UNIVERSITI PUTRA MALAYSIA

MANAL M. ABOOD

FK 2005 128

EFFECTS OF NAPIER AND CATTAIL GRASSES ON OPEN CHANNEL FLOW CHARACTERISTICS

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EFFECTS OF NAPIER AND CATTAIL GRASSES ON OPEN CHANNEL FLOW

CHARACTERISTICS

By

MANAL M. ABOOD

Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia, in

Fulfilment of the Partial Requirements for the Degree of Master of Science

October 2005

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DEDICATION

I dedicate this work

To My Country Iraq,

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Abstract of the thesis presented to the Senate of Universiti Putra Malaysia in fulfilment

of the partial requirement for the degree of Master of Science

EFFECTS OF NAPIER AND CATTAIL GRASSES ON OPEN CHANNEL

FLOW CHARACTERISTICS

By

MANAL M. ABOOD

October 2005

Chairman : Badronnisa Yusuf

Faculty : Engineering

Laboratory study has been conducted to analyze the effects of two types of vegetations

namely Napier grass and Cattail grass on the characteristics of flow in an open channel.

The main objectives of this study are to determine the effects of vegetations on

Manning’s roughness coefficient and velocity distribution, and to develop relationships

between the characteristics of vegetation (density, degree of submergence and

distribution) with the properties of flow (Manning roughness coefficient, velocity and

Reynolds number).

The resistance properties for each of vegetation were examined in the flume which is

rectangular in cross section and has dimensions of 12m length, 0.32m width and 0.32m

height.

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The results show that the presence of vegetations increases the values of Manning’s

roughness coefficient, n, and affected significantly the vertical velocity profiles. The

effects depend on factors such as flow depth, degree of submergence, density and

arrangement of plant.

The Manning’s roughness coefficient, n, for flows with Napier grass increased with the

increased in flow depth for both submerged and unsubmerged situations, and this

increments varied from 0.017 to 0.065 with flow depth for high vegetation density (100

veg/m2) and from 0.0058 to 0.0427 for low vegetation density (20 veg/m

2). In the

presence of Cattail grass, the effects were reversed. The increased in flow depth leads to

reduction in the roughness coefficient, and this decrements varied from 0.031 to 0.022

for the high density and from 0.024 to 0.0157 for the low density. This may be due to

the physical characteristics of the cattail, which has no branching stems and leaves.

Manning’s n in the case of low density (20 veg/m2) of Napier grass decreased with the

increase of Reynolds number, Re for both submerged and unsubmerged vegetations.

However, for higher density (100 veg/m2), this phenomenon only occurred for

submerged vegetation. In the case of unsubmerged vegetation the n values increased

with the increased of Re. For cattail, the n values decreased with Re for all densities of

vegetation.

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The dependence of n on density of vegetation was found to be represented by a linear

relationship (R2=0.93-0.96) for both submerged and unsubmerged vegetations. The

results indicate a tendency for n to increase with increasing values of density for the

same value of flow depth. Napier grass increased the Manning’s, n with the increased of

density by 35%, while the Cattail grass increased the value of n with the increased of

density by 25%. Increment in Manning’s, n with the density of vegetation is not only

with the flow depth but also with the different types of vegetation. The Manning

roughness coefficient, n was also found to be affected by the vegetation arrangement.

The results show that the arrangement where the vegetations were at both sides of the

channel gave the highest values of n followed by the vegetations at the channel center

and then the vegetations were randomly distributed. The n value increased almost

linearly with the depth of flow in three types of arrangements.

The effects of vegetations in the vertical velocity distribution of flow were examined,

the results showed that the present of vegetation change the shape of velocity

distribution and reduced the velocity by 61.5% inside the canopy and 36% above the

canopy.

