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Journal of Hydraulic Research

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Hydraulics: science, knowledge, and culture

John D. Fenton

To cite this article: John D. Fenton (2016) Hydraulics: science, knowledge, and culture, Journalof Hydraulic Research, 54:5, 485-501, DOI: 10.1080/00221686.2016.1218370

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Journal of Hydraulic Research Vol. 54, No. 5 (2016), pp. 485–501http://dx.doi.org/10.1080/00221686.2016.1218370© 2016 International Association for Hydro-Environment Engineering and Research

Vision paper

Hydraulics: science, knowledge, and cultureJOHN D. FENTON (IAHR Member), Guest Professor, Institute of Hydraulic Engineering, Vienna University of Technology,Karlsplatz 13/222, 1040 Vienna, AustriaEmail: johndfenton@gmail.com

ABSTRACTThe processes of thinking, research, dissemination, and use of research results and knowledge in hydraulics are examined, differentiating it fromhydrology, and suggesting greater use of scientific methods and theories. At highly technical levels this is already done, but it is suggested thatthere is room for a greater simplicity of approach, based on scientific rigour, recognizing that much of what is done in hydraulics is modelling.This would make understanding of, access to, and participation in research easier for members of the profession. A number of recommendationsand conclusions are made. The article has a critical tone, but its main intention is to be helpful to individual hydraulicians and to the profession atlarge. Suggestions are made as to how the profession might use the Web to give open access to research findings and to create an open resource forhydraulics knowledge, as connection by colleagues in all countries is now possible and feasible.

Keywords: Applied fluid mechanics and hydraulic engineering; computational methods in hydro-environment research and fluiddynamics; continuing education; general theory in fluid mechanics; hydraulic education; hydraulics research; hydraulics training;open access; professional practice

1 Introduction

When the author started to write this article, he considered whattitle to use. He intended naming it Hydraulics – A Love Story.Then his courage failed, thinking of a hydraulics indexing orabstracting service somewhere reporting the M articles this yearwith “nonlinear” in the title, N with “turbulent”, and 1 with“love”, together with the author’s name. This is not, then, enti-tled “a love story”, but it is a declaration of love for hydraulics:water is wonderful, water with a free surface even more wonder-ful, and so is water with a moveable boundary of soil particles.Just as wonderful is the nature of our subject itself, with itsmixture of simple and powerful theories, sometimes incorrecttheories, fundamental theories, ad hoc theories, faddish theories,field and laboratory measurements and control, sophisticatednumerical methods, complicated and sometimes wrong numer-ical methods, complicated phenomena being described simply,simple phenomena being described complicatedly, and so on.Also, of course, there is the hydraulics community of schol-ars and practitioners which, like the subject itself, is innatelygentle. Its soft characteristics attract such people, and in returnlend something back to those who study and use it. However

one should mention the comment made by an associate editor,J. Aberle, reviewing this manuscript: not all authors are soft!

The title finally adopted by the author, Hydraulics: science,knowledge, and culture describes the range of the intellectualapproaches to hydraulics along an axis from science to non-science: science is “knowledge about or study of the naturalworld based on facts learned through experiments and obser-vation”, knowledge is “information, understanding, or skill thatyou get from experience or education” and culture “the beliefs,customs, arts, etc., of a particular society, group, place, ortime”.

The intentions of the author are to explore the processesof thinking, research, dissemination, and use of research andknowledge in hydraulics; to examine how effective each is; andto make suggestions for possible improvement. The article isdifferent from almost any other that the author has written andfrom other articles in hydraulics journals. Instead of followinga definite path with a clear scientific objective and establish-ing that with evidence, the article is written in an unscientificmanner, with statements, assertions, quotations, and evalua-tions in a wandering path where the author was free to choosearbitrarily at any stage which bifurcation to take and which

Received 22 June 2016; accepted 26 July 2016/Open for discussion until 30 April 2017.

ISSN 0022-1686 print/ISSN 1814-2079 onlinehttp://www.tandfonline.com

485

486 J.D. Fenton Journal of Hydraulic Research Vol. 54, No. 5 (2016)

arbitrary groupings of sections to make. In fact, it is almostexactly not how the author suggests hydraulics research itselfshould progress.

At the end there are suggestions for rejuvenating hydraulics,particularly at the simple end, so that it is more accessible toreaders and writers, wherever they live and work in the world.There will also be some suggestions for individuals, generallyof an anarchic nature, in the hope that they will gain and willenergize our fascinating field.

In particular it is hoped that younger members of our pro-fession, female and male, and from all continents, might beencouraged, by the critical tone, that neither the scientific “laws”nor established practice are necessarily correct, and that dis-obeying them is not only good fun, but productive for research,professional practice, and life.

Throughout, the author will occasionally refer to universityteaching contexts, to learning contexts, to research contexts, andoccasionally to contexts of professional practice. They are notmeant to be fixed boundaries, and the reader, whether as student,teacher, researcher or practitioner, should be able to see past anyapparent boundaries. Ideally, learning is for life, and life is betterwhen it is about learning.

2 The nature of hydraulics

What is hydraulics? The author searched books and the Web,and arrived at this definition:

Hydraulics is a topic in applied science and engineering deal-ing with the mechanical properties of fluids, usually liquids.Fluid mechanics provides the theoretical foundation for practicalapplications.

“Applied science and engineering” has a good generality, incor-porating two strands of IAHR’s interests, the “mechanical prop-erties” sets it clearly apart from hydrology, “fluid mechanics” asa foundation seems to be correct, and there is a strong element of“practical applications”. We could, of course, argue about thatdefinition interminably.

2.1 Hydraulics and fluid mechanics

Part of hydraulics is fluid mechanics, and part of fluid mechan-ics is hydraulics. They are inextricably intertwined. That alsoapplies to mathematical and computational fluid mechanics,where one is more likely to be dealing with a whole flow field,rather than just approximations as to velocity and pressure dis-tributions. However, part of the attraction of hydraulics for theauthor is that much of it is actually avoiding solving the wholeflow field, and making approximations which work satisfac-torily. The continuous interplay between fundamental scienceon one side and modelling on the other is always interesting.Modelling is best when it can be related to the real physics.A very successful modeller, who operated close to the full equa-tions with rigorous systematic approximations was L. Prandtland his school. Even he, when the situation arose, could model

less rigorously, for example u ∝ y1/7 for the time mean velocityu in a turbulent shear flow as a function of distance y fromthe boundary. Another successful modeller, slightly earlier, wasJ.V. Boussinesq, who simply incorporated real velocity and den-sity distributions and curvature of streamlines in turbulent flowsand in irrotational flows, taking each as far as it could in eachsituation.

2.2 Hydraulics and hydrology

The author understood better the difference between hydraulicsand hydrology (“ . . . the scientific study of the movement, dis-tribution, and quality of water”), when last year he attendeda hydrology workshop. There was one session devoted to theupstream influence of river changes and obstructions, but lit-tle progress was being made. The author thought that that wasthe right time to mention that there is in fact a simple the-ory for the upstream length scale of disturbances. It is actuallyfrom a favourite paper of the author. It uses simple modellingto give insight into an important problem. The paper is bySamuels (1989) and is entitled “Backwater lengths in rivers”.It shows (here making assumptions of small Froude number anda wide channel, and using a factor 3 coming from the Chézyformula rather than the 10/3 from Manning) that a backwatercurve decays like exp(3S0x/h), where S0 is the slope, h is thedepth, and x is distance along the stream, positive downstream,so that as x → −∞ upstream, the disturbance decays exponen-tially at that rate. The assembled participants at the workshopwere most unhappy about this, and some disparaging remarkswere made about hydraulics and such theory. The author retortedwith the admittedly unkind joke, that “hydraulics and hydrologybear the same relationship as do astronomy and astrology”. Itcan be imagined that the rest of the session was not very happy.But several people continued to lament that what was reallyneeded was more data. Much more data. And presumably, manypublications.

Hydrology is more different from hydraulics than thatanecdote reveals. There are important differences betweenhydrology and hydraulics concerning scale and the number ofprocesses involved. In hydrology there is an interplay of phys-ical, biological, geomorphological, etc., processes making itmore difficult to be as rigorous as we can be in fluid mechanicsand hydraulics. Hydraulics is not hydrology.

