY

3.0 Introduction 24

3.1 Equipments 24

3.1.1 Cylinder tank 24

3.1.2 Transporting fluid 24

3.2 Material 24

3.2.1 Preparation of sand 25

3.3 Experimental rig 26

3.4 Research Method 29

3.5 Experiment procedure 30

3.6 Experimental calculation 31

3.6.1 Percentage Drag reduction calculations 31

3.6.2 Velocity and Reynolds number calculation 31

3.7 Summary of Research Procedure 32

3.7.1 Summary of Preparation of sand particle diameter 32

3.7.2 Summary of Experimental Procedure 33

CHAPTER 4 RESULTS AND DISCUSSIONS

4.0 Injection of gas into two phase flow caused drag reduction 34

4.1 Effect of pressure drop in the different particle concentrations 34

4.2 Effects of liquid flow on the drag reduction efficiency 35

4.3 Effect of sand particle concentration 36

4.4 Effect of Reynolds numbers in addition solid particle 38

xi

4.5 Effect between Reynolds number and percentage of drag

reduction with different particle size 40

CHAPTER 5 CONCLUSION AND RECOMMENDATIONS

5.1 Conclusion 42

5.2 Recommendation 43

REFERENCES 45

APPENDIX

A Experimental calculation 50

B Experimental data table 55

xii

LIST OF TABLES

TABLE NO. TITLES PAGE

3.1 Diesel fuel oil properties at T = 293 K and 1 atm 25

3.2 Size of particle sand and weight 26

B.1 Detail Description of the Pipe 56

B-2.1.1 Drag Reduction Result for 71 µm with no additional

of sand concentration 57

B-2.1.2 Drag Reduction Result for 71 µm with 100ppm of

sand concentration 58

B-2.1.3 Drag Reduction Result for 71 µm with 200ppm of

sand concentration 58

B-2.1.4 Drag Reduction Result for 71 µm with 300ppm of

sand concentration 59

B-2.2.1 Drag Reduction Result for 315µm with no additional

of sand concentration 60

B-2.2.2 Drag Reduction Result for 315µm with 100ppm of

sand concentration 61

B-2.2.3 Drag Reduction Result for 315µm with 200ppm of

sand concentration 61

B-2.2.4 Drag Reduction Result for 315µm with 300ppm of

sand concentration 62

B-2.3.1 Drag Reduction Result for 630µm with no additional

of sand concentration 63

B-2.3.2 Drag Reduction Result for 630µm with 100ppm of

sand concentration 64

B-2.3.3 Drag Reduction Result for 630µm with 200ppm of

sand concentration 64

B-2.3.4 Drag Reduction Result for 630µm with 300ppm of

sand concentration 65

B-3.1 Data of pressure drop increasing with time taken

during the investigation for each additional sand

particle size diameter 66

B-4.1.1 Reynolds numbers for 71 µm of sand particle size 70

B-4.1.2 Reynolds numbers for 315 µm of sand particle size 71

xiii

B-4.1.3 Reynolds numbers for 630 µm of sand particle size 71

B-5.1 Liquid flow rate with percentage of drag reduction 72

xiv

LIST OF FIGURES

FIGURE NO TITLES PAGE

1.1 Types of gas injector 4

2.1 Velocity profile of laminar and turbulent flow 9

2.2 Diagram of Laminar Flow 10

2.3 Diagram of Turbulent Flow 11

2.4 Examine the x- component of the velocity, µ A

at a point A 12

2.5 Variation of the velocity component u with time at a

specified location in turbulent flow 13

2.6 Characteristic of turbulent and laminar flow in the

rough and smooth pipe with correlates to friction

factor of pipe 15

2.7 Phenomenon of drag reduction 17

3.1 Experimental rig design 28

3.2 Portable gas injector device 29

4.1 Behavior of the pressure drop influenced by different

particle sand 35

4.2 Behavior of the liquid flow rate on the drag reduction

efficiency influenced by different particle sand and

addition concentration 35

4.3.1 Relationship between percentages of drag reduction

with different sand particle concentration for size

71µm. 37

4.3.2 Relationship between percentages of drag reduction

with different sand particle concentration for size

315µm 37

4.3.3 Relationship between percentages of drag reduction

with different sand particle concentration for size

630µm 38

4.4.1 Relationship between Reynolds number and percentage

of drag reduction with different sand particle

concentration for size 71µm. 39

xv

4.4.2 Relationship between Reynolds number and percentage

of drag reduction with different sand particle

concentration for size 315µm. 39

4.4.3 Relationship between Reynolds number and percentage

of drag reduction with different sand particle

concentration for size 630µm 40

4.5.1 Relationship between Reynolds number and percentage