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Abstrak tesis dikemukakan kepada Senat Universiti Putra Malaysia sebagai memenuhi

sebahagian keperluan Ijazah Master Sains

KESAN TUMBUHAN (RUMPUT NAPIER DAN CATTAIL) KE ATAS CIRI

ALIRAN DALAM SALURAN TERBUKA

Oleh

MANAL M. ABOOD

October 2005

Pengerusi : Badronnisa Yusuf

Fakulti : Kejuruteraan

Kajian makmal telah dilakukan untuk menganalisis kesan dua jenis tumbuhan yang

berbeza, iaitu rumput Napier dan Cattail, ke atas ciri-ciri aliran dalam saluran terbuka.

Objektif utama kajian ialah untuk mendapatkan kesan tumbuhan ke atas pekali

kekasaran Manning dan profil halaju, dan untuk membangunkan hubungan antara ciri-

ciri tumbuhan (ketumpatan, tahap ketenggelaman dan agihan/susunan) dengan sifat-

sifat aliran (pekali kekasaran Manning, dan nombor Reynolds).

Sifat rintangan untuk setiap tumbuhan kepada aliran telah kaji di dalam flum terbuka

segiempat yang berdimensi 12 m panjang, 0.32 m lebar dan 0.32 m tinggi.

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Keputusan menunjukkan tumbuhan meningkatkan nilai pekali kekasaran Manning dan

memberi kesan yang ketara terhadap profil tegak aliran. Kesan ini bergantung kepada

faktor seperti kedalaman aliran, tahap ketenggelaman, kepadatan serta agihan dan

susunan tumbuhan.

Pekali kekasaran Manning, untuk aliran dengan rumput Napier didapati meningkat

dengan peningkatan kedalaman aliran dalam keadaan tenggelam dan juga separa

tenggelam. Peningkatan ini berubah dari 0.017 ke 0.065 untuk kepadatan tumbuhan

tinggi (100veg/m2) dan dari 0.0058 ke 0.0427 untuk kepadatan tumbuhan rendah (20

veg/m2). Manakala rumput Cattail memberi kesan yang berbeza. Peningkatan

kedalaman aliran menyebabkan penurunan pekali kekasaran. Penurunan ini berubah

dari 0.031 ke 0.022 untuk kepadatan tumbuhan tinggi dan dari 0.024 ke 0.0157 untuk

kepadatan rendah. Ini berlaku mungkin kerana ciri-ciri fizikal rumput Cattail yang tiada

batang dan daun bercabang.

Manning n, untuk aliran dengan rumput Napier berkepadatan rendah didapati menurun

dengan peningkatan nombor Reynolds, Re, di dalam kedua-dua keadaan, iaitu

tenggelam dan separa tenggelam. Walaubagaimanapun, pada kepadatan tinggi

pemerhatian ini hanya benar dalam kes tumbuhan tenggelam. Dalam kes tumbuhan

separa tenggelam, nilai n meningkat dengan peningkatan Re. Untuk aliran dengan

rumput Cattail, nilai n menurun dengan Re pada semua kepadatan tumbuhan.

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Kebergantungan nilai n kepada kepadatan tumbuhan, didapati mempunyai hubungan

linear (R2=0.93-0.96) untuk kedua-dua keadaan, tenggelam dan separa tenggelam.

Rumput Napier meningkatkan nilai n dengan peningkatan kepadatan tumbuhan.

Keputusan menunjukkan pada kedalaman aliran yang sama nilai kekasaran meningkat

sebanyak 35% dengan peningkatan kepadatan tumbuhan sebanyak 33.3%.. Manakala

rumput Cattail dengan peningkatan kepadatan tumbuhan yang sama telah meningkatkan

nilai n sebanyak 25%. Peningkatan nilai Manning n, dengan kepadatan tumbuhan tidak

hanya dengan bergantung kepada kedalaman aliran tetapi juga dengan jenis tumbuhan.

Pekali kekasaran Manning’s juga didapati dipengaruhi oleh agihan tumbuhan.

Keputusan menunjukkan agihan tumbuhan pada kedua-dua sisi saluran memberi

rintangan tertinggi, diikuti dengan agihan tumbuhan ditengah saluran dan kemudian

agihan tumbuhan rawak. Nilai n meningkat hampir linear dengan kedalaman aliran

untuk semua jenis agihan tumbuhan.