Here evidence is presented of some problems currently beset-ting hydrology, after which an important paper will be brieflydescribed, drawing attention to those problems and making pro-posals to solve them. The solution is undoubtedly some wayaway, but there is some hope.

Carl Friedrich Gauss (“greatest mathematician since anti-quity”) did not publish quickly. His personal motto was paucased matura, “Few, but Ripe”. He would not have been amusedtoday to observe papers judged on the quality of the journalthey appear in, where that quality might be quantified by theconcept of “Impact Factor” which rewards people rushing into

Journal of Hydraulic Research Vol. 54, No. 5 (2016) Hydraulics: science, knowledge, and culture 487

print and publishing papers very quickly. This is highly depen-dent on which discipline one works in. For example consider thelatest issues of two journals, Water Resources Research, whichhas a strong hydrological orientation, and our own Journal ofHydraulic Research:

Number of authors 1 2 3 4 5 6 9 18

Water Resources Research, 52(4)

Number of papers 2 4 15 11 9 5 1 1

Journal of Hydraulic Research, 54(3)Number of papers 1 1 1 4 0 1

It can be seen that rewarding people and journals by theamount of churning (modern meaning: the too-rapid buying andselling of financial quantities to profit from both) can lead tohigh levels of collective rapid publishing. It may be that the48 papers in that single issue of WRR are all important. It maybe that the paper with 18 authors (from eight institutions) mayhave had contributions from all. However, one is suspicious.Particularly as at the above-mentioned hydrology workshop,after a two-hour discussion session on a hydrology topic, asenior member of that profession invited everyone in the roomwho had made a verbal contribution, later to write it down; theywould all be collated and it would be submitted to a journal as aresearch paper. The present author could only compare with thetypical painstaking research in hydraulics, as measured here bythe figures for the Journal of Hydraulic Research in the table.

All these problems have, however, been grandly recognizedin a recent paper by Koutsoyiannis et al. (2016), each of whom isan editor of a hydrology journal. The article makes a number ofpoints which can also be found in this article, including address-ing problems of “publish or perish”, how peer review should bedone, what a scientific paper really should try to accomplish,how research should be evaluated, problems of multi-authorpapers and modifications in citation metrics, and a change in cul-ture of the peer-review process toward enhanced transparency.The present author recommends it strongly to all readers of thispaper. It is openly accessible and short.

2.3 Hydraulics and scientific method

The experience with the hydrologists caused the author to reflecton the nature of data and such measurements, without an under-lying theory, and was reminded of the quotation that he hadinscribed on his lecture note folder in 1962–1964 at a technicalcollege in rural Australia where he first studied civil engi-neering, which he now knows was from the psychologist KurtLewin:

Nothing is so practical as a good theory.

What the people in the above-mentioned workshop seemed towant to do was to use induction, gathering enough information

so as to make an empirical generalization. The Scottishphilosopher David Hume (1711–1776) identified the troublewith that, the Problem of Induction, where inductive reasoningleads to knowledge, which, however much evidence one has,one still cannot make a definitive conclusion. In general scien-tific terms this was answered by Karl Popper in his 1934 book,Logik der Forschung, first appearing in English in 1959 as TheLogic of Scientific Discovery (Popper, 2002). He stated that sci-entific method should be based on falsifiability, whereas a theorycan never be proved by any number of experiments, it can bedisproved by just one.

For years the author has wondered how falsification might beused in engineering. Possibly the above experience with a num-ber of enthusiastic data collectors and Samuels’ theory providesthe answer, that a field like hydrology might concentrate on col-lecting and approximating data, whereas one like hydraulics ismore scientific, in Popperian terms. It aims to describe some-thing simply and in usable terms. It could possibly be disproved,but in the case of hydraulics it is more likely that it might just berefined, improved, or limits be established. In Samuels’ theory,a limit is if an obstacle raises the water level to a finite amountcompared with the depth, when it is not so accurate becausethe theory is based on linearization of the gradually-varied flowequation. That seems unimportant if one considers the benefitof having a simple formula to estimate the magnitude of some-thing. If one needed accuracy, a solution would be just to solvethe gradually-varied flow equation as a differential equation.Doing that, one obtains a lot of numbers, and maybe a localauthority, as is commonly done, insisting on the application ofa widely-known computer program (HEC-RAS, 2010) mightbe satisfied. They would be less satisfied, if they were to lookat the methods in that program of simulating flow past bridgepiers, where a bridge pier is treated as a simple narrowing of thechannel, thereby violating all assumptions of gradual variation,rather than as an abrupt loss of momentum and hence elevation,plain to see in comparisons between measurements and compu-tations (HEC, 1995). To the present author the results there seemlike a falsification, but elsewhere never seem to have arousedconcern.

Recently the present author and a colleague did publish apaper which proved a theory false with two examples (one ofthem would have sufficed). Fenton and Darvishi (2016) consid-ered Massé’s Singular Point Theory for calculating transcriticalflow over a broad-crested weir. The theory is based on the asser-tion that, when flow passes through critical, and the denominatorof the gradually-varied flow equation goes to zero, so does thenumerator, so that their ratio, and hence the free surface slope,is finite, and the equation can be used to generate an internalboundary condition and to describe the whole flow. There is noreason, hydraulically or mathematically, why this should be so.Fenton and Darvishi (2016) considered a single experimentalexample of their own, in which, due to a manufacturing defect,the top of a laboratory broad-crested weir was not exactly flat,but had a very small dip with a negative slope on one side. In that

488 J.D. Fenton Journal of Hydraulic Research Vol. 54, No. 5 (2016)

case, the quasi-normal depth, an artifice of the theory, becameimaginary and the theory a nonsense. Computing the surfacedue to the theory showed how it had an angular discontinuityand looked nothing like a real transcritical flow. That is differentfrom just being inaccurate, and is in itself a disproof.

A different point of view from falsification is that ofKuhn (1996, originally published in 1959) in his book TheStructure of Scientific Revolutions. His view was also that afield of science does not progress in a continuous manner,but instead of requiring the disproofs of Popper, it proceeds,gradually accumulating evidence of inconsistencies and inaccu-racies until there is a revolution in thinking, called a paradigmshift, which provides new understanding and methods but whichincorporate and explain the old results and those contradictingthe old paradigm. The received “truth” cannot be established byobjective criteria but by a subjective consensus in the researchcommunity. When a paradigm is successful, the science pro-ceeds well: “During the period of normal science, the failureof a result to conform to the paradigm is seen not as refut-ing the paradigm, but as the mistake of the researcher, contraPopper’s falsifiability criterion.” It is not possible to understandone paradigm through the ideas and structure and methods ofanother.

2.3.1 A preliminary calculation – a theory for channel flowon steep slopes

In case technical readers are becoming a little bored with somany words – as the author readily does – an example of theapplication of rational mechanics is included here to show howa more general result than is usually known can be obtainedsimply, whereas using a traditional empirical theory such as theGauckler–Manning formula for uniform channel flow would bemore difficult to apply.

Consider a horizontal length L of uniform channel flow,inclined at an angle θ to the horizontal, with discharge Q, andcross-sectional area A as conventionally measured in a verticalplane. The vertical gravitational force on the water is ρgAL,and the component of this along the slope is ρgAL sin θ . Theresistance force along the slope is τPn(L/ cos θ), where τ is themean shear stress, Pn is the wetted perimeter as measured in aplane normal to any line along the channel. The stress accord-ing to the Darcy–Weisbach resistance formulation is τ = ρ�V2,where the coefficient � = l/8 = g/C2, where l is the dimen-sionless Weisbach coefficient, often written f, and C is the Chézycoefficient, in a more familiar notation; V is the mean velocitycomponent along the slope, related to the mean horizontalvelocity Q/A by V = (Q/A)/ cos θ . Equating the gravitationalcomponent and the resisting force and substituting for τ and Vgives:

QA

=√

gA�Pn

sin θ cos3 θ = 11 + S2

√g�

APn

S (1)

where simple trigonometry has been used to express the resultin terms of S = tan θ , the slope of the flow. This equation is ageneralized form of the Chézy–Weisbach equation for a chan-nel of arbitrary slope, which might be useful for flows on steepspillways and ramps. The perpendicular wetted perimeter Pn

cannot be simply related to the conventional wetted perimeterP measured in a vertical plane, as it depends on the sectiongeometry. That can be understood by considering a simple rect-angular section where the bottom, horizontal across the channel,gives the same contribution to P and Pn, but the contribution ofthe sides would be multiplied by a cos θ factor. For the majorityof channels, rather wider than deep, Pn ≈ P would be a goodapproximation. Of course, in almost all river and canal flows Sis so small that the S2 term can be neglected and Pn ≈ P veryclosely. Even if the finite-slope result, Eq. (1) were rarely used,it is nice to know that when we use the simpler form, we areworking well inside our limitations.