of drag reduction with different sand particle

concentration for 300ppm 41

xvi

LIST OF ABBREVIATIONS/ SYMBOLS

DRA Drag Reducing Agent

DR Drag Reduction, dimensionless

D.I Internal pipe diameter, meter

%DR Percentage Drag Reduction

m Mass, kg

ppm Parts per million

∆Pa Pressure difference after adding additives, N/m2

∆Pb Pressure difference before adding additives, N/m2

NRe Reynolds number, dimensionless

Q Volumetric flow rate, m3/hr

ρ Density, kg/m3

µ Viscosity, kg/s.m

Dp Diameter Pipe

PDRA Polymer Drag Reduction Agent

MDR Maximum Drag Reduction

xvii

LIST OF APPENDIX

APPENDIX TITLE PAGE

A Experimental Calculation

A-1: Calculation for Required Additives 55

A-2: Calculation of Reynolds Number 56

A-3: Calculation for Drag Reduction 58

B Experimental Data Table 59

B-1: Detail Description of the Pipe 60

B-2: Flow Detail for injection of gas into the pipe 61

B-3: Flow detail for injection of gas into the pipe with pressure

drop data 70

B-4: Flow detail for injection of gas into the pipe with Reynolds

number data 74

B-5: Flow detail for injection of gas into the pipe with liquid

flow rate and percentage of drag reduction 76

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND OF STUDY

Since from the past, drag in the pipeline has been identified as the major

problem for the losses of energy during transportation. Drag or sometimes called fluid

resistance is referring to the forces that opposite to the relative motion of an object

though in the fluid dynamics. Drag happened between the fluids, and the pipe wall

causes substantial pressure drops along such pipelines as the fluid flow there though.

These energy losses can be identified through pressure drop, which will result in more

pumping power consumption.

The drag reduction phenomenon was first observed by Toms (1948) about 60

years ago. The idea of drag reduction when he studied the effect of polymer added into

a turbulent Newtonian fluid. He revealed that the addition of small amounts of polymers

in turbulent flow can produce a significant result in reducing frictional drag. Since that

time, nearly 7000 studies on drag reduction have been published.

Drag reduction serves as a typical approach to save pumping power in pipelines

or other transportation channels and equipments, particularly those which handle crude

oil and refined products. Pumping power saving corresponds to the reduction of

pressure drop in these media. Studies of the drag reduction agent have proven its ability

in reducing pressure drop.

2

Drag Reducing Agents can be classified into three major categories such as

polymers, surfactants and suspended solids. The most effective drag reducing agent that

commonly used in industry is polymers. A few parts per million (ppm) of the additive

can greatly reduce the turbulent friction factor of fluid flow in a pipe (Toms, 1948).

There are two types of polymer, which are synthetic polymer and natural polymers.

Synthetic polymers are come from petroleum oil and meanwhile natural polymers can

be extracted from resources in nature.

Synthetic polymers such as polyethylene oxide (PEO), co- polymer (Magnafloc

1011) of polyacrylamide, carboxymethyl cellulose, polythene oxide, and sodium-

acrylate are rarely used as a drag reducing agent in turbulent flow. The results after

injections of these polymers into pipelines caused drag reduction in pressure loss;

especially at high mixture velocity by clearly change in the flow pattern (Al-Sarkhi et

al., 2001; Soleimani et al., 2004; Al-Wahaibi et al., 2007; Al-Yaari et al., 2009).

However, natural polymeric additives attracted less attention in industrial

applications but the benefits of a natural polymeric are similar to the synthetic polymers.

The explorations of newer sources of mucilage are increased with increasing in industry

demand. Currently, many researchers have discovered the potential of natural polymers

in the drag reduction phenomenon. The successful in a formulation Okra-natural

mucilage and Aloe Vera mucilage as a natural drag reduction agent gave the impressive

result and able to increase the flow rate of fluid in a pipeline at the same pressure drop

by reducing the friction drag (Hayder et al., 2011).

