Unsteady Discharge Calibration of a Large V-Notch Weir

THE UNIVERSITY OF QUEENSLAND

REPORT CH88/12

AUTHORS: Hubert CHANSON and Hang WANG

UNSTEADY DISCHARGE CALIBRATION OF A LARGE V-NOTCH WEIR

SCHOOL OF CIVIL ENGINEERING

HYDRAULIC MODEL REPORTS This report is published by the School of Civil Engineering at the University of Queensland. Lists of recently-published titles of this series and of other publications are provided at the end of this report. Requests for copies of any of these documents should be addressed to the Civil Engineering Secretary. The interpretation and opinions expressed herein are solely those of the author(s). Considerable care has been taken to ensure accuracy of the material presented. Nevertheless, responsibility for the use of this material rests with the user. School of Civil Engineering The University of Queensland Brisbane QLD 4072 AUSTRALIA Telephone: (61 7) 3365 4163 Fax: (61 7) 3365 4599 URL: http://www.eng.uq.edu.au/civil/ First published in 2012 by School of Civil Engineering The University of Queensland, Brisbane QLD 4072, Australia © Chanson and Wang This book is copyright ISBN No. 9781742720579 The University of Queensland, St Lucia QLD

Unsteady Discharge Calibration of a Large V-Notch Weir

by

Hubert CHANSON

Professor, The University of Queensland, School of Civil Engineering, Brisbane QLD 4072,

Australia, Email: [email protected]

and

Hang WANG

Ph.D. student, The University of Queensland, School of Civil Engineering, Brisbane QLD 4072,

Australia

REPORT No. CH88/12

ISBN 9781742720579

School of Civil Engineering, The University of Queensland, June 2012

Rapid opening of the V-notch weir: initial free-falling motion and its extent in the upstream

reservoir

ii

ABSTRACT

In open channels, the knowledge of the water discharge is a key parameter. Many measurement

techniques rely upon some empirical coefficients and there is a need to obtain new accurate

physical data to complement the existing evidence. Thin-plate weirs are commonly used as

measuring devices in flumes and channels, enabling an accurate discharge measurement with

simple instruments. In the present study, the discharge calibration of a large 90º V-notch thin plate

weir was performed using an unsteady volume per time technique. The V-notch weir was initially

closed by a fast-opening gate. The sudden opening induced an initial phase of the water motion

followed by a gradually-varied flow phase. The initial phase was dominated by the free-falling

motion of a volume of fluid in the vicinity of the weir and the generation of a negative wave

propagating upstream into the reservoir. The water volume affected by the sudden opening was

encompassed by a quasi-circular arc during the initial phase. During this gradually-varied phase,

some seiche was observed in the tank. A frequency analysis of the water elevation data yielded

results which compared favourably with the first mode of natural sloshing in the longitudinal and

transverse directions of the intake basin. The relationship between water discharge and upstream

water elevation was derived from the integral form of the continuity equation based upon high-

frequency water elevation recordings. The water elevation data were de-trended before processing.

The results yielded a dimensionless discharge coefficient Cd = 0.58 close to previous findings for

90º V-notch weirs. The findings showed that the unsteady discharge calibration of the V-notch weir

yielded similar results to a more traditional calibration approach based upon steady flow

experiments.

Keywords: 90 V-notch weir, calibration, discharge measurement, unsteady experiments, seiche,

sloshing, dam break wave, physical modelling, triangular V-notch thin-plate weir.

iii

TABLE OF CONTENTS

Page

Abstract ii

Keywords ii

Table of contents iii

List of symbols iv

1. Introduction 1

2. Facility and instrumentation 4

3. Basic observations and results 8

4. Conclusion 14

5. Acknowledgements 15

APPENDICES

Appendix A - Photographic observations of the experiments 16

Appendix B - Video movies of the experiments 24

Appendix C - Basic results 26

REFERENCES 38

Bibliography

Internet bibliography

Bibliographic reference of the Report CH88/12

iv

LIST OF SYMBOLS

The following symbols are used in this report:

B intake basin width (m);

b V-notch opening (m) at its highest extent; C celerity (m/s) of a small distance in a shallow water: C = )hp(g ;

Cd dimensionless discharge coefficient;

FL frequency (Hz) of first mode of natural sloshing in the longitudinal direction of intake

basin;

FT frequency (Hz) first mode of natural sloshing in the transverse direction of intake basin;

g gravity constant: g = 9.80 m/s2 in Brisbane QLD, Australia;

H total head (m);

h upstream water depth (m) measured above the notch;

ho initial upstream water depth (m) measured above the notch;

ho' standard deviation of initial upstream water depth (m) measured above the notch;

L intake basin length (m);

p vertical distance (m) from the tank bottom to the notch;

Q water discharge (m3/s);

s specific density;

To absolute time (s) of gate opening;

t 1- time (s) since gate opening;

2- absolute time (s);

Vol volume (m3) of water in the intake tank;

opening angle of V-notch;

dynamic viscosity (Pa.s);

kinematic viscosity (m2/s);

density (kg/m3);

surface tension (N/m);

Subscript

o initial flow conditions before gate opening;

Abbreviations

PDF probability density function;

Std standard deviation;

s second.

1

1. INTRODUCTION

In open channel flows, the knowledge of the water discharge is a key parameter to solve the basic

equations. A range of measurement techniques were developed (DARCY and BAZIN 1965, BOS

1976, ACKERS et al. 1980). Many techniques rely upon some empirical coefficients (HERSCHY

1995) and there is a need to obtain new accurate physical data to complement the existing evidence.

It is a requirement for the operators to ascertain the rating curves of the devices which need to be

checked in terms of their accuracy whilst based on some standard equations. Flow measuring

structures in waterworks, canals and wastewater plants consist mainly of flumes and thin plate weirs

(BOS et al. 1991). Standard equations are given in international, British and Australian standards.

A weir is a structure placed across a channel which raises the upstream water level. Thin-plate weirs

are commonly used as measuring devices enabling an accurate discharge measurement with simple

instruments (TROSKOLANSKI 1960). The V-notch weirs, also called triangular weirs, have an

overflow edge in the form of an isosceles triangle. Figure 1-1 presents a sketch a 90º V-notch weir

and Figure 1-2 shows a prototype application. The Australian Standards (1991) expresses the

discharge calibration of a triangular V-notch thin-plate weir in the form:

5d hg2tan

15

8CQ (1-1)

where Q is the water discharge, Cd a dimensionless discharge coefficient, the notch opening

angle, g the gravity acceleration and h the upstream water elevation above the notch (Fig. 1-1).