2.3.2 A candidate for a paradigm shift

Consider the two well-known formulae for uniform channelflow with a small slope S:

QA

=

⎧⎪⎪⎪⎨⎪⎪⎪⎩

1n

(AP

)2/3 √S Gauckler–Manning

√g�

(AP

)1/2 √S Chézy–Weisbach

where the second is simply obtained from Eq. (1) using Pn ≈ Pand ignoring S2. Written like this the two forms look almostequivalent, yet there are important differences, and problemswith the Gauckler–Manning formulation. We turn to it, includ-ing the Strickler variant, with kSt = 1/n, and examine theiraccumulation of inadequacies:

• The Gauckler–Manning form has little basis in fluid mechan-ics. It is more difficult to obtain more general results using it,such as those shown in Eq. (1).

• The coefficient n has no physical significance other than itsrelation to other quantities obtained from its use.

• The equation is dimensional, such that n is the Manningcoefficient in SI units of dimensions L−1/3T. Different unitsystems require different formulae,

• It is based on empiricism, in common with Chézy’s origi-nal formula, such that neither contain the driving force in theform of gravitational acceleration g, or the resisting force dueto boundary stress.

• A common method of obtaining n is by looking at tablesor pictures in books, in which the important underlyingroughness is not known or is not visible.

• There are formulae for n, notably many forms of Strickler’sformula n = αd1/6

x , where α is a coefficient and dx is a char-acteristic grain size. There is a variety of such formulaeand various numerical values of the coefficient, with muchconfusion between imperial and SI units.

Journal of Hydraulic Research Vol. 54, No. 5 (2016) Hydraulics: science, knowledge, and culture 489

• Possibly the greatest problem is that the empiricism of theformulation has somehow allowed or even encouraged peo-ple to indulge in any form of irrational and non-scientificdeterminism, as exemplified by the list of 26 different com-pound or composite section formulae in Yen (2002, table 3) ,or Cowan’s composite formula (see, for example, Yen, 2002,p. 36) n = (∑

i ni)m, where the ni are different contributions,

including a base value contribution, and those due to surfaceroughness, shape and size of channel cross-section, obstruc-tions, and vegetation, while m corrects for meandering. Thereis no reason at all why they might be combined in thisform. Using the Chézy–Weisbach form, which is based onan approximation to boundary stress, for a compound sectionone can linearly combine force contributions from differentparts of the boundary. This still has problems, but it is at leastrational.

More than 50 years ago the ASCE Task Force onFriction Factors in Open Channels (1963) stated that theChézy–Weisbach formulation was more fundamental than theGauckler–Manning form, and was based on more research. Onthe other hand, the Gauckler–Manning formula is based onlyon empiricism and leads to tortuous further excursions intoempiricism, as has just been seen.

Surely it is time for a paradigm shift?

2.4 Hydraulics and mathematics

Mathematics is a problem for many people, and can lead to earlyalienation and the internalizing of a sense of failure and of igno-rance, as discussed below in section 3.5. The following anecdotemight help to reassure people.

In 1994 the mathematician Fritz John died. He had madea number of important research contributions, of a more-or-less pure mathematical nature, and, of interest to the author,in the area of water waves. One of his colleagues from theCourant Institute of Mathematical Sciences at New York Uni-versity wrote an obituary, in which he recounted the story ofone day walking past John’s open office door, to find him sittingat his desk reading a book, looking bothered:

“Why are you shaking your head, Fritz?” And nearing the desk:“Oh – is it because it’s written in Russian?”Fritz’s response: “No, because it’s written in Mathematics!”

That from a distinguished mathematician. Every student – orpractising engineer – experiencing problems learning or read-ing a technical paper, should know that they are not uniqueand neither are they limited to what they might think they are.Effort is worth pursuing: Understanding is difficult, but it hasrewards – and lasts for a lifetime. Ignorance also lasts for alifetime. Understanding is better.

On the subject of how much mathematics to learn, one couldparaphrase the former Duchess of Windsor: “You can never betoo rich or too thin” – but here “One can never know too muchmathematics”. One could possibly introduce a limitation as to

the type of mathematics. In reality, we all have our boundaries:the author reached his recently when he was forced to considera paper with 35 pages of abstract mathematics, at the end ofwhich the paper had established the existence of solutions forsymmetric waves.

Being young is the best time to learn mathematics, and beingforced to learn mathematics is an even more efficient and wide-ranging way of doing it. However enthusiastic we might beabout buying a mathematics book and reading it in our matu-rity, there is nothing quite like struggling through EngineeringMathematics 1 and 2, and maybe 3 and 4, as the author waslucky enough to do. He did not know that later he would haverather more to do with mathematics. He is probably a livingexample of the engineer in a rather scornful mathematics joke:Mathematician: “Do you understand integration?” Engineer:“Well, no, but I got used to it.”

There is one field of mathematics that is now essential tohydraulics, but in which hydraulics is particularly unsophisti-cated, and that is numerical methods. There are a number ofmethods or formulae which are wrong, silly, or unnecessarilycomplicated. These include:

• Using complicated implicit methods to solve problems, whenexplicit methods are simpler to understand, to teach, toresearch, and to implement. Examples include the routing offloods through reservoirs using the modified Puls method, andthe calculation of the steady surface profile in a stream byboth Direct and Standard Step methods.

• This criticism also applies to unsteady wave propagationmethods. The simplest possible numerical method for thelong wave equations, using explicit finite differences, for-ward in time and centred in space, is actually quite stable,with a not ungenerous limit on time step. It is not unstableas was asserted in 1975, when it was given the humiliatingname “the unstable method”. It has been believed to be soever since, such that complicated implicit schemes have beenthought to be necessary. They are more stable, but they are notnecessary. This has disempowered ordinary hydraulicians andpartly helped the commercial centralization of computationalhydraulics.

• Spatial integration methods used in hydrometry are clumsyand the most-commonly used one for transverse integrationof vertical velocity profiles is wrong. Using a more gen-eral method for the vertical profile can significantly speedup stream-gauging and make it more accurate. This appliesalso to implementations of ultrasonic time-of-travel methods,where the wrong transverse method has also been imple-mented vertically. Manufacturers make claims for accuracythat are unjustified and unchallenged.

Recently, 53 years after his first exposure to universitymathematics, the author was sitting with a research student talk-ing about her research problem of vortices and sluice gates,when one of his colleagues, a friend, came past the door, put

490 J.D. Fenton Journal of Hydraulic Research Vol. 54, No. 5 (2016)

his head in and said to her “Don’t listen to him. He only makesthings complicated with mathematics.” Well, occasionally yes,when it might solve a problem or explain the mechanics ofsomething. Occasionally, however, it can be simplifying andrevealing. An example is taking the conservation of momen-tum principle for an obstacle such as a bridge pier in a pris-matic channel, using familiar hydraulics. Then a simple seriesapproximation is made which gives an explicit solution andreveals the nature of an obstacle as a partial channel control.