Kesan tumbuhan kepada profil menegak juga di kaji. Keputusan menunjukkan

kehadiran tumbuhan telah merubah bentuk profil halaju dan menurunkan halaju

sebanyak 61.5% di dalam tumbuhan dan 36% di aliran di atas tumbuhan.

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ACKNOWLEDGEMENTS

All praise to supreme almighty Allah swt. The only creator, cherisher, sustainer and

efficient assembler of the world and galaxies whose blessings and kindness have

enabled the author to accomplish this work successfully.

I would like to express my deepest gratitude to my supervisor, Puan Badronnisa Yusuf,

for her kind supervision and for accepting me as her thesis student. Her cheery nature

and her unfailing patience has been a great motivation for me to excel in my work.

Without her guidance, this thesis would not have been completed successfully. Sincere

appreciation is also due to Assoc. Prof. Dr. Abdul Halim Ghazali and Assoc. Prof. Dr.

Thamer Ahmed Mohammed for their constructive suggestions and guidance during the

execution of this project, as well as for critical reviewing of the manuscript.

The gratitude also goes to the Department of Agriculture and Biological and

Engineering for providing the facilities to accomplish this project. Not forgetting to the

technician En. Muhamed Hafiz Ramli for lent me his helping hands.

I would never forget my mother's continuous sacrifice, advice and prays for my success.

I would like to thank my wonderful husband Mohamad A. Hussain for his unbelievable

support and understanding during the work of this thesis; his encouragement to me

during that time was invaluable.

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I would like also to thank my daughter Marwa and my son Mustafa for their support,

encouragement, immense help and cooperation during the whole period of study.

Last but not least, special appreciation goes to my friend, Mr. Sivanesan Nadaraja who

helps me a lot in providing information related to this study.

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I certify that an Examination Committee met on 7th October 2005 to conduct the final

examination of Manal M. Abood on her Master thesis entitled “effects of Napier and

Cattail grasses on open channel flow characteristics” in accordance with Universiti

Pertanian Malaysia (Higher Degree) Act 1980 and Universiti Pertanian Malaysia (Higher

Degree) Regulation 1981. The Committee recommends that the candidate be awarded the

relevant degree. Members of the Examination Committee are as follows:

Mohd Amin Mohd Soom, PhD,Ir Faculty of Engineering

Universiti Putra Malaysia

(Chairman)

Lee Teang Shui, PhD Associate Professor Faculty of Engineering

Universiti Putra Malaysia

(Internal Examiner)

Katayon Saed, PhD Faculty of Engineering Universiti Putra Malaysia

(Internal Examiner)

Othman A. Karim, PhD

Associate Professor

Faculty of Engineering Universiti Kebangsaan Malaysia

(External Examiner)

________________________________

HASANAH MOHD.GHAZALI, PhD

Professor/Deputy Dean School of Graduate Studies

Universiti Putra Malaysia

Date:

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This thesis submitted to the Senate of Universiti Putra Malaysia and has been accepted as

fulfilment of the requirement for the degree of Master of Science. The members of the Supervisory Committee are as follows:

Badronnisa Yusuf, Msc

Faculty of Engineering

Universiti Putra Malaysia (Chairman)

Abdul Halim Ghazali, PhD AssociateProfessor

Faculty of Engineering

Universiti Putra Malaysia

(Member)

Thamer Ahmed Mohammed, PhD

AssociateProfessor Faculty of Engineering

Universiti Putra Malaysia

(Member)

_______________________

AINI IDERIS, PhD

Professor/Dean School of Graduate Studies

Universiti Putra Malaysia

Date:

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DECLARATION

I hereby declare that the thesis is based on my original work except for quotations and

citations, which have been duly acknowledged. I also declare that it has not been

previously or concurrently submitted for any other degree at UPM or other institution.