Basic dimensional considerations show that the discharge coefficient Cd is a function of the notch

angle , the relative weir height p/W and relative upstream depth h/p (Fig. 1-1). LENZ (1943)

presented some seminal experiments conducted with 5 different fluids (Table 1-1) and the results

were recently re-analysed by FENTON (2000). For a 90 V-notch weir with h/p < 0.2, the

dimensionless discharge coefficient is about Cd 0.58 (TROSKOLANSKI 1960, HERSCHY

1995).

The most robust discharge measurement technique is the volume per time method: "the only

rational method of calibrating weirs, i.e. in accordance with hydrometric principles, is the

volumetric method, which depends on measuring the volume, with a measuring reservoir, and the

time of flow" (TROSKOLANSKI 1960, p. 310). The technique may be adapted to unsteady flow

situations (e.g. CHANSON et al. 2002).

The report herein presents a novel approach to determine the discharge calibration of a large 90º V-

notch weir and associated accuracy based upon a comprehensive physical study undertaken at the

University of Queensland. The calibration was undertaken using a volume per time approach by

measuring the upstream water level at high frequency following a sudden gate opening. The results

2

showed the application of the technique and highlighted a number of practical issues. The report is

complemented by a digital appendix with four movies (App. B).

Fig. 1-1 - Sketch of a triangular V-notch thin-plate weir

Fig. 1-2 - V-notch weir used to measure wastewater release at Swanbank power station (Ipswich

QLD, Australia) on 6 September 2002 - Left: general view with the upstream water level sensors in

background; Right: details of the overflow above the notch

3

Table 1-1 - Experimental studies of 90º V-notch weirs

Ref. Fluid(s) h p B Fluid properties Remarks m (m) m

(1) (2) (3) (4) (5) (7) (7) LENZ (1943)

Water 0.070 to 0.152

0.91 1.07 s = 1 Tests at University of Wisconsin

Fuel oil (Oil A)

0.018 to 0.122

s = 0.90-0.91 = 0.5 to 1.5×10-4 m2/s = 0.03-0.031 N/m

Dustproofing oil (Oil G)

0.046 to 0.122

s = 0.89-0.91 = 0.12 to 0.5×10-4 m2/s, = 0.03-0.032 N/m

Oil C 0.03 to 0.055

-- 0.263 s = 0.87-0.88 = 0.25 to 0.7×10-4 m2/s = 0.033 N/m

Tests at University of California, Berkeley

Oil M 0.037 to 0.061

s = 0.85-0.86 = 0.07 to 0.2×10-4 m2/s = 0.032 N/m

Water 0.046 to 0.67

2.44 1.83 s = 1 Tests at Cornell University

Present study

Water 0.40 0.82 1.66 s = 1 Water temperature: 16.5 C = 998.8 kg/m3 = 1.10×10-6 m2/s = 0.0739 N/m

Unsteady tests.

Notes: h: upstream water elevation above notch; s: relative density; : density; : kinematic

viscosity; : surface tension.

4

2. FACILITY AND INSTRUMENTATION

2.1 EXPERIMENTAL FACILITY AND INSTRUMENTATION

The experiments were performed with a 400 mm high 90 V-notch thin-plate weir. The weir was

installed at one end of a 2.36 m long, 1.66 m wide and 1.22 m deep tank (Fig. 2-1 & 2-2). The

bottom of the V-notch was located 0.82 m above the tank invert. The V-notch was made out of

brass and designed based upon the Australian Standards (1991) (also International Organization for

Standardization 1980). The notch was initially closed with a fast-opening gate hinging outwards and

upwards.

During static tests, the water depths were measured using a pointer gauge. For the dynamic tests,

the unsteady water depth was measured using a series of three acoustic displacement meters

MicrosonicTM Mic+25/ IU/TC located 1.11 m upstream of the weir. The data accuracy and response

of the acoustic displacement meters were 0.18 mm and 50 ms respectively (1). All the displacement

sensors were synchronised and sampled simultaneously at 200 Hz. Additional visual observations

were recorded with 2 HD digital video cameras, 2 dSLR cameras PentaxTM K-01 and K-7 with

16Mp and 14Mp resolution respectively, and a PentaxTM Optio WG-01 digital camera (Table 2-1).

The dSLR cameras PentaxTM K-01 and K-7 were equipped with PentaxTM DA40mm f2.8 XS and

PentaxTM SMC FA31mm f1.8 Limited prime lenses respectively, exhibiting only slight barrel

distortions: that is, about 0.6% and 0.8% respectively. Further details on the cameras are listed in

Table 2-1. Some coloured vegetable dye was added to the water to improve the visibility of the

streamlines. Further photographs of the experiments are presented in Appendix A, while some

movies are included in the digital appendix (Appendix B).

1 as per the manufacturer's specifications {http://www.microsonic.de}. The authors observed however that

the response time of the three sensors was less than 25 ms in practice.

5

(A, Left) General view with the V-notch weir gate closed

(B, Right) Details of the V-notch with the acoustic displacement meters in the background

(C) Looking downstream with the V-notch in the background and the gate closed - Note the support

holding the acoustic displacement meters in the centre of the tank

Fig. 2-1 - Photographs of the experimental facility

6

Figure 2-2 - Dimensioned sketch of the 90º V-notch weir facility - Top: view in elevation; Bottom:

side view; Inset: front view of the V-notch brass plate

2.2 EXPERIMENTAL FLOW CONDITIONS

The displacement meters were located 1.11 m upstream of the weir about the tank centreline (Fig.

2-2). The video-cameras were placed around the tank at various locations to cover both the water

motion in the tank and weir overflow during each test.

For each experimental run, the tank was filled slowly to the brink of the brass plate. The water was

left to settle for at least 5 minutes prior to start. The experiment started when the gate was opened

7

rapidly and the water level was recorded continuously for 500 s. The gate was operated manually

and the opening times were less than 0.15 to 0.2 s (Table 2-2, column 4). Such an opening time was

small enough to have a negligible effect on the water motion in the tank (Lauber 1997). After the

rapid gate opening, the gate did not intrude into the flow as seen in Appendices A and B.

The experimental flow conditions are summarised in Table 2-2 where ho is the initially steady water

level above the lower edge of the notch. Table 2-2 includes further the fluctuations in upstream

water level prior to gate opening and the gate opening time. Altogether 5 experiments were

conducted.

Table 2-1 - Digital camera equipments and settings

Camera Lens Shots Comments (1) (2) (3) (4)

Pentax K-7 SMC Pentax-FA 31mm f1.8 AL Limited

Photographs (4672×3104 pixels)

Hi continuous shooting (5.2 fps)

Pentax K-01 SMC Pentax-DA 40mm f2.8 XS

HD Movies (1280×820 pixels) at 60 fps

Video mode.

Pentax Optio WG-1 5-25mm f3.5-5.5 Movies (1280×720 pixels) at 30 fps

Video mode.