Consider a river flow with an upstream Section 1 and a down-stream Section 2, with an obstacle such as a bridge pier betweenthem which exerts drag, leading to the classical hydraulicformulation of momentum:

CD12γ

Q2

A21

a1 =(

gAh̄ + βQ2

A

)1−(

gAh̄ + βQ2

A

)2

(2)

where γ is a coefficient that recognizes that the velocity whichimpinges on the object is not necessarily equal to the meanvelocity in the flow; CD is the drag coefficient of the obstacle,Q is the discharge, A is the stream cross-sectional area, a1 is thecross-sectional area of the object, with water at level η1, h̄ isthe depth to the centre of gravity, β is a Boussinesq momentumcoefficient.

So far, the formulation is in conventional hydraulic terms.A typical problem is in sub-critical flow, where we want toknow how much the water level will be raised if a bridge isbuilt. Conditions at 2 can be evaluated from conditions furtherdownstream. Then, as A1,2 and h1,2 are functions of the sur-face elevations η1,2, the equation becomes a nonlinear equationfor the unknown η1, which can be solved numerically usingany method for such problems. This is somewhat complicated,and does not reveal the important quantities of the problem, orits implications. It is simpler to obtain an approximate explicitsolution. We consider a small change of surface elevation η,presumed positive, going upstream from 2 to 1, we write Taylorseries in η for the upstream area of the stream A1, the blockagearea a1, and the first moment of area about the surface (Ah̄)1 interms of values at 2. Substituting into the momentum Eq. (2) andrecognizing that η is small, we expand each side as a powerseries in η, neglecting terms like (η)2. This gives a linearequation which can be solved to give an explicit approxima-tion for the dimensionless drop across the obstacle η/(A2/B2),where B2 is the surface width, such that A2/B2 is the meandownstream depth:

η

A2/B2= 1

2γ CDF2

2

1 − βF22

a2

A2(3)

This explicit approximate solution has revealed the importantquantities of the problem to us and how they affect the result:velocity ratio parameter γ , drag coefficient CD, downstreamFroude number F2

2 = Q2B2/(gA32), and the relative blockage

area a2/A2. For subcritical flow the denominator in Eq. (3) is

positive, and so is η, so that the surface drops from 1 to 2,as we expect. If the flow is supercritical, βF2

2 > 1, we find η

negative, and the surface rises between 1 and 2. If the flow isnear critical (βF2

2 ≈ 1) the change in depth will be large andthe theory will not be valid, which is made explicit by the the-ory. Another benefit of the approximate analytical solution ofEq. (3) is that it shows that such an obstacle forms a control inthe channel, such that the finite sudden change in surface ele-vation η is a function of Q2, or, Q a function of

√η, in a

manner analogous to a broad-crested weir. In numerical rivermodels it should ideally be included as an internal boundarycondition between different reaches as if it were a type of fixedcontrol. The little mathematical step of using a power series hasrevealed much to us about the hydraulics of the problem.

2.4.1 Some simple mathematical tips for any theory, formula,or computer program

That example leads us to the following, some of which might betrivial and obvious, but worth repeating.Always check the dimensions – especially if it is to do withManning’s n (L−1/3T).Test the sensitivity to parameters – the total differential is help-ful. Consider an example where we want to understand howchannel changes affect rating curves. A model is developedusing the Gauckler–Manning equation for a wide rectangularchannel, rearranged to give an expression for stage (water level)h at the station in terms of discharge Q:

h = Z +(

Qn

B√

S

)3/5

(4)

where Z is the bed elevation at the station, B is the width, S isslope, and n is the Manning coefficient. Consider a flow eventwhich changes the mean bed elevation by Z and the resistancecoefficient by n. The total differential of the stage is:

h = ∂h∂Z

Z + ∂h∂n

n (5)

Differentiating the right side of Eq. (4) with respect to Z and nand with a back-substitution using Eq. (4) the result is:

h = Z + 35(h − Z)

nn

(6)

The first term is obvious: if the bed changes by a certain amountZ, the water level for that flow will also change by thatamount – and is independent of flow, so it is the same for allflows. That is, the whole rating curve is displaced vertically(they are plotted with Q or log Q horizontally and h vertically).The second term, the change in stage due to resistance changing,is proportional to the fractional change in resistance coefficient,and is multiplied by the mean depth, which shows that changein stage due to change in resistance actually varies with stage,and so the rating curve is stretched vertically by a resistance

Journal of Hydraulic Research Vol. 54, No. 5 (2016) Hydraulics: science, knowledge, and culture 491

change. Examining the relative contributions of the terms inEq. (6), dividing through by depth h − Z gives, for the first term,Z/(h − Z), the relative change in depth, which is usually smallfor any fill or scour event, while the second term due to resis-tance change becomes 3

5n/n. This can be relatively large, assmall changes in bed arrangement (grain packing and arrange-ment, armouring, development of bed forms, etc.) can have afinite effect, and so the effects of changing resistance might bemore important than is usually recognized. This means that asthe resistance in a moveable bed river would tend to continuallychange, so would the rating, which has important implicationsfor the measurement of stage and the corresponding publicationof hourly or daily flows.Make a series approximation – this can be very revealing, as hasalready been done here in obtaining Eq. (3) for the water levelchange due to an obstacle. Even more simply:Examine results in the limits of an important parameter – andmaybe use those simpler results instead.

We have already done this in presenting Samuels’ result forthe rate of decay of backwater, and emphasize that the Froudenumber is small in many rivers and canals, such that terms in F2

can often be ignored, such as in the denominator on the right ofEq. (3), giving:

η = 12γ CD

U22

ga2

A2(7)

where U2 is the mean velocity. The observant reader might wellask, well, if F2

2 is small, is not the whole term on the rightalso small, and could we not neglect the backwater effect of thebridge completely? Whereas simplifying 1 − βF2

2 to 1 was obvi-ous, to do this we do not use mathematics, just typical numbers,which is always a good thing to do, as we now see.

2.4.2 Examine the magnitudes of wholes or of partsof expressions with typical numbers

We examine Eq. (7) for a case where γ = 1 (bridge piersextending the whole depth), CD ≈ 1 (which is roughly cor-rect), in a river where mean velocity U2 ≈ 1 m s−1, g = 10 m s−2

(of course!), and a2/A2 = 10%, giving η = 0.5 × 0.1 × 0.1 ≈5 mm. So very small! In this case it seems as if we do not needthat expensive laboratory testing program after all. That littletheory has saved a lot of money. Generally, however, the back-water caused by obstacles might have to be included, such as inthe results of the numerous examples in HEC (1995).

Whereas η is the mean change of stage across the wholeriver, Eq. (7) is looking familiar, with a term U2

2/(2g) andencourages us to remember Bernoulli’s law and to calculate howhigh the water might rise up the front of the bridge pier itself.Application of the law along a surface streamline would giveus a stagnation height greater than U2

2/(2g) = 5 cm because thesurface velocity is actually greater than the mean U2. We couldstart to wonder about the interplay of energy and momentumhere – but we do not have space or time. It can be seen that mod-elling can lead us into further explorations and understanding.

To end this section advocating the knowledge and use ofmathematics, a little story is recounted, not specifically to dowith mathematics but with university education generally: at acommencement day welcome for new students and their fam-ilies at the University of Auckland in the late 1980s, the thenchancellor of the university Michael Brown, an imposing Maoriman and prominent judge, said to the new students, fresh fromschool:

New students are particularly welcome, because they bring somuch knowledge and enthusiasm to the university. I have alwaysbeen surprised at how little our graduates take away!

A cynical view, which the author thought very funny. MaybeJudge Brown, like this author, believed in the old saying:

Education is what remains after you have forgotten everythingyou learnt.

This author liked to think that his own students had beeneducated, even if they had forgotten the details, by the scepti-cal content of the lectures, a mixture of theory and disbelief,explanations and criticisms.

2.5 Hydraulics and modelling

In the author’s experiences with applied mathematicians, hehas often found them more prepared to approximate and modelthan engineering colleagues. It is possibly in the nature of anengineer to want to be precise. This desire can be misplacedand misjudged. A botanist colleague, with whom the authorwas working on a restoration project for a river, had identi-fied this. She told him how she once met an engineer who haddeveloped a numerical model of the Murray River in Australia,the country’s longest – 2500 km, highly meandering, and withmany obstructive trees, alive and dead, standing and lying, in itscourse. She said to him, as one might, “How accurate is yourprogram, Wayne?”. The engineer replied, with an air of excite-ment: “Jane, it is exact!”. She had the good judgement not tobelieve him.