--------------------------

MANAL M. ABOOD

Date:

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TABLE OF CONTENT

Page

DEDICATION

ABSTRACT

ABSTRAK

ACKNOWLEDGMENTS

APPROVAL

DECLARATION FORM

LIST OF TABLES

LIST OF FIGURES

LIST OF SYMBOLS

ii

iii

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xvi

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CHAPTER

1 INTRODUCTION 1.1

1.1 General 1.1

1.2 Effect of Vegetation 1.2

1.3 Statement of Problem 1.3

1.4 Objective 1.4

1.5 Scope of Study 1.5

2 LITERATURE REVIEW 2.1

2.1 Uniform Flow in Open Channel 2.1

2.2 Empirical Formula for Uniform Flow Computation 2.2

2.3

2.4

Resistance Coefficient in Vegetated Channel Prediction

of Flow Resistance for Vegetated Channel

2.4

2.4.1 Theoretical Analysis to Predict Resistance

Coefficient

2.9

2.4.2

2.4.3

Field study to Predict Resistance Coefficient

Laboratory Experiments to predict Resistance

Coefficient

2.12

2.14

2.5 Vertical Velocity Distribution in Vegetated Channel 2.21

3 METHODOLOGY 3.1

3.1 Introduction 3.1

3.2 Material and Equipments 3.1

3.2.1 Open Channel 3.1

3.2.2 Vegetation 3.3

3.2.2.1 Napier Grass 3.3

3.2.2.2 Cattail Grass 3.4

3.2.3 Velocity meter 3.6

3.3 Experimental Design 3.9

3.3.1 Investigation the Relationship Between Flow 3.10

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Depth and Manning’s, n

3.3.2 Investigation the Effects of Vegetation Density

on the Manning’s, n

3.11

3.3.3 Investigation the Effects of Vegetation

Arrangement on the Manning’s, n

3.11

3.3.4 Investigation the Effects of Vegetation in the

Velocity Distribution

3.12

3.4 Velocity Measurement 3.13

3.4.1 Points of Measurement 3.13

3.4.2 Determination of the average velocity 3.14

3.4.3 Determination of vertical velocity 3.14

3.5 Calculation of Roughness Coefficient 3.14

3.5.1 Roughness Coefficient with vegetation 3.14

3.5.2 Roughness coefficient Contributed by the

Vegetation

3.16

3.6 State of flow and Reynolds Number 3.17

3.7 Analysis of data 3.17

4 RESULTS AND DISCUSSION 4.1

4.1 Introduction 4.1

4.2 Mean Velocity and Roughness Coefficient, n

(with vegetation)

4.1

4.3 Vegetation Roughness coefficient, n veg 4.4

4.4 Roughness Coefficient for Different Arrangement of

Vegetation

4.6

4.5 Vertical Velocity Distribution 4.7

4.6 Effects of Napier and Cattail grass on hydraulic

roughness

4.7

4.6.1 Influence of Degree of Submergence (Y/H) of

vegetation on Manning Roughness coefficient, n

4.7

4.6.2 Influence of Vegetation Density on Manning

Roughness Coefficient, n,

4.12

4.6.3 Influence of Vegetation Arrangement on

Manning Roughness Coefficient, n

4.14

4.7 Variation Of Roughness Coefficient, n, With Reynolds

Number, Re

4.16

4.8 Influence of Vegetation on the Velocity Distribution 4.18

5 CONCLUSION 5.1

REFERENCES

BIODATA OF THE AUTHOR

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LIST OF TABLES

Table Page

2.1 Summary of previous studies

2.6

2.2 Summary of previous studies

2.7

2.3 Summary of previous studies

2.8

2.4 Different Methods To Modify Prandtl's Log Law (Stephan and

Guthnecht, 2002)