Sony HDR-XR160E Sony G 2.1-63mm f1.8-3.4


Standard HQ HD quality.

Sony HDR-SR11E Carl Zeiss Vario-Sonnar T* 1.9-58.8mm f1.8-3.1


SD HQ 9M quality.

Table 2-2 - Experimental investigations of the large 90 V-notch weir

Run ho ho' Gate opening

time

Instrumentation Remarks

m m s (1) (2) (3) (4) (5) (6) 1 0.402 0.13×10-3 0.183 Videos, photographs, displacement meters. 2 0.399 0.29×10-3 0.20 Videos, photographs, displacement meters. 3 0.401 0.13×10-3 0.183 Videos, photographs, displacement meters. 4 0.400 -- 0.175 Videos, photographs. Dye injection. 5 0.400 0.12×10-3 0.167 Videos, photographs, displacement meters. Dye injection.

Notes: ho: initial water level above the weir V-notch; ho': standard deviation of initial water level.

8

3. BASIC OBSERVATIONS AND RESULTS

The water level in the tank was initially still prior to gate opening. The water level fluctuations

recorded by the sensors were within the accuracy of the sensor: ho' 0.17 mm on average (Table 2-

2, column 3). The gate opening was rapid and lasted less than 0.2 s. Figure 3-1 illustrates a typical

gate opening sequence. The sudden opening of the gate initiated an initial phase dominated by a

free-falling motion in the close proximity the V-notch weir and the generation of a negative wave

propagating upstream into the reservoir.

The unsteady flow above the weir consisted of an initial phase dominated by the free-falling motion

of a volume of fluid in the vicinity of the notch, followed by a gradually-varied flow motion.

During the initial phase, only a limited volume of water was reached by the initial wave and the rest

of the upstream tank water was still unaffected by the gate opening. The extent of the volume of

water affected by the free-falling motion was encompassed by a quasi-circular arc as illustrated in

Figure 3-2. The free-surface shape appeared somehow similar to the inlet shape of a minimum

energy loss (MEL) structure with its curved profile (Fig. 3-3). The resulting equipotential lines in a

plan view highlighted the flow contraction under the action of gravity. The initial phase lasted less

than 0.45 s: that is, for t×(g/ho)1/2 < 2.23 with t = 0 at the start of gate opening.

The initial phase was followed by a dynamic phase during which the flow above the weir was close

a quasi-steady overflow motion. The time-variations of the water elevation are illustrated in Figure

3-4. The ensemble-averaged water elevation data were best fitted by:

696.0

o

o62.37

h

gt

72.12

h

h

for 0.45 < oh

gt < 2,400 (3-1)

with a normalised correlation coefficient of 0.9999 for 76,621 data points. Equation (3-1) was valid

for the gradually-varied motion phase. During the initial phase, the time-variation of the water

elevation exhibited a different shape as illustrated in Figure 3-4B.

The rapid gate opening generated some disturbance in the water tank with the initial propagation of

a three-dimensional negative wave illustrated in Figure 3-2. The reflections of the negative wave on

the sidewalls and end walls of the tank yielded a complicated three-dimensional wave motion.

During this gradually-varied phase, some seiche was observed in the tank. It was associated with

both longitudinal as well as transverse sloshing. This is illustrated in Figure 3-5 presenting the

details of a typical water elevation signal. The data highlighted some pseudo-periodic oscillations

about a mean data trend (Fig. 3-5A). Some spectral analyses of the de-trended water elevation

signals were performed and a typical data set is shown in Figure 3-5B. In Figure 3-5B, the dominant

frequencies are 0.830 and 1.074 Hz. Further details are presented in Appendix C.

9

The frequency analysis results are summarised in Figure 3-6, where the data (dashed black lines)

are compared with the first mode of natural sloshing in the longitudinal and transverse directions of

the intake basin:

)hp(g

L2FL

(3-2A)

)hp(g

B2FB

(3-2A)

where L is the tank length and B the tank width. Despite some data scatter, the findings were close

to the theoretical calculations (Fig. 3-6).

Fig. 3-1 - Photographs of the gate opening - Experimental Run No. 2, ho = 0.40 m, Camera: Pentax

K-7, lens: Pentax FA31mm f1.8 Limited, shutter 1/80 s - From Left to Right, Top to Bottom: t = 0,

0.19 s, 0.38 s & 0.58 s

10

(A) Experimental Run No. 1

(B) Experimental Run No. 5

Fig. 3-2 - Photographs of the initial free-falling motion and its extent in the upstream reservoir

(t×(g/ho)1/2 < 2.23)

Fig. 3-3 - Inlet of the minimum energy loss (MEL) weir spillway of Lake Kurwongbah (Petrie

11

QLD, Australia) on 22 May 2009

t(g/ho)1/2

h/h o

0 300 600 900 1200 1500 1800 2100 24000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Run 1Ensemble-average (4 runs)

t(g/ho)1/2

h/h o

-2 -1 0 1 2 3 4 50.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

-2 -1 0 1 2 3 4 50.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

Initial phase

Run 3

(A, Left) Comparison between a single data set (run 1) and the ensemble averaged data

(B, Right) Details of the initial phase (run 3)

Fig. 3-4 - Dimensionless time-variation of the upstream water elevation in the water tank

t(g/ho)1/2

h/h o

h/h o

- d

etre

nded

dat

a

0 4 8 12 16 20 24 28 32 36 400.5 -0.06

0.55 -0.02

0.6 0.02

0.65 0.06

0.7 0.1

0.75 0.14

0.8 0.18

0.85 0.22

0.9 0.26

0.95 0.3

1 0.34

0 4 8 12 16 20 24 28 32 36 400.5 -0.06

0.55 -0.02

0.6 0.02

0.65 0.06

0.7 0.1

0.75 0.14

0.8 0.18

0.85 0.22

0.9 0.26

0.95 0.3

1 0.34Run 3TrendDe-trended signal

Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.2 0.3 0.40.5 0.7 1 2 3 4 550.01

0.02

0.03

0.050.07

0.1

0.2

0.3

0.50.7

1

2

3

(A) Raw signal and de-trended water elevation signal

(B) Power spectrum density function of the de-trended signal for 0 < t < 12 s and 0.205 < h < 0.4 m

Fig. 3-5 - Frequency analysis of the water elevation signal (Run 3, sensor 3)

12

Natural sloshing frequency, Observed frequency (Hz)

h (m

)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Sensor 3

Sensor 2

Sensor 1

LongitudinalTransversePhysical data

Fig. 3-6 - Summary of frequency analyses of the free-surface elevation data - Comparison between

experimental observations (black dashed lines) and the first mode of natural sloshing frequency

The instantaneous discharge Q through the V-notch weir was estimated using the integral form of

the equation of conservation of mass for the water tank:

Qdt

dVol (3-3)

where t is the time and Vol is the instantaneous volume of water in the intake structure:

)ph(BLVol (3-4)

Equation (3-4) assumed implicitly that the intake basin surface was horizontal and neglected the

local drop in water elevation in the vicinity of the weir notch where the fluid was accelerated. The

combination of Equations (3-3) and (3-4) gives an expression for the instantaneous overflow

discharge:

dt

hdBLQ (3-5)

In the present study, Equation (3-5) was calculated based upon the smoothed water elevation data.