There is a famous French quotation “le mieux est l’ennemi dubien”, which has been attributed to Thomas Aquinas, Molièreand Voltaire, in that chronological order. It means, variously,in decreasing literalness of translation and quality of language:“the best is the enemy of the good”; “in looking for the best,one risks losing that which is good”; “less is often more”; “leavewell enough alone”; or “if it ain’t broke, don’t fix it”. That is rel-evant to the process of modelling, which will now be discussed.It could be a good motto for hydraulics in general.

William of Ockham, a mediaeval British monk and philoso-pher, developed the principle known as Ockham’s Razor. Thisstates that if something can be explained without a furtherassumption, there is no reason to assume it. Any explanationshould be in terms of the fewest factors or parameters. This wasparaphrased, possibly even better, by Albert Einstein as:

Make things as simple as possible, but not simpler.

492 J.D. Fenton Journal of Hydraulic Research Vol. 54, No. 5 (2016)

Another way of stating that, more prosaically, is the saying ofan unknown engineer:

Any equation more than 5 cm long is probably wrong!

As the width of each of the two columns in this journal is 9 cm,the reader has a ready guide as to what can be trusted here . . .

Most hydraulics is about modelling, and modelling is approx-imate. Generally we need to show less hubris – we need toaccept that what we are doing is approximate. Claude Shannondescribed a model as “a representation of an object, system oridea in some form other than itself”. This nice general definitionincludes both physical and mathematical modelling, the formerthe traditional mainstay of hydraulics, often using scale mod-els. When one uses physical modelling it is obvious that oneis modelling, that it is approximate, and that usually the effectsof viscosity, turbulence, resistance, and surface tension are notbeing modelled well. This sense of reality is not always thecase with mathematical models, as suggested by the example ofWayne above. In hydraulics, however, mathematical models canperform quite heroic deeds: consider a meandering river withturbulent flow throughout and a free surface, all modelled by thelong wave equations, two one-dimensional partial differentialequations in distance and time. The equations could form a verygood model of reality, if the actual geometry, slope, and resis-tance coefficient were known well, but they are not. The lack ofexactness of the model should ideally be included by examin-ing the sensitivity of mathematical and computational results tovariations in the important unknowns. It could be shown wherefurther approximations could be made and simple deductionsmade. The simpler the model, the more useful it is likely tobe. Solving the Navier–Stokes equations numerically will nottell us what the resistance in a stream is or how a flood wavepropagates.

Any books on mathematical modelling emphasize that it is aniterative process – the model can be tested and refined, as manytimes as necessary. To try to help with that process, in differ-ent places where the author has worked, he has tried to organize“Ante-seminars”. That word was a pun on “anti” (against) and“ante” (before), namely, the presentation of what was not-a-proper-seminar and before the work was completed, just whena researcher most needs information and discussion with her/hisfellows. The seminars never really worked – people were tooproud to parade the unfinished state of their work, and the authorwas never assertive enough.

While numerical results in engineering are often important,understanding is also important, and that is what a model pro-vides. We note the comment of Birta and Arbez (2013, p. 37) ina book on modelling:

The reader is cautioned not to dismiss the issue with the simplis-tic and naive assertion that the goal is to solve the problem!

Often one finds, among students, that a ready capacity to plugin formulae and come up with numbers drives out the desire forunderstanding.

The author has just praised the virtues of modelling andapproximation, that “near enough is good enough”; however,he has a guilty secret, that often in his research he has erredin the other direction, for example, working on high-order peri-odic water wave theories to produce accurate results, even if theavailable design information and the physical situation mightbe only approximately modelled. The theories could solve anidealized problem accurately, so they have had a certain appealin the profession. They were satisfying to work on, also, and ifthe author’s botanist colleague had asked him the same questionas she did Wayne, he might also have said “Jane, it is exact!” Inproducing such results, the searching for accuracy did lead occa-sionally to extra discoveries. Also, in seeking perfection, therewas an innate Zen satisfaction.

In view of that, the author views research and modelling withsomething of a Janus-like approach. Janus was the Roman godof beginnings, gates, transitions, time, doorways, passages, andendings, who is usually personified as having two faces, as helooks to the future and to the past. He is often used to describesomething with two opposing aspects. It is interesting and usefulto be able to take two different approaches, for one enhances theother, and possibly reveals things that looking in one directionmight not have done: one can generalize, one can particularize;one can simplify, one can complicate.

2.6 Hydraulics and dimensional analysis – and anautobiography

In the 1980s at the University of New South Wales the authorattended a seminar by S. Irmay from the Technion in Haifa, whosaid:

All of the named numbers of fluid mechanics are either upsidedown, or raised to the wrong power, or both.

One thinks immediately of the Reynolds number, which isdimensionless viscosity ν/(UD) written upside down, where ν

is kinematic viscosity, U is mean velocity of flow, and D isa transverse dimension. Or, maybe a dimension parallel to theflow? Dimensional analysis can need help with physical insightwhen different length scales are involved.

In the spirit of Irmay again, one might think of the num-ber U/

√gh in open channel hydraulics, where g is gravitational

acceleration, and h is mean depth. It is usually called the Froudenumber, although Froude’s original number used a horizontallinear ship’s dimension for length scale. It is written as F, andis pronounced “Frood” (to rhyme with food), and not “Froud”,according to the delightful one-page article by Rouse (1965),whose own name, apparently paradoxically, was pronounced“Rous” and not “Roos”. As a dimensionless velocity or speed,Froude number is appropriate in this form, but as a dimension-less expression of the importance of gravity it is both upsidedown and raised to the wrong power. And as an expression ofthe importance of velocity in the equations of motion, whetherenergy or momentum, it is its square F2 which is important.

Journal of Hydraulic Research Vol. 54, No. 5 (2016) Hydraulics: science, knowledge, and culture 493

D

C

Assumed pressureActual pressure

Assumed crest velocityActual crest velocity

H2H/ 3

Figure 1 Sharp-crested weir showing dimensions and comparison ofphysical quantities, both actual and assumed in the classical derivation

2.6.1 Conventional sharp-crested weir theory

Some problems are much better solved by dimensional analy-sis than by a theory with very rough assumptions. Consider asharp-crested weir of infinite length in water of infinite depth asshown in Fig. 1. The head is H. The actual pressure distributionand actual crest velocity are shown by dashed lines. The tradi-tional theory uses the assumed pressure and crest velocity shownby dotted lines, with hydrostatic pressure and then horizontalvelocity given by Bernoulli’s law using that pressure. It can beseen that the assumptions have little to do with reality, espe-cially the horizontal component of velocity, which is integratedvertically to give the discharge per unit width q. It is actuallyzero at the crest, but in the theory is assumed equal to

√2gH .

After integrating the velocity contributions and assuming thewater surface above the crest is yD = 2

3 H , a numerical resultis obtained which has been found experimentally to be too high,so a coefficient of discharge Cd is introduced and the expressionwritten:

q = 23

Cd√

2gH 3/2 (8)

This is the expression which is traditionally used. The coeffi-cient of discharge in practice covers the fact that the underlyingassumptions are poor. Before applying dimensional analysis, theauthor interpolates here a personal note and autobiography.

2.6.2 An autobiographical diversion

At this stage of his life the author can confess that when he sawthe derivation of the sharp-crested weir formula at the age of18 at a technical college in rural Australia, it caused him tofall in love with hydraulics. He did not identify that some ofthe assumptions of the theory were very bad. He had grown upon a farm, went to the local primary school, with 6–12 pupils,then went to the high school in the nearby town, after whichhe went to Bendigo Technical College for the equivalent ofthe first two years of a bachelor’s degree, where he becameenamoured with hydraulics as described. He then completedthe degree plus a master’s degree at Melbourne University incivil engineering and then went to do a doctorate in applied

mathematics at Cambridge University. His minor specializa-tion throughout that period was participating in opposition tothe Australian government’s military actions in supporting theUSA in the Vietnam War (the “American War” in Vietnam).His master’s degree supervisor was I.C. O’Neill, who taughthim many things about hydraulics, classical (irrotational) hydro-dynamics, and the (new!) fast Fourier transform, and who gavehim his career. His PhD supervisor was M.J. Lighthill, who wassimilarly kind and inspirational. This author, to be frank, wassomething of a problem student who took longer than usual tofinish. One day student met supervisor in the corridor and con-gratulated him on becoming Sir James Lighthill. The new knightreplied, “But John, you don’t believe in that sort of thing.”Well, true, but his student liked and respected him and the com-ment had come from the heart. He was surprised that Lighthillknew about his egalitarian tendencies, until he remembered thathis hair and clothes were following the alternative style of thelate 1960s. One did not have to be the Lucasian professor ofmathematics to interpret such things.