The second drag reducing agents are surfactants. Surfactant is a blend of surface

active agent. It works as an agent who can greatly lower the surface tension of a liquid

even though it presents in a very low concentration. The surfactant concentrations

necessary to achieve maximum drag reduction in order of a few hundred or thousand

ppm, depending on the surfactant type, Reynolds number, and temperature and flow

geometry (Andrej et al., 2010).

3

The third drag reduction agents are suspended solid as known as fibers. Fibers in

suspension can interact and entangle even at low populations and can form bundles or

entities that behave differently from the individual fibers. According to Duffy et al.

(2002), fibers interlock at moderate concentrations to form three-dimensional structures

or networks which in liquid suspension alter the transport properties of the suspension

Another phenomenon that can be defined as the drag reduction is the injection of

gas into non- Newtonian liquid. The injection of gas with high speed into liquid metals

or slag is widely used in the pipelines industry. The injection of gas could reduce the

pressure loses in the liquid flow rates .There are some speculations that the injection of

gas can change the critical concentration of oil and water where phase inversion occurs

and that the pressure drop increase during phase inversion can become larger by

Ioannou et al. (2005).

In the single liquid cases with low mixture velocity, the pressure drop decreases

with increasing gas injection. It can decrease more at large values of the water fraction

than at smaller values at the point of phase inversion (Descamps et al., 2006). At low

superficial gas velocities the pressure drop decreases as mean velocity superficial gas

phase is increased. It also can reaches to a minimum value for the critical velocity in the

transition from laminar to turbulent flow.

The pressure gradient increases steadily after past this velocity. The drag

reduction by gas injection in Newtonian fluid is more effective than that for shear

shinning fluid when the dimensionless liquid height remains in the area of high value in

the turbulent gas-laminar liquid stratified flown (Jing-yu et al., 2009).

There are three types of gas injectors that used in industry as drag reduction.

Although the methods of gas injector have different way but it has the same purpose to

reduce the pressure in the pipelines.

4

Figure 1.1: From top to bottom: nozzle injector, conical porous injector, circular porous

injector

Source: Descamps (2006)

In the present investigation, air will be injected in gas oil – solid two phase flow

in pipelines. Drag reduction performance will be investigated with different gas flow

rates due to the injection of air gas. The injection of gas can reduce pressure drop and

the pattern flow will move smoothly. The benefits when using drag reducing

phenomenon is allowing a greater production flow rate at an economical cost and

reduction of operating costs such as pumping power.

5

1.2 PROBLEM STATEMENT

Cost saving is one of the most essential concerns in any industry. One of the key

to the present concern is by cutting down on the power consumption. Many flows in

industrial applications such as oil pipelines are in turbulent flow. The turbulent flow

with high velocity in the pipe flow system causes the formation of eddies in many

different length scales and characterized by larger pressure drops and pumping power

requirements than those of laminar flows. The scale of turbulent eddies in a larger

contribution of turbulent energy production to mean mechanical energy loss. The energy

losses in the pipe flow system can affect the production efficiency and economical cost

like pumping power. Pump is widely use for effective fluid transportation before drag

reduction phenomenon. The installations of pump cause the plant more costly because

of drag in the turbulent flow. By using pump into the plant, the high energy

consumption is needed.

1.3 OBJECTIVES

Based on the research background and problem statements described in the

previous section, there are the following objectives of this research:

1. To investigate the effects of gas flow rate on the drag reduction in the gas

oil- solid two phase flow system.

2. To study the effects of liquid flow on the drag reduction efficiency

3. To investigate the effect of powder addition concentration

4. To investigate the effect of particle size diameter of sand as suspended solid

in the pipeline systems.

6

1.4 SCOPES OF STUDY

The following scopes have been identified in order to achieve the objectives:

1. Injection of air gas will be applied to study the influence of gas as drag

reduction performance in the flow system

2. The pressure readings of the testing section will be collected to calculate

pressure drops, followed by the percentage of drag reduction.

3. Diesel will be used as the transporting fluid in this study.

4. The addition of sand particle concentration.

5. 71 µm and 315 µm and 630 µm of particle size as suspended solid

6. Volumetric flow rate of fluid will be used to calculate the velocity and

Reynolds Number (Re) of the fluid.