The results are presented in Figure 3-7. Further details on the calculations and the complete data

sets are presented in Appendix C. Overall the data were best correlated by:

5d hg2

15

8CQ (3-6A)

where Q is the water discharge, g the gravity acceleration and Cd = 0.58 (Fig. 3-7). The result was

close to earlier findings (LENZ 1943, TROSKOLANSKI 1960, HERSCHY 1995). It may be

13

rewritten in dimensionless form:

5

o2

oo h

h2

15

858.0

hhg

Q

(3-6B)

Basically the present findings showed that the unsteady discharge calibration of the V-notch weir

yielded similar results to a more traditional calibration approach based upon steady flow

experiments.

h (m)

Q (

m3 /s

)

0 0.1 0.2 0.3 0.40

0.03

0.06

0.09

0.120.588/15(x)2sqrt(29.8x)Run 1Run 2Run 3Run 5

Fig. 3-7 - Relationship between instantaneous discharge Q and upstream water depth h for the 90º

V-notch weir - Comparison between experimental data and Equation (3-6)

Discussion

The present experiments were conducted for 0.022 < h < 0.40 m. Although the results herein

focused on water elevations within the range 0.025 < h < 0.40 m, the Reynolds number )h/(Q

became less than 1×104 for h < 0.038. It is conceivable that viscous scale effects might affect the

findings for the smallest water elevations.

During some unsteady experiments with a two-dimensional orifice flow, CHANSON et al. (2002)

used the following discharge equation:

hg2ACQ d (3-7)

where A is the orifice cross-section area and Cd was found to be Cd 0.58. Assuming A = h2 for a

triangular V- notch weir, Equation (3-7) yields to Equation (3-6).

14

4. CONCLUSION

A discharge calibration of a large 90º V-notch thin plate weir was performed using an unsteady

volume per time technique. The V-notch weir was initially closed by a fast-opening gate. The

sudden opening induced an initial phase of the water motion followed by a gradually-varied flow

phase. The initial phase was dominated by the free-falling motion of a volume of fluid in the

vicinity of the weir and the generation of a negative wave propagating upstream into the reservoir.

The water volume affected by the sudden opening was encompassed by a quasi-circular arc during

the initial phase. During this gradually-varied phase, some seiche was observed in the tank. A

frequency analysis of the water elevation data yielded results which compared favourably with the

first mode of natural sloshing in the longitudinal and transverse directions of the intake basin,

although the wave motion was three-dimensional.

The relationship between water discharge and upstream water elevation was derived from the

integral form of the continuity equation based upon high-frequency water elevation recordings. The

water elevation data were de-trended before processing. The results yielded a dimensionless

discharge coefficient Cd = 0.58 close to previous findings for 90º V-notch weirs. The findings

showed that the unsteady discharge calibration of the V-notch weir yielded similar results to a more

traditional calibration approach based upon steady flow experiments.

15

5. ACKNOWLEDGMENTS

The authors thank Dr Oscar CASTRO-ORGUAZ (Institute of Sustainable Agriculture, Spanish

National Research Council, IAS-CSIC, Spain) for his detailed review. They acknowledge the

helpful comments of Professor John FENTON (TU Wien, Austria).

The authors thank all the people who assisted with the large-scale experiments, especially the

technical staff of the School of Civil Engineering at the University of Queensland (Chris, Fraser,

Jason, Ruth, Shane, Stewart, Troy). The financial support of the Australian Research Council (Grant

DP120100481) is acknowledged.

16

APPENDIX A - PHOTOGRAPHIC OBSERVATIONS OF THE EXPERIMENTS

(A, Left) General view with the V-notch weir gate closed

(B, Right) Details of the V-notch with the acoustic displacement meters in the background

(C) Looking downstream with the V-notch in the background and the gate closed

17

(D) Side view of the setup during the experiments on 23 May 2012 - The V-notch is on the left

Fig. A-1 - Photographs of the experimental facility

18

Fig. A-2 - Dimensioned sketch of the facility

19

Fig. A-3 - Experimental Run No. 1 on 23 May 2012 - ho = 0.40 m - Camera: Pentax K-7, lens:

Pentax FA31mm f1.8 Limited, shutter 1/80 s - From Left to Right, Top to Bottom: t = to, to+0.19 s,

to+0.38 s, to+0.58 s, to+2.88 s, to+6.15 s, to+11.92 s, to+15.38 s

20


Pentax FA31mm f1.8 Limited, shutter 1/80 s - From Left to Right, Top to Bottom: t = To, To+0.19

s, To+0.38 s, To+0.58 s, To+0.77 s, To+0.96 s, To+2.5 s, To+85 s

21


Pentax FA31mm f1.8 Limited, shutter 1/80 s - From Left to Right, Top to Bottom: t = to, to+0.19 s,

to+0.38 s, to+0.58 s, to+1.35 s, to+3.08 s

22



s, To+0.38 s, To+0.58 s, To+2.31 s, To+4.61 s

23



s, To+0.38 s, To+0.58 s, To+0.77 s, To+0.96 s, To+2.88 s, To+4.42 s

24

APPENDIX B - VIDEO MOVIES OF THE EXPERIMENTS

B.1 INTRODUCTION

Some unsteady calibration experiments of a large 90º V-notch weir were undertaken at the

University of Queensland. A series of short movies were taken during the experiments, and a

selection is deposited with the digital record of the publication at the institutional open access

repository of the University of Queensland: {http://espace.library.uq.edu.au/}. They are listed as

part of the technical report deposit at {http://espace.library.uq.edu.au/list/author_id/193/}. The list

of the movies is detailed in section B.2, including the filenames, file format, and a description of

each video.

All the movies are Copyrights Hubert CHANSON 2012.

B.2 LIST OF MOVIES

Filename Original format Deposited format

Description

IMGP0123.MPG HD movie (1280×820 pixels) at 60 fps taken with Pentax K-01 & SMC Pentax-DA 40mm

f2.8 XS

MPEG-2 (25 fps)

Run 2. Sudden gate opening. Side view. Duration: 8 s.

IMGP0571.MPG Movie (1280×720 pixels) at 30 fps taken with Pentax Optio

WG-1

MPEG-2 (25 fps)

Run 5. Sudden gate opening. View from upstream. Duration: 12 s.