The author returned to Melbourne University again manyyears later, after some time at Imperial College in Londonworking with R.A. Bagnold, amongst others, Atkins Researchand Development in south London, Monash University inMelbourne, the University of New South Wales in Sydney,Auckland University, and Monash University again. His formermaster’s degree supervisor then arranged an honorary positionfor him at Melbourne University. He, who had taught the authorso much, now many years later pointed out to him that dimen-sional analysis was much better for the weir problem. Let usnow follow his advice, but before we do, let us just mention thatthe author subsequently retired, and has enjoyed being a guestat the University of Karlsruhe and then the Vienna University ofTechnology.

2.6.3 The weir problem solved by dimensional analysis

Neglecting viscosity, the variables of the problem are q, Hand g. We have three variables and two physical dimensionsinvolved, and so by the Buckingham π theorem we have a singledimensionless quantity, which dimensional analysis gives:

π1

(q√gH 3

)= 0

where the π1(. . .) indicates a functional relationship, and so wecan write:

q√gH 3

= α = a constant (9)

The dimensional analysis has shown us very simply that q isproportional to

√gH 3/2 and it is rather more honest to repre-

sent the proportionality constant by a coefficient α with almostno physical assumptions, rather than from the very rough theoryleading to Eq. (8), giving the coefficient in the form 2

3

√2 × Cd.

Dimensional analysis has shown that the relationship must be

494 J.D. Fenton Journal of Hydraulic Research Vol. 54, No. 5 (2016)

as shown in Eq. (9), which explains the practical success ofthe conventional hydraulic approach – it simply had to comeup with such an expression.

Another memory of the former supervisor at that much latertime was when the author was loosely talking about Manning’sformula as “Manning’s law”. O’Neill corrected him, calmly andquietly saying: “I . . . don’t . . . think . . . it . . . is . . . a . . .

law”. Ouch. One could imagine him thinking he had failed 30years previously.

3 Different ways of thinking and doing in educationand practice

Here the great diversity required in hydraulics will beexplored through several different scales, or axes, of modesof thinking and doing, as we might refer to them. Theyare: numbers–understanding; thinking: convergent–divergent;creative–formulaic; and accuracy: approximate–precise. If wewere to think of them as being mutually-orthogonal, like(x, y, z), one not correlated with another, then we would beleft with hydraulics being in a 4-dimensional space. However,some of those are not independent of each other, so our spaceis more complicated. And, there may be others. At the end wewill consider some pathologies of knowledge processing thatcan limit us.

3.1 Numbers–understanding

This is a crucial point for learning and for practice. Often,numbers are given far too much importance, at the cost of under-standing and communication. This is where hydraulicians canstraddle both fields, whereas in structural engineering design,one might place greater importance on numbers. This, however,can have negative consequences too. The author once workedin a university where structural design was considered moreimportant than hydraulics, and one of the colleagues, by the endof the course, used to distribute a stack of lecture notes some15 cm high. That colleague came into the author’s office oneday in a state of distress:

I’ve just had a phone call from one of our former students: “Onwhich side of a retaining wall should the reinforcing be placed?”When I told him the answer, the reply was: “Oh! That’s why ithas collapsed.”

Fewer lecture notes might have helped him know to place thereinforcing on the tension side.

Unfortunately there seems to be something of a competitionbetween authors of textbooks, confusing quantity with quality.In a well-known book on fluid mechanics written by a mechani-cal engineer, in the chapter on hydrostatics, there are 7 problemswith an algebraic answer, 9 “word problems”, and 3 “designprojects”, each requiring some demonstration of understandingand knowledge. However there are 171 numerical problems! Ifthe author were a student, seeing that many numerical problems

with stationary fluids arranged in close association with variousplanes, circular arcs, spheres and tubes, 171 times, he wouldhave fallen out of love with his hydraulics.

Paradoxically, that book is actually very good at explainingthe field, and is the author’s favourite textbook for teaching thefluid mechanics part of hydraulics. He just does not use the tuto-rial problems. Rather, he prefers setting as problems, a few, withanswers like F = ρgAh̄ (hydraulicians will know what the termsmean!). This encourages students to think and to understand,and not to go automatically through a calculation. The algebraicanswer tells us much more than a solution with the answer, say,F = 1350 kN.

The process of examining students by testing their arith-metic is also often quite defective. Consider an examinationpaper, typical of many institutions, where formulae are printedat the front or back, there might be, but often not, some shortword questions trying to force demonstration of understand-ing which usually show little more than if the examinee hasabsorbed the lecture notes, and then a numerical calculation, forwhich the above answer F = 1350 kN might have been good,F = 1349.99 kN not so good, and F = 1273.37 kN requiring alot of work by the examiner to find out where the error wasmade and then to decide how to reward the partial success withmarks. All arbitrary and meaningless. Far better is the proce-dure in central Europe, where the lecturer sits in an interviewwith the student and asks questions to ascertain their level ofunderstanding.

The real role of the teaching processes is, even more than inthe context of the opening statement by Hamming (1973) in hisbook on numerical methods:

The Purpose of Computing is Insight, not Numbers.

One can substitute many alternatives for “Computing”; here wesuggest “Teaching”.

3.2 Thinking: convergent–divergent

Convergent thinking is where a single solution is sought. Oneobtains an answer to a problem without showing much imagi-nation but a great deal of concentration. Many engineers showthis characteristic. We are like that. On the other hand, diver-gent thinking is where personality traits such as openness andextraversion are associated and imaginative solutions sought.

If it is true that engineers are convergent thinkers, then howmight we be brought to think more divergently? An immediateanswer is for people to ask, and be asked, questions. Immedi-ately the perceptions of other people force themselves on ourconsciousness, possibly not welcome, but therein lies the suc-cess of the method. Asking questions stimulates debate, thoughtand alternative views. Many times in personal experience, thepresentation of one’s own work, or the forcing of a research stu-dent to present theirs, brings new ideas and ways of looking atit. Managers know this.

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Another way to develop divergent thinking is via lateralthinking. A number of stimuli for this have been given byEdward de Bono. In particular his concept of “po” might beeffective. First, a little linguistic diversion: the word has littleto do with the Maori word for night (with a long “o”), noth-ing to do with the great Italian river, and nothing to do with thecolloquial German word (with a short “o”) for the human but-tocks. A “po” of de Bono is an unconnected idea or statementwhich in direct association might help to generate ideas thatwould otherwise not be the case. The author has occasionallytried it with research students, to see if it helps them, usually bystarting with the word “purple” as a concept apparently uncon-nected with hydraulics or ocean waves. Success was mediocre,usually due to the student’s reluctance to have anything to dowith such a strange idea.

A more effective method is to use what we might facetiouslycall a “Po” approach, after Popper, which is to approach pre-vious research with a deliberately negative attitude, attemptingto falsify it: “What is wrong with this approach? There mustbe something wrong with it. There is something wrong witheverything”. Sometimes the author has found that it led to falsi-fication, sometimes it has led, if not to falsification, to discoveryof limitations, boundaries, problems with the work, or dishonestcomputational results.