2.26

3.1 Napier and Cattail grasses details 3.3

3.2 Details Of Experiments (Napier grass)

3.9

3.3 Details Of Experiments (Cattail grass)

3.10

4.1 Average Velocity and Roughness Coefficient, n for channel with

Cattail Grass

4.2

4.2 Average Velocity and Roughness Coefficient, n for channel with

Napier Grass

4.3

4.3 Vegetation Roughness Coefficient (Cattail Grass)

4.4

4.4 Vegetation Roughness Coefficient (Napier Grass) 4.5

4.5 Roughness Coefficient Of The Channel With Different

Arrangement Of Napier Grass

4.6

4.6 Vertical Velocity Distribution With And Without Vegetation 4.7

4.7 Increment Of Manning Roughness For Napier Grass 4.10

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LIST OF FIGURES

Figure Page

2.1 Flow Resistance Model (Petryk, and Bosmajian, 1975) 2.9

2.2 Vertical velocity profile above aquatic vegetation (Stephan and

Guthnecht, 2002)

2.24

3.1 Open channel flume

3.2

3.2 Schematic Diagram of Experimental Setup (Not to scale)

3.2

3.3 Napier grass in the flume 3.4

3.4 Cattail grass in the field 3.5

3.5 Cattail grass in the flume 3.5

3.6 View of Area-velocity flow meter (ISCO 4250,USA) 3.7

3.7 Current Meter (BRAYSTOKE, BFM001, UK) 3.7

3.8 Vegetation arrangement; Vegetations at the (a) center of the channel,

(b) both sides of the channel, (c) staggeredly distributed across the

channel section

3.12

3.9 Locations of mean velocity measurement points

3.13

4.1 Relation of degree of submergence, Y/H and Manning’s n for Napier

grass

4.8

4.2 Relation of degree of submergence, Y/H and Manning’s n for Napier

grass: Comparisons with Jarvela, 2002 and Maghdam, 1997

4.9

4.3 Relation of degree of submergence, Y/H and Manning’s n for

Cattailgrass: Comparisons with Wu et al (1999) and Reza Mahbub

(1998)

4.11

4.4 Roughness coefficients, n vs. density of plant for Napier grass 4.13

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4.5 Roughness coefficients, n vs. density of plant for Cattail grass 4.13

4.6 Roughness coefficient vs vegetation density for both submerged and

unsubmerged vegetation (Napier grass)

4.14

4.7 Roughness coefficient vs Y/H for three different vegetation

arrangements (Napier grass)

4.15

4.8 Roughness coefficient vs Re for different densities, Dv for Napier

grass

4.17

4.9 Roughness coefficient vs Re for Napier grass: Comparison with

Wu et al (1999) and Jarvela (2002)

4.17

4.10 Roughness coefficient vs. Re for different densities, Dv for Cattail

grass

4.18

4.11 Velocity distribution to describe flow in three zones (El Hakim and

Salama, 1992)

4.19

4.12 Comparison of velocity inside and above submerged Napier

(staggered distribution) with El Hakim and Salama (1992) and

Kouwen et al (1969)

4.20

4.13 Velocity distribution inside and above Cattail grass (staggered

distribution)

4.21

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LIST OF SYMBOLS

A Flow cross- sectional area normal to direction of flow.

Ai Projected area of ith plant in upstream direction

C Chezy coefficient

Cd

Drag coefficient vegetation

Cd ΣAi/AL

Density of vegetation

D Mean water depth (assumed as R for wide channel)

Di

Drag force on ith plants

Dv

Density of plant (veg/m2)

E Modulus of elasticity

Fx

Force in x direction

G Gravitational constant

h Roughness height

I Second moment of area

k Roughness height (deflected)

L Length of channel

m Number of roughness elements

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n Manning roughness coefficient including boundary and vegetation effect

n (ave)

Equivalent Manning’s roughness coefficient

nb

Manning boundary roughness coefficient which excludes influence of

vegetation

nveg Vegetative roughness coefficient

P Wetted perimeter

R Hydraulic radius defined as a ratio of cross- sectional area of flow to the

wetted perimeter

Re Reynolds number

S Bed slope of channel

Sw Water surface slope (cm/cm)