00065.MPG HD movie (1440×1080 pixels) at 25 fps taken with Sony HDR-SR11E & Carl Zeiss

Vario-Sonnar T* 1.9-58.8mm f1.8-3.1

MPEG-2 (25 fps)

Run 2. Sudden gate opening. Three-quarter view from upstream. Duration: 16 s.

M2U00180.MPG HD movie (1920×1080 pixels) at 25 fps taken with Sony

HDR-XR160E & Sony G 2.1-63mm f1.8-3.4

MPEG-2 (25 fps)

Run 5. Sudden gate opening. View from downstream looking straight at the V-notch.Duration: 15 s.

B.3 MOVIE FILES

The movies files of Appendix B are available in the institutional open access repository of the

University of Queensland (Brisbane, Australia) and they are deposited at UQeSpace

{http://espace.library.uq.edu.au/}. The deposited digital files are MPEG-2 movies. The deposited

files (Section B.2) were converted to Flash video for video streaming.

At request, the writer may provide each movie as a single compressed file (Filename

Movie_File.7z). Such a file was prepared with 7-zip version 9.20. The software 7-zip is an open

25

source software. Most of the source code is under the GNU LGPL license. The unRAR code is

under a mixed license: GNU LGPL + unRAR restrictions. The software 7-zip may be freely

downloaded from {www.7-zip.org}.

The copyrights of the movies remain the property of Hubert CHANSON. Any use of the movies

available in the digital appendix must acknowledge and cite the present report:

CHANSON, H., and WANG, H. (2012). "Unsteady Discharge Calibration of a Large V-Notch

Weir." Hydraulic Model Report No. CH88/12, School of Civil Engineering, The University of

Queensland, Brisbane, Australia, 50 pages & 4 movies (ISBN 9781742720579).

Further details on the report including the digital appendix may be obtained from Prof. Hubert

CHANSON {[email protected]}.

26

APPENDIX C - BASIC RESULTS

C.1 INTRODUCTION

Some unsteady discharge calibration experiments of a large 90º V-notch weir were undertaken at

the University of Queensland. The weir was installed at one end of a 2.36 m long, 1.66 m wide and

1.22 m deep tank (App. A). The triangular V-notch weir was 400 mm high, and the notch's lower

edge was located 0.82 m above the tank invert. The V-notch was made out of brass and designed

based upon the Australian Standards (1991). The V-notch was initially closed with a water-tight

fast-opening gate hinging outwards and upwards.

During a series of tests, the water depths in the intake structure were measured using three acoustic

displacement meters MicrosonicTM Mic+25/ IU/TC sampled simultaneously at 200 Hz. The sensors

were placed at different elevations to cover the full range of the V-notch height, with the sensor 1

being the lowest, the sensor 3 being the highest, and the sensor 2 covering a range of elevations

overlapping the other sensors. The displacement meters were located at 1.11 m upstream of the weir

about the tank centreline (App. A).

For each experimental run, the tank was filled slowly to the brink. The water was left to settle for at

least 5 minutes prior to start. The experiment started when the gate was opened rapidly and the

water level was recorded continuously for 500 s. The gate was operated manually and the opening

times were less than 0.15 to 0.2 s (Table C-1, column 4).

Table C-1 - Experimental investigations with the large 90 V-notch weir

Run ho ho' Gate opening

time

Instrumentation Remarks

m m s (1) (2) (4) (5) (6) 1 0.402 0.13×10-3 0.183 Videos, photographs, displacement meters. 2 0.399 0.29×10-3 0.20 Videos, photographs, displacement meters. 3 0.401 0.13×10-3 0.183 Videos, photographs, displacement meters. 4 0.400 -- 0.175 Videos, photographs. Dye injection 5 0.400 0.12×10-3 0.167 Videos, photographs, displacement meters. Dye injection

Notes: ho: initial water level above the weir V-notch; ho': standard deviation of initial water level.

Notation

B intake basin width (m);

h upstream water depth (m) measured above the notch;

27

ho initial upstream water depth (m) measured above the notch;

ho' standard deviation of initial water level (m);

L intake basin length (m);

Q water discharge (m3/s);

To absolute time (s) of gate opening;

t time (s);

Vol water volume (m3) in the intake basin.

C.2 INSTANTANEOUS WATER ELEVATION DATA

t (s)

h (m

m)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450Sensor 1Sensor 2Sensor 3

Fig. C-1 - Instantaneous water elevation data h as functions of time for Run 1

28

t (s)

h (m

m)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400



t (s)

h (m

m)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400



29

t (s)

h (m

m)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400



C.3 SPECTRAL ANALYSES OF THE WATER ELEVATION DATA

Immediately after the gate was opened, the water elevation data showed some pseudo-periodic

oscillations about a mean data trend, as illustrated in Figure C-5. These oscillations about the mean

trend were believed to be linked with some seiche in the longitudinal and transverse directions of

the intake basin. Some spectral analyses of the de-trended water elevation signals were performed.

The data sets were de-trended by removing the smoothed data tend from the instantaneous signal:

De-trended signal = Instantaneous signal - Smoothed data tend (C-1)

Figure C-5 illustrates an example of de-trended signal. Herein three smoothing window sizes were

tested systematically: 300, 600 and 1,200 points. Qualitatively a smoothing window of 300 points

was relevant immediately after the gate opening (sensor 3), while a smoothing window of 600 or

1,200 points was best at a latter stage (sensors 1 and 2). Figure C-5 shows the smoothed data trend

(300 points) and the de-trended signal immediately after gate opening (1).

A fast Fourier transform (FFT) was performed on the de-trended data set for each run and for each

sensor. The results for three smoothing window sizes (300, 600, 1,200 points) are presented in

terms of the power spectrum density functions. A summary of the frequency analyses is presented

in Table C-2. The results suggested little effect of the smoothing window size on the dominant

frequencies.