3.3 Creative–formulaic

How might the education of engineers develop greater sensesof criticism and disbelief, rather than adherence to theories andmethods without question? People trained in science seem tohave such a capability, that nothing is entirely to be believed. Inthat sense, the Popperian approach has fallen on fertile ground.When it comes to engineering, however, things are different. Theauthor attended the 21st Congress of the IAHR in Melbourne in1985. At the conference dinner, the speaker was Dr J.R. Philip,an Australian mathematician and soil scientist. His words ofwarning cut through the conviviality to this author’s ears, andapparently lodged in his brain:

Whereas the cry of an engineer used to be “What’s the formulafor that?”, now it is “Have you got software for that?”

That was 31 years ago, and we have gone much further downthe path that he warned against.

Commercial hydraulic computer software has played a role inlimiting the knowledge, judgement and creativity of hydrauli-cians – because it can solve a number of problems. Thedominance in hydraulics of large software houses has broughtan industrial revolution to the field. Once, in every water officeand university hydraulics department everyone could under-stand and solve hydraulic problems, and extract the importantthings, the equivalent of craftsmen in a cottage industry suchas spinning and weaving. With the then industrial revolutionthey were turned into powerless operators of mechanical spin-ning machines and mechanical looms, and now the hydraulic

engineers have fallen victim to our more modern industrial rev-olution: they might be little more than software operators. Or,even more disparagingly in the words of a former Australianprime minister describing people working in the finance indus-try in front of monitors, as “screen jockeys”. Maybe we needmore people like the displaced French spinners and weaversthrowing their wooden clogs (“sabots”) into the new machines –and coining a new word “saboteur”.

Simple theories can also be used to provide numbers, use-ful numbers, and more quickly because of simplicity, as hasbeen shown above. Moreover, those numbers will be approxi-mate, and therefore possibly more useful. This is often forgottenin computing in river engineering. The equations that are usedmay be more-or-less accurate, but often the parameters, inputs,and the modelling of processes such as resistance, are poorlyknown at best. Accordingly, the results of computations maynot be very accurate, but will represent a solution whose accu-racy is in accordance with that of the problem that was posed.Too much importance is attached to the use of sophisticated –and expensive – software, when often a simple and conceptualmodel that reveals the real nature of the problem is adequate.

3.4 Accuracy: approximate–precise

A problem for all university teachers is the use by students of toomany significant figures in calculations. This can even be seen inpostgraduate dissertations and research papers. Often it is obvi-ous, for example, in a table of experimental results, 1.23456.The author used to deduct examination marks for such lack ofjudgement.

A not-so-obvious example where excessive accuracy hasbeen consistently shown is in the specification in many booksand papers of the value of gravitational acceleration as g =9.81 m s−2 . This might be a Canadian conspiracy, but it is morelikely to be a northern European one. The value g = 9.8 m s−2

is simple, concise and accurate, with an error of +0.2% at theequator and −0.06% at 45◦. It is actually more accurate than9.81 for all places with a latitude of less than 45◦, includingsouthern Europe, all of Africa, Turkey, Central Asia and all ofthe Middle East, India, almost all of China, Japan, almost allof the USA and South America, all of Australia, and most ofNew Zealand. That is, for most of the world’s population. Addi-tionally it is specified to just two digits so that it is correctlyrounded to this for all places on Earth. In fact, the author hasalways wanted to use g = 10 m s−2 for teaching purposes, withthat correct to 2%, quite reasonable for hydraulics formulae andwhich would provide some emphasis to students that what weare doing is approximate; however, it is more difficult to identifyerrors in students’ work.

3.5 Ignorance, and pathologies of knowledge processing

There are some pathologies of perception and thinking thathumans show, and these might have some relevance to this

496 J.D. Fenton Journal of Hydraulic Research Vol. 54, No. 5 (2016)

discussion of hydraulics knowledge. In particular, it may explainwhy people cling to paradigms much longer than they should,leading to the spasmodic progress of science as analysed byKuhn, described in section 2.3. One of these is the presence ofconfirmation bias, where we seek, process, and favour informa-tion and knowledge such that our existing prejudices, beliefs,and hypotheses are confirmed. It has been called “a systematicerror of inductive reasoning”. This explains the polarization ofattitudes and the retention of beliefs long after the evidence forthem has been shown to be false. It has also been described aswishful thinking, and our limited capacity to deal with informa-tion. Also, people might do it, because not to do it might costthem in some way. It leads to misplaced confidence in oneselfand a possible “bunker mentality”, when the more one seemsisolated and wrong, the more one might adhere to false beliefs.

There is often a deliberate underplaying of ignorance in uni-versity teaching. The less we actually know about a subject, theless we are likely to say that we do not know much. An exampleof this that the author can think of is the subject of resistance,especially in open channels. The important overall view is oftenneglected – that we usually do not know, and it might changein the next day anyway. It would be good to think that univer-sity lecturers would always point out what is not known, butoften that is not done. There have been suggestions that if sucha lecturer reveals the uncertainty and ignorance about a certaintopic, paradoxically it can lead to greater curiosity on the part ofstudents.

This could, however, also lead to another pathology, that ofcognitive dissonance, which is “the mental stress or discomfortexperienced by an individual who holds two or more contradic-tory beliefs, ideas, or values at the same time, performs an actionthat is contradictory to one or more beliefs, ideas, or values,or is confronted by new information that conflicts with existingbeliefs, ideas, or values”. One can imagine someone applying atheory or method that that person knows to be wrong. It is saidthat if a person experiences inconsistency, then they are likelyto try to reduce it by avoiding situations and information whichmight increase it, leading to a turning inwards and away, andsomehow valuing their state of ignorance.

3.6 Language

Another problem is the different languages we learnt as children.The active processing of words (writing) in a foreign languageis more difficult than passive processing (reading). This must bea problem for a number of readers of this journal, however goodtheir English is.

A departmental head of the German Federal WaterwaysEngineering and Research Institute (BAW), J. Stamm, openeda research presentation in 2006 with the words: “I will bedelivering my talk in the International Language of Science –broken English”. The author, who believes himself sympa-thetic to anybody forced to use another language, found thatvery funny – and of course, the presentation was not exactly

in broken English. However recently the author was bemusedto find, 10 years later, on that same institute’s website longafter Stamm’s departure, a site with “Leichte Sprache” (EasyLanguage), describing the institute in simplified German, withdifficult words emphasized and with a click, an explanation win-dow appeared. Not exactly “broken German”, but simplified!The former International Language of Science might be makinga welcome return by being flexible.

Is there anything that we could do to lessen dependence onEnglish and to make matters easier for people who may not useit at a high level? In a draft of this paper the author, with lit-tle personal experience, suggested allowing the use of machinetranslation and tolerance of less-than-perfect English in sub-missions. The editor, V.I. Nikora, with much more experience,disagreed and suggested that that was not the path to follow, as“ . . . in most cases it is just impossible to unambiguously under-stand the argumentation with such translation”, and made a pleafor high standards of English. An associate editor, J. Aberle,agreed emphatically. The author completely accepts theircorrection.

4 Hydraulics science – some difficulties

4.1 Orthodoxy and the persistence of ourdominant paradigms

The most successful cities, societies, and countries have beenthose that have been open to trade, people, change and ideas.Those winds of change have often caused some resentmentby settled and careful people, but they have always broughtbenefits. It is also those sciences which have been open, thathave been the most successful. One can think of physics andthe revolutions of the twentieth century which have broughtso many practical benefits. The practice of hydraulics, in theform of automatic measurement, monitoring, calibration andcomputer control is contemporary and innovatory. Those toolsare effective at what they do but they are placed on top of aconservative culture of conformity and resistance to change inthe science of hydraulics, where in the knowledge and cultureof hydraulics there is a reluctance to follow more scientificmethods. Examples already mentioned above include the useof the Gauckler–Manning formula for open channel flow; over-simplified expressions in hydrometry obtaining the integratedvelocity to give the discharge in a stream; or indeed the over-simplified and difficult use of the power law in rating curveapproximation causing the continued use of laborious manualmethods. A more fundamental one is the use of what is calledBernoulli’s law in textbooks, properly valid only along a stream-line, when what is effectively being used is simply conservationof energy, integrated across a pipe or channel, which is mucheasier to derive, and more fundamental. If a student were askedto consider Bernoulli’s law along a streamline in the turbu-lent flow between a reservoir surface and a kitchen tap, onecan imagine them beginning to lose faith in the teacher, and

Journal of Hydraulic Research Vol. 54, No. 5 (2016) Hydraulics: science, knowledge, and culture 497

especially if that teacher were to tell them that it is actually anintegrated momentum equation.