So Bed slope

U*

Shear velocity

V Mean velocity

Vi

Average approach velocity to ith plant

γ

Specific weight of liquid

τw Shear force per unit area on channel boundary

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CHAPTER 1

INTRODUCTION

1.1 General

Vegetations present in many rivers, streams, and man made channels throughout the

country. Vegetations can be found growing naturally on the bed of the channel or on the

riverbanks or have been purposely planted. They are often classified by their shape and

the locations where they grow. Vegetations that grow on the river floodplains typically

comprises of various combination of trees, herbs, shrubs, hedges, bushes and grasses.

The in-channel vegetations usually consist of aquatic plants and these may be divided

into four categories: emergent, submerged, floating-leaf, and free-floating.

Emergent plants are rooted in the soil close to or below the water level but stems,

flowers and most of the mature leaves are protruding above the water surface. They are

generally found by the banks of the river. Submerged aquatic plants have flexible stems

and leaves, are rooted in the soil, and are completely covered by water. The floating-

leaf plants are rooted in the submerged soil with many of their leaves floating on the

water surface. These are usually seen along the margin of river that is not fast flowing.

The last group is free-floating plants, most of their leaf and stem tissue are at or above

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the water surface. They obtain their nutrients directly from the water, since they are not

rooted to the soil.

The presence of vegetations in river channel provides both benefits and problems. From

environmental point of view, aquatic plants are essential parts of natural aquatic

systems and form the basis of a waterbody’s health and productivity. From engineering

point of view, vegetation can improve the strength of bank materials through buttressing

and root reinforcement. However, invariably aquatic plants become over abundant or

unsightly and require control. The obvious problem related to excessive growth are flow

retardment , flow capacity reduction and causing flood. Although the flow capacity can

be increased by complete or partial removal of vegetation, this is a costly procedure. A

complete removal of the vegetation in channels can lead to erosion of the banks and

turbidity of the water. Unrestricted growth of such vegetation can lead to a nearly

complete loss of capacity to convey water. Therefore, it is essential that the balance

between risk and benefit of having vegetation in the channel is weighed and proper

engineering judgement be made.

1.2 Effects of Vegetation

The vegetations in a channel influence the flow across the channel and the degree of

influence depends on vegetations characteristics such as vegetations species,

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distribution, flexibility, degree of submergence and density as well as flow

characteristics, including flow area, depth and boundary characteristics (Jarvela, 2002).

The effect of vegetation in the channel is mainly on the velocity of flow. The average

water velocity at a cross section tends to decrease, because of roughness presented by

the stems and leaves of the plants. Vegetation generally increases roughness or flow

resistance (Frschenich, 2000). Increases in roughness due to vegetation can be as much

as higher than that due to channels particle size alone (Chow, 1959). According to

Thompson and Roberson (1976), the growth of thick vegetation in channel can reduce

capacity by up to 50% in less than a year. Righetti and Armanini (2002) reported that

the vegetations effect varies seasonally. Vegetations in wet season give less resistance

to flow compared with vegetations that are partially submerged during dry season. Shih

and Rahi (1982) discovered that during the growing season the value of Manning

roughness coefficient, n increased by 300%.

1.3 Statement of the Problem

An understanding of flow resistance is the most fundamental and essential to hydraulics

engineers and the effects of vegetations on overall flow resistance are significant and

cause difficulties in many hydraulic designs (Jarvela, 2004). The planning, design and

operation of water resources projects often require knowledge of discharge in a given

channel as a function of flow depth. In area where flow occurs through vegetation, the

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1.4

flow depth may be largely determined by the roughness and resistance provided by the

vegetation.

Well-established flow resistance formulas, such as the Manning, Darcy– Weisbach, and

Chezy equations, have long been used to analyze river flows but yet the accounts on the

effect of vegetation on the resistance are still widely studied. Research on vegetative

resistance in open-channel flows has been motivated by an increase in awareness of the

importance of the ecological and environmental effects of vegetation in a river system.