1 Note that the data smoothing was applied only to the data set starting at t = To (gate opening time).

30

t (s)

h (m

m)

h -

Sm

ooth

ed d

ata

tren

d (m

m)

37.5 42.5 47.5 50190 -16

210 -8

230 0

250 8

270 16

290 24

310 32

330 40

350 48

370 56

390 64

410 72Sensor 3Sensor 3, Smoothed (300 points)De-trended data

Fig. C-5 - Instantaneous water elevation data h as functions of time for Run 5 - Details of pseudo-

periodic oscillations about the mean trend immediately after gate opening - Comparison with the

smoothed data trend (smoothing based upon 300 points) and fluctuations about the data trend

Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20200.0030.005

0.01

0.02

0.05

0.1

0.2

0.5

1

2

55Sensor 3

Data-Trend(Smoothed 300pts)Data-Trend(Smoothed 600pts)Data-Trend(Smoothed 1200pts)

Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20200.0001

0.0002

0.0005

0.001

0.002

0.005

0.01

0.02

0.05

0.1

0.20.3

Sensor 2


31

Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20202E-52E-5

5E-5

0.0001

0.0002

0.0005

0.001

0.002

0.005

0.01

0.02

0.05Sensor 1


Fig. C-6 - Power spectrum density function of the water elevation after gate opening during Run 1

Frequency (Hz)

PSD

(D

epth

- T

rend

)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20200.005

0.01

0.020.03

0.05

0.1

0.20.3

0.5

1

23

55Sensor 3


Frequency (Hz)

PSD

(D

epth

- T

rend

)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20200.001

0.0020.003

0.005

0.01

0.020.03

0.05

0.1

0.20.3

0.5Sensor 2


32

Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20201E-5

2E-5

5E-5

0.0001

0.0002

0.0005

0.001

0.002

0.005

0.01

0.02

0.05

0.1Sensor 1



Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20200.001

0.002

0.005

0.01

0.02

0.05

0.1

0.2

0.5

1

2

55Sensor 3


Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20200.0002

0.0005

0.001

0.002

0.005

0.01

0.02

0.05

0.1

0.2

0.5Sensor 2


33

Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20200.0001

0.00020.0003

0.0005

0.001

0.0020.003

0.005

0.01

0.020.03

0.05

0.1Sensor 1



Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20200.002

0.005

0.01

0.02

0.05

0.1

0.2

0.5

1

2

55Sensor 3


Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20200.001

0.0020.003

0.005

0.01

0.020.03

0.05

0.1

0.20.3

0.5Sensor 2


34

Frequency (Hz)

PS

D (

Dep

th -

Tre

nd)

0.02 0.05 0.1 0.2 0.5 1 2 3 4 5 7 10 20201E-5

2E-5

5E-5

0.0001

0.0002

0.0005

0.001

0.002

0.005

0.01

0.02

0.05

0.1Sensor 1



Table C-2 - Dominant frequencies observed in the de-trended water elevations signals

Run ho Gate opening

time

Sensor Dominant frequencies

t-To h

m s Hz s m (1) (2) (3) (4) (5) (6) (7) 1 0.402 0.183 3 0.830 & 1.074 0-14 0.20-0.40 2 0.79-1.51 30-147 0.047-0.134 1 0.07-1.55 217-480 0.022-0.039 2 0.399 0.20 3 0.830 & 1.074 0-13 0.202-0.40 2 0.54-1.41 8-152 0.047-0.250 1 0.6-1.7 33-441 0.022-0.129 3 0.401 0.183 3 0.830 & 1.074 0-12 0.205-0.40 2 0.53-1.43 8-152 0.047-0.247 1 0.66-1.4 27-437 0.123-0.121 5 0.400 0.167 3 0.830 & 1.074 0-13 0.202-0.40 2 0.66-1.40 8-132 0.047-0.252 1 0.5-3 32-462 0.023-0.128

Note: dominant frequency(ies) deduced from the sensor signal's power spectrum density function.

C.4 RELATIONSHIP BETWEEN WATER ELEVATION AND INSTANTANEOUS

DISCHARGE

The instantaneous discharge Q through the V-notch weir was calculated based upon the integral

form of the equation of conservation of mass:

35

Qdt

dVol (C-2)

where t is the time and Vol is the instantaneous volume of water in the intake basin estimated as:

)ph(BLVol (C-3)

with L the basin length, B the basin width and h the water elevation above the notch. Note that

Equation (C-3) assumes implicitly that the intake basin surface was horizontal and neglects the local

drop in water elevation in the vicinity of the weir notch where the fluid was accelerated.

Combining Equations (C-2) and (C-3), the instantaneous discharge was estimated as:

dt

hdBLQ (C-4)

Herein Equation (C-4) was calculated based upon the smoothed data set and the results Q(h) are

presented below by preserving every Nth point where N is the smoothing window size in points:

e.g., N = 300 for a smoothing window of 300 points.

h (mm)

Q (

m3 /s

)

0 50 100 150 200 250 300 350 4000

0.03

0.06

0.09

0.120.588/15(x/1000)2sqrt(29.8x/1000)Sensor 1 (smoothing 600 points)Sensor 1 (smoothing 900 points)Sensor 1 (smoothing 1200 points)Sensor 2 (smoothing 600 points)Sensor 2 (smoothing 1200 points)Sensor 3 (smoothing 300 points)Sensor 3 (smoothing 600 points)Sensor 3 (smoothing 1200 points)

Fig. C-10 - Relationship between instantaneous discharge Q and upstream water depth h for the 90º

V-notch weir during Run 1 - Calculations based upon the smoothed data trend and preserving every

Nth point with N the smoothing window size

36

h (mm)

Q (

m3 /s

)

0 50 100 150 200 250 300 350 4000

0.03

0.06

0.09

0.120.588/15(x/1000)2sqrt(29.8x/1000)Sensor 1 (smoothing 600 points)Sensor 1 (smoothing 1200 points)Sensor 2 (smoothing 600 points)Sensor 2 (smoothing 1200 points)Sensor 3 (smoothing 300 points)Sensor 3 (smoothing 600 points)




h (mm)

Q (

m3 /s

)

0 50 100 150 200 250 300 350 4000

0.03

0.06

0.09





37

h (mm)

Q (

m3 /s

)

0 50 100 150 200 250 300 350 4000

0.03

0.06

0.09





38

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FENTON, J.D. (2000). "Some Notes on V-Notch Weirs." Personal Communication, 1 page.

HERSCHY, R. (1995). "General Purpose Flow Measurement Equations for Flumes and Thin Plate

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Channels using Weirs and Venturi Flumes-Part 1: Thin-Plate Weirs." ISO 1438/1-1980,

International Organization for Standardization.

LENZ, A.T. (1943). "Viscosity and Surface Tension Effects on V-Notch Weir Coefficients."

Transactions, ASCE, Vol. 108, paper 2195, pp. 759-782. Discussion: Vol. 108, pp. 783-802.

TROSKOLANSKI, A.T. (1960). "Hydrometry: Theory and Practice of Hydraulic Measurements."

Pergamon Press, Oxford, UK, 684 pages.

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Experiments on the Flow of Water over Weirs.') Mémoires et Documents, Annales des Ponts et

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pp. 249-357; 1896: Sér. 7, Vol. 12, 2nd Sem., pp. 645-731; 1898: Sér. 7, Vol. 15, 2nd Sem., pp.

151-264 (in French).