1.5 RATIONALE AND SIGNIFICANCE

Drag reduction is the alternative way to reduce pumping power losses during

transportation through pipelines. So that, injecting the drag reduction would decrease

the friction pressure losses in a pipeline. The reduction of the frictional pressure during

flow can exceedingly reduce the cost of pumping power. Furthermore, power saving is

very important to save the cost in the plans. The present study focuses on injecting gas

into the gas oil – solid two phase in the pipelines that can reduce pressure loses and save

the environmental. The gas that used to inject in the pipelines is a gas air. Under some

conditions, the available quantities of gas with associated liquid could be transported

without building a new pipeline or perhaps without increasing pump horsepower.

CHAPTER 2

LITERATURE REVIEW

Drag reduction is a term that frequently used to characterize the reduction in

friction turbulent flow through pipes resulting in an increase of fluid flow or decrease in

pressure loss. Drag reduction in turbulent flow is an important phenomenon for practical

applications in fluid transport. The friction pressures in laminar flow cannot be changed

unless the physical properties of the fluid are changed.

2.1 TYPE OF FLOW

There are three types of flow which are Laminar, Transitional and Turbulent

flow. The purpose when calculating heat transfer or pressure and head loss it is

important to know if the fluid flow is laminar, transitional or turbulent. Laminar flow

happens when dealing with small pipes and low flow velocities. Laminar flow can be

regarded as a series of liquid cylinders in the pipe. Non – laminar flow is called

turbulent flow.

Turbulent flow happens at high flow rates and with larger pipes. In turbulent

flow, eddies and wakes make the flow is unpredictable. The transitional flow actually is

a mixture of laminar and turbulent flow. This happens when the turbulent in the center

of pipe and the laminar flow near the edges. Each of these flows behaves in different

equations that predict their behavior and have different manners in terms of their

frictional energy loss while flowing in the pipelines (Witold et al., 2008).

In these cases, turbulent or laminar flow could be determined by the

dimensionless Reynolds Number. The Reynolds number is important in analyzing at

8

any type of flow when there is substantial velocity gradient such as shear. The Reynolds

number is proportional to inertial force that divided by viscous force.

Re = ρVD

µ (2.1)

Where V is the mean velocity of the object relative to the fluid (m/s), µ is the dynamic

viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s)), D is diameter of the pipe ( m)and ρ is

the density of the fluid (kg/m³) .

At high Reynolds numbers, the inertial forces, which are proportional to the

fluid density and the square of the fluid velocity, are more significant compared to

viscous forces, and therefore the viscous forces cannot inhibit the random and rapid

fluctuation of the fluid. This condition of flow is known as turbulent flow. Whereas in

low or moderate Reynolds number, the viscous forces are significant enough to restrict

the fluid fluctuation and keep the fluid under smooth ordered motion; and this is known

as laminar flow (Abulencia et al., 2009).

Critical Reynolds number, Recr is the value where the flow becomes turbulent

and this value varies for different geometries and flow conditions. The transition from

laminar to turbulent flows is also dependent on other factors; such as pipe surface

roughness, surface temperature, vibration and fluctuations in the flow. In most practical

conditions, having Reynolds number lower than 2300 is considered as laminar flow,

above 4000 is turbulent flow and in-between is transitional (Abulencia et al., 2009).

Figure 2.1 shows the velocity profile of both laminar and turbulent flow. A

laminar flow has a true parabola velocity profile, slightly pointed at the middle and

tangent to the wall of the pipe. The average velocity of a fully developed laminar flow is

about one-half of the maximum velocity flow in a pipe. In turbulent flow, the profile is

resembles a flattened parabola and the average velocity is about 0.8 times the maximum

velocity (Abulencia et al., 2009).

9

Figure 2.1: Velocity profile of laminar and turbulent flow

Source: Cengel (2006).

2.1.1 Laminar Flow

Laminar flow sometimes known as streamline flow has motion that is very

regular and predictable. This can be seen when a water faucet is turned on low. The

flow of water in straight lines and the motion is rather smooth. The laminar flow usually

would be in the smooth flow of a viscous liquid through a tube or pipe. There are

different velocities of flow from zero at the walls to a maximum along the centerline of

the pipelines (Abulencia et al., 2009).