Advances in understanding the behavior of flow over vegetation will improve both the

knowledge of flow-velocity profiles and flow resistance. This will lead to the

development of better way in estimating resistance or roughness due to vegetations.

In Malaysia, there are many kinds of tropical vegetation and aquatic plants and their

effects on the channel flow yet to be studied. Research in this area played important role

in determining the flow capacity and water surface elevation in vegetated channel or

wetland.

1.4 Objectives

The general objective of this study is to determine the effect of vegetations on the

characteristic of flow in an open channel. The specific objectives are to analyze the

effects of Napier and Cattail grasses on hydraulic roughness and velocity distributions

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1.5

as well as to develop empirical relationship between characteristics of vegetation and

flow.

1.5 Scope of the Study

The study involved collecting data through experimental works. Two types of

vegetation (Napier and Cattail grass) were tested. The effects of the vegetation on the

velocity profile and hydraulic roughness were analysed and empirical equations that

relate these parameters with the various characteristics of vegetation were developed.

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REFERENCES

Abdelsalam, M.W, Khatab, A. F , Khalifa, A.A and Bakry, M. F. (1992). Flow capacity

through wide and submerged vegetation channels. Journal of Irrigation and

Drainage ASCE, Vol. 118. pp 25-44.

Backry, M. A. (1992). Field measured hydraulic resistance characteristics in vegetation

invested canals. Journal of Irrigation and Drainage Engineer. ASCE. Vol 118.

No2. pp 256-273.

Chanson, H. (1999). The Hydraulic of Open Channel Flow. John Wiley & Sons Inc.

Chow, V.T. (1959). Open Channel Hydraulics. New York: Mc Graw Hill .

Christensen, B.A.(1985). Open Channel and sheet flow over flexible roughness,

proceedings of the 1st IAHR congress in Melbourne, Australia, 462-467.

Copeland, R.R.(2000).Determination of flow resistance coefficient due to shrubs and

woody vegetation. Technical Notes, US Army Engineer Research and

Development Centre, Vicksburg, MS.

El Hakim, O. and Salama, M.M (1992). Velocity distribution inside and above branched

flexible roughness. Journal of Irrigation and Drainage. ASCE. Vol.118. No. 6.

pp 914-927.

Frschenich G. (2000). Resistance due to vegetation. EMRRP Technical Notes

Collection(ERDC TN-EMRRP-SR-07),U.S. Army Engineer Research and

Development Center, Vicksburg, MS.

French, R. H. (1985). Open Channel Hydraulic. New York:Mc Graw Hill.

Hwang, N.H.C. and Hita, C.E. (1987). Fundamental of Hydraulic Engineering System.

Second Edition, Englewood Cliffs, New Jersey.

Jarvela, J. (2002). Flow resistance of flexible vegetation, a flume study with natural

plants. Journal of Hydrology. 269. pp 44-54.

Jarvela, J. (2004). Flow resistance due to lateral momentum transfer in partially vegetated

rivers. Water Resources Research. Vol. 40, W05206.

Kao D.T.Y. and Barfield B.J. (1978). Properties of flow hydraulics for vegetated

channels. Transaction of the ASAE, pp 489-494.

Kouwen, N., Unny, M. and Hary M. H. (1969). Flow retardance in vegetated channel.

Journal of Irrigation and Drainage Division. ASCE. Vol.95, No.1, pp 329-343.

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Kouwen, N and Unny, T. E.(1973). Flexible roughness in open channels. Journal of

Hydraulic Division. ASCE. Vol. 99. No. 5. pp 713-729.

Maghdam, F. and Kouwen, N. (1997). Nonrigid, nonsubmerged vegetation roughnes on

flood plains. Journal of Hydraulics Engineering. ASCE. Vol.123. No.1. pp

51- 56.

Nnaji,S. and Wu, I. (1973) Flow resistance from cylindrical roughness. Journal of

Irrigation and Drainage Division. 99 (IRI), 15-26.

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