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BAZIN, H. (1888). "Expériences Nouvelles sur l'Ecoulement par Déversoir." ('Recent Experiments

on the Flow of Water over Weirs.') Mémoires et Documents, Annales des Ponts et Chaussées,

Paris, France, 1888: Sér. 6, Vol. 16, 2nd Sem., pp. 393-448 & Plates 20 to 22 (in French).

BELANGER, J.B. (1849). "Notes sur le Cours d'Hydraulique." ('Notes on a Course in Hydraulics.')

Mém. Ecole Nat. Ponts et Chaussées, Paris, France, session 1849-1850, 222 pages (in French).

British Standard (1943). "Flow Measurement." British Standard Code BS 1042:1943, British

Standard Institution, London.

CHANSON, H. (2009). "Applied Hydrodynamics: An Introduction to Ideal and Real Fluid Flows."

CRC Press, Taylor & Francis Group, Leiden, The Netherlands, 478 pages.

ROUSE, H. (1938). "Fluid Mechanics for Hydraulic Engineers." McGraw-Hill Publ., New York,

USA (also Dover Publ., New York, USA, 1961, 422 pages)

ROUSE, H. (1946). "Elementary Mechanics of Fluids." John Wiley & Sons, New York, USA, 376

pages.

ROUSE, H. (1959). "Advanced Mechanics of Fluids." John Wiley, New York, USA, 444 pages.

Internet bibliography

Research papers in hydraulic engineering (open

access)

{http://espace.library.uq.edu.au/list/author_id/193/}

40

Bibliographic reference of the Report CH88/12 The Hydraulic Model research report series CH is a refereed publication published by the School of

Civil Engineering at the University of Queensland, Brisbane, Australia.

The bibliographic reference of the present report is:

CHANSON, H., and WANG, H. (2012). "Unsteady Discharge Calibration of a Large V-Notch

Weir." Hydraulic Model Report No. CH88/12, School of Civil Engineering, The University of

Queensland, Brisbane, Australia, 50 pages & 4 movies (ISBN 9781742720579).

The Report CH88/12 is available, in the present form, as a PDF file on the Internet at UQeSpace:

http://espace.library.uq.edu.au/

It is listed at:

http://espace.library.uq.edu.au/list/author_id/193/

41

HYDRAULIC MODEL RESEARCH REPORT CH

The Hydraulic Model Report CH series is published by the School of Civil Engineering at the

University of Queensland. Orders of any reprint(s) of the Hydraulic Model Reports should be

addressed to the School Secretary.

School Secretary, School of Civil Engineering, The University of Queensland

Brisbane 4072, Australia - Tel.: (61 7) 3365 3619 - Fax : (61 7) 3365 4599

Url: http://www.eng.uq.edu.au/civil/ Email: [email protected]

Report CH Unit price Quantity Total price

CHANSON, H., and WANG, H. (2012). "Unsteady Discharge Calibration of a Large V-Notch Weir." Hydraulic Model Report No. CH88/12, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 50 pages & 4 movies (ISBN 9781742720579).

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FELDER, S., FROMM, C., and CHANSON, H. (2012). "Air Entrainment and Energy Dissipation on a 8.9° Slope Stepped Spillway with Flat and Pooled Steps." Hydraulic Model Report No. CH86/12, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 82pages (ISBN 9781742720531).

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BROWN, R., CHANSON, H., McINTOSH, D., and MADHANI, J. (2011). "Turbulent Velocity and Suspended Sediment Concentration Measurements in an Urban Environment of the Brisbane River FloodPlain at Gardens Point on 12-13 January 2011." Hydraulic Model Report No. CH83/11, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 120 pages (ISBN 9781742720272).

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JANSSEN, R., and CHANSON, H. (2010). "Hydraulic Structures: Useful Water Harvesting Systems or Relics." Proceedings of the Third International Junior Researcher and Engineer Workshop on Hydraulic Structures (IJREWHS'10), 2-3 May 2010, Edinburgh, Scotland, R. JANSSEN and H. CHANSON (Eds), Hydraulic Model Report CH80/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 211 pages (ISBN 9781742720159).

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CHACHEREAU, Y., and CHANSON, H., (2010). "Free-Surface Turbulent Fluctuations and Air-Water Flow Measurements in Hydraulics Jumps with Small Inflow Froude Numbers." Hydraulic Model Report No. CH78/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 133 pages (ISBN 9781742720036).

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DOCHERTY, N.J., and CHANSON, H. (2010). "Characterisation of Unsteady Turbulence in Breaking Tidal Bores including the Effects ofBed Roughness." Hydraulic Model Report No. CH76/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 112pages (ISBN 9781864999884).

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CHANSON, H. (2009). "Advective Diffusion of Air Bubbles in Hydraulic Jumps with Large Froude Numbers: an Experimental Study." Hydraulic Model Report No. CH75/09, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 89 pages & 3 videos(ISBN 9781864999730).

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GOURLAY, M.R., and HACKER, J. (2008). "Reef-Top Currents in Vicinity of Heron Island Boat Harbour, Great Barrier Reef, Australia: 2. Specific Influences of Tides Meteorological Events and Waves."Hydraulic Model Report No. CH73/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, 331 pages (ISBN 9781864999365).

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LARRARTE, F., and CHANSON, H. (2008). "Experiences and Challenges in Sewers: Measurements and Hydrodynamics." Proceedings of the International Meeting on Measurements and Hydraulics of Sewers,Summer School GEMCEA/LCPC, 19-21 Aug. 2008, Bouguenais, Hydraulic Model Report No. CH70/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia (ISBN 9781864999280).

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CHANSON, H. (2008). "Photographic Observations of Tidal Bores (Mascarets) in France." Hydraulic Model Report No. CH71/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, 104 pages, 1 movie and 2 audio files (ISBN 9781864999303).

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FELDER, S., and CHANSON, H. (2008). "Turbulence and Turbulent Length and Time Scales in Skimming Flows on a Stepped Spillway. Dynamic Similarity, Physical Modelling and Scale Effects." Report No. CH64/07, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, March, 217 pages (ISBN 9781864998870).

AUD$60.00

TREVETHAN, M., CHANSON, H., and BROWN, R.J. (2007). "Turbulence and Turbulent Flux Events in a Small Subtropical Estuary." Report No. CH65/07, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, November, 67 pages (ISBN 9781864998993)

AUD$60.00

MURZYN, F., and CHANSON, H. (2007). "Free Surface, Bubbly flow and Turbulence Measurements in Hydraulic Jumps." Report CH63/07, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, August, 116 pages (ISBN 9781864998917).

AUD$60.00

KUCUKALI, S., and CHANSON, H. (2007). "Turbulence in Hydraulic Jumps: Experimental Measurements." Report No. CH62/07, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, July, 96 pages (ISBN 9781864998825).

AUD$60.00

CHANSON, H., TAKEUCHI, M, and TREVETHAN, M. (2006). "Using Turbidity and Acoustic Backscatter Intensity as Surrogate Measures of Suspended Sediment Concentration. Application to a Sub-Tropical Estuary (Eprapah Creek)." Report No. CH60/06, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, July, 142 pages (ISBN 1864998628).

AUD$60.00

CAROSI, G., and CHANSON, H. (2006). "Air-Water Time and Length Scales in Skimming Flows on a Stepped Spillway. Application to the Spray Characterisation." Report No. CH59/06, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, July (ISBN 1864998601).

AUD$60.00

TREVETHAN, M., CHANSON, H., and BROWN, R. (2006). "Two Series of Detailed Turbulence Measurements in a Small Sub-Tropical Estuarine System." Report No. CH58/06, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, Mar. (ISBN 1864998520).

AUD$60.00

KOCH, C., and CHANSON, H. (2005). "An Experimental Study of Tidal Bores and Positive Surges: Hydrodynamics and Turbulence of the Bore Front." Report No. CH56/05, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, July (ISBN 1864998245).

AUD$60.00

CHANSON, H. (2005). "Applications of the Saint-Venant Equations and Method of Characteristics to the Dam Break Wave Problem." Report No. CH55/05, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, May (ISBN 1864997966).

AUD$60.00

44

CHANSON, H., COUSSOT, P., JARNY, S., and TOQUER, L. (2004). "A Study of Dam Break Wave of Thixotropic Fluid: Bentonite Surges down an Inclined plane." Report No. CH54/04, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, June, 90 pages (ISBN 1864997710).

AUD$60.00

CHANSON, H. (2003). "A Hydraulic, Environmental and Ecological Assessment of a Sub-tropical Stream in Eastern Australia: Eprapah Creek, Victoria Point QLD on 4 April 2003." Report No. CH52/03, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, June, 189 pages (ISBN 1864997044).

AUD$90.00

CHANSON, H. (2003). "Sudden Flood Release down a Stepped Cascade. Unsteady Air-Water Flow Measurements. Applications to Wave Run-up, Flash Flood and Dam Break Wave." Report CH51/03, Dept of Civil Eng., Univ. of Queensland, Brisbane, Australia, 142 pages (ISBN 1864996552).

AUD$60.00

CHANSON, H,. (2002). "An Experimental Study of Roman Dropshaft Operation : Hydraulics, Two-Phase Flow, Acoustics." Report CH50/02, Dept of Civil Eng., Univ. of Queensland, Brisbane, Australia, 99 pages (ISBN 1864996544).

AUD$60.00

CHANSON, H., and BRATTBERG, T. (1997). "Experimental Investigations of Air Bubble Entrainment in Developing Shear Layers." Report CH48/97, Dept. of Civil Engineering, University of Queensland, Australia, Oct., 309 pages (ISBN 0 86776 748 0).

AUD$90.00

CHANSON, H. (1996). "Some Hydraulic Aspects during Overflow above Inflatable Flexible Membrane Dam." Report CH47/96, Dept. of Civil Engineering, University of Queensland, Australia, May, 60 pages (ISBN 0 86776 644 1).

AUD$60.00

CHANSON, H. (1995). "Flow Characteristics of Undular Hydraulic Jumps. Comparison with Near-Critical Flows." Report CH45/95, Dept. of Civil Engineering, University of Queensland, Australia, June, 202 pages (ISBN 0 86776 612 3).

AUD$60.00

CHANSON, H. (1995). "Air Bubble Entrainment in Free-surface Turbulent Flows. Experimental Investigations." Report CH46/95, Dept. of Civil Engineering, University of Queensland, Australia, June, 368 pages (ISBN 0 86776 611 5).

AUD$80.00

CHANSON, H. (1994). "Hydraulic Design of Stepped Channels and Spillways." Report CH43/94, Dept. of Civil Engineering, University of Queensland, Australia, Feb., 169 pages (ISBN 0 86776 560 7).

AUD$60.00

POSTAGE & HANDLING (per report) AUD$10.00 GRAND TOTAL

OTHER HYDRAULIC RESEARCH REPORTS

Reports/Theses Unit price Quantity Total priceTREVETHAN, M. (2008). "A Fundamental Study of Turbulence and Turbulent Mixing in a Small Subtropical Estuary." Ph.D. thesis, Div. of Civil Engineering, The University of Queensland, 342 pages.

AUD$100.00

GONZALEZ, C.A. (2005). "An Experimental Study of Free-Surface Aeration on Embankment Stepped Chutes." Ph.D. thesis, Dept of Civil Engineering, The University of Queensland, Brisbane, Australia, 240 pages.

AUD$80.00

45

TOOMBES, L. (2002). "Experimental Study of Air-Water Flow Properties on Low-Gradient Stepped Cascades." Ph.D. thesis, Dept of Civil Engineering, The University of Queensland, Brisbane, Australia.

AUD$100.00

CHANSON, H. (1988). "A Study of Air Entrainment and Aeration Devices on a Spillway Model." Ph.D. thesis, University of Canterbury, New Zealand.

AUD$60.00

POSTAGE & HANDLING (per report) AUD$10.00 GRAND TOTAL

CIVIL ENGINEERING RESEARCH REPORT CE

The Civil Engineering Research Report CE series is published by the School of Civil Engineering

at the University of Queensland. Orders of any of the Civil Engineering Research Report CE should

be addressed to the School Secretary.


Brisbane 4072, Australia

Tel.: (61 7) 3365 3619 Fax : (61 7) 3365 4599


Recent Research Report CE Unit price Quantity Total priceCALLAGHAN, D.P., NIELSEN, P., and CARTWRIGHT, N. (2006). "Data and Analysis Report: Manihiki and Rakahanga, Northern Cook Islands - For February and October/November 2004 Research Trips." Research Report CE161, Division of Civil Engineering, The University of Queensland (ISBN No. 1864998318).

AUD$10.00

GONZALEZ, C.A., TAKAHASHI, M., and CHANSON, H. (2005). "Effects of Step Roughness in Skimming Flows: an Experimental Study." Research Report No. CE160, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, July (ISBN 1864998105).

AUD$10.00

CHANSON, H., and TOOMBES, L. (2001). "Experimental Investigations of Air Entrainment in Transition and Skimming Flows down a Stepped Chute. Application to Embankment Overflow Stepped Spillways." Research Report No. CE158, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, July, 74 pages (ISBN 1 864995297).

AUD$10.00

HANDLING (per order) AUD$10.00 GRAND TOTAL

Note: Prices include postages and processing.

46

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QUEENSLAND and crossed "Not Negotiable".

Orders of any Research Report should be addressed to the School Secretary.


Brisbane 4072, Australia - Tel.: (61 7) 3365 3619 - Fax : (61 7) 3365 4599