Unlike in many countries and societies where there has beenan imposed dominance of economic life and politics by an eliteclass, in hydraulics there is no compulsory or de facto compul-sory imposition by an elite on the science and on the professionof cultural and scientific norms. Rather, to quote William Blakein his poem “London”, it is our own “mind-forged manacles”that limit us. We place limitations on ourselves by our ownthought without imagination. How and why do we do that? Isthe problem within ourselves, or are there cultural, professionaland societal methods by which this is done? The answer is, ofcourse, both:

Mind-forged manacles. Considering the first problem, ourinnate resistance to change or experiment, one could talk atsome length about theories of psychological determinants as westarted to above. It is enough for us to consider how they appearand work out, and Kuhn (see section 2.3) provides a such asociological description rather than a psychological explanation.Much of his book, entitled The Structure of Scientific Revolu-tions is more to do with scientific non-revolutions, where peoplecling to paradigms for much longer than they ideally should, inwhatever field. Hydraulics is no exception.

Externally-applied limitations. The second way in whichlimitations are placed upon us is by the external workings ofour reward systems. Here, if one is practising as an hydraulicengineer, there are time pressures not to stray too far fromthe traditional path. On the other hand, if one is engaged inresearch, one might have thought that being innovative wouldbe very advantageous. Yet if one examines the products ofresearch, in the author’s opinion there are few radical or revolu-tionary contributions, and certainly not at the more accessiblesimple end of the simple/complex range. There, despite theease of understanding and the simplicity, is little that is new.Any advances are at the complex end, where complicated andnew experimental and computational methods are likely to befound.

The question is then, why is modern published hydraulicresearch all at the complex end of the spectrum? Part of thereason is the peer review system. It seems to have an inbuilttendency to being conservative and hegemonic. Below, this willbe examined at more length. In turn, reward systems such asresearch grants and promotion in universities, which dependon publishing and hence peer review, further the feedbackloop.

Another factor is what might be called the Mallory princi-ple, a powerful psychological reason which spurs researchers,exemplified by the famous response from the mountaineerG.L. Mallory when asked why he wanted to climb Mt Everest:“Because it is there”. The goal of obtaining difficult and accu-rate solutions has attracted many people often because of somespirit of personal achievement – and competition. Mallory didnot add what he was probably thinking at the time (the 1920s)“ . . . and to be the first to do it”.

4.2 Hierarchy and hegemony

The IAHR and this journal, the Journal of Hydraulic Research,seem to be truly internationalist and egalitarian in their idealsand practices, encouraging people from all round the world.It is not their fault that important aspects of “the system” ofhydraulics research are not internationalist and egalitarian, butfollow those of the economic and political world. Financialresources in the world are unevenly distributed, and so it iswith research funding. Rich countries have greater resources forthe funding of large well-equipped laboratories and for com-puter equipment, and so they can do Big Science. Whereas thatterm is usually applied to projects like the Large Hadron Col-lider under Geneva, we could well introduce another concept,of Big Hydraulics, which might consist of large laboratories,large wave tanks and models, large computers and large staffs.To obtain funding for such projects, not only must the moneybe available, but also a certain conformity of thinking, one thatdoes not rock the boat, but is acceptable to referees and politi-cians and to private companies, as such facilities are often partlydevoted to commercial investigations rather than real research.The projects are unlikely to come up with revolutionary or sim-ple ideas. All this leads to centralization and hegemony. Toquote the Christian Saint Matthew, who preceded Karl Marx andAntonio Gramsci:

Whoever has will be given more, and he will have an abundance.Whoever does not have, even what he has will be taken awayfrom him.

In a hierarchical system, it is no surprise that those who benefitfrom that tend to rather enjoy delineating hierarchy even further,and here one must single out the use of ranking tables for uni-versities, of which there is a notable British one and a Chineseone. The author has always enjoyed his academic colleagueswith their anarchy and iconoclasm (“managing university staffsis like herding cats”) and formerly, universities used to be runby people like that. Now, however, they are run by profes-sional managers who prefer hierarchy to anarchy, and attachimportance to those ranking tables. The author views them aspoisonous, and they do nothing positive for anybody other thanfeed the vanity of a few people. They infect attitudes, and ifsomeone works at University No. 71 in the rankings, they areviewed as automatically being better than someone who worksat University No. 96, in whatever department they are. The real-ity is, of course, that there are good people everywhere. Theyapplied for and got their jobs when a position there and thenwas available, and not at another institution in another year.Such an accident of history, or an accident by an appointmentscommittee, does not make someone better than somebody else.

4.3 Publish or perish

The current author, along with many others, has long been crit-ical of the procedures and practices associated with promotionand evaluation of research in universities, peer reviewing and

498 J.D. Fenton Journal of Hydraulic Research Vol. 54, No. 5 (2016)

publishing in journals operated by companies for a profit. Onecan find such criticism in many places, but Colquhoun (2011)provides a good example. He is bitterly critical of the peoplewho have imposed a publish-or-perish culture, namely researchfunders and senior people in universities. University publicrelations departments encourage exaggerated claims, and hard-pressed authors go along with them. The only people whobenefit from the intense pressure to publish are those in the pub-lishing industry. Colquhoun goes on: “There is an alternative:publish your paper yourself on the web and open the com-ments. This sort of post-publication review would reduce costsenormously, and the results would be open for anyone to readwithout paying. It would also destroy the hegemony of half adozen high-status journals . . . I suspect this sort of system hasto come and there are things that could be done to ameliorate theproblems. First, it would be essential to allow anonymous com-ments. Most reviewers are anonymous at present, so why notonline? Second, the vast flood of papers that make the presentsystem impossible should be stemmed. I’d suggest scientistsshould limit themselves to an average of two original papers ayear. They should also be limited to holding one research grantat a time. It’s well known that small research groups give bettervalue than big ones, so that should be the rule.”

Universities around the world seem to have been capturedby interests that are not intellectual but managerial, and a cer-tain commodity fetishism prevails, where quantity of anythingis important – salaries, numbers of students, money earnedexternally, and research grants. This seems to extend also tothe over-valuing of the quantity of research money brought in,rather than quality of research.

4.4 Peer reviewing

There is much dissatisfaction with the peer-review process. Forexample, Tipler (2003) recounted at length evidence that thepeer review process is severely flawed and that it is no guaran-tee of quality at all. He gave several examples, including quotingthe inventor of chaos theory, M.J. Feigenbaum, who describedthe reception that his revolutionary papers received:

Papers on established subjects are immediately accepted. Everynovel paper of mine, without exception, has been rejected by therefereeing process. The reader can easily gather that I regard thisentire process as a false guardian and wastefully dishonest.

Unfortunately the experience of the present author with peerreviewing is much the same. Anonymous reviewing seems tobring out some of the worst in us human beings. As one wouldnot want selfish and greedy people controlling an economicsystem, one would not want people, some of whom might becompetitors, who might allow unpleasant passions and emo-tions and a possible lack of competence to determine the fateof research work. Over a period of some 20 years working inopen channel hydraulics, submitting some 12 papers to the mainhydraulics journals of two learned societies, the present authorhas had one paper and one discussion published in them. One

reviewer tried to stop him publishing anything for 10 years.Other reviewers were not as unfair, but were incompetent andunwilling to approve anything. The silliest referee commentreceived by this author was about a paper where he had derivedthe long wave equations for waterways curved in plan (not allrivers are straight!). The referee in question (triumphantly – itwas the only comment in the review, and they were pleased thatthey thought of something to say!) observed that the author hadnot allowed for the separation of flow around bends. He/she pre-sumably believed that the usual straight-channel approximationdoes allow for the separation of flow around bends! The editoraccepted the comment and rejected the paper.

With this sort of experience, the present author for decadeshas published mostly in the form of book chapters (few, but withhigher levels of reviewing and a greater sense of sympathy forthe author), conference proceedings (reviewed lightly and withless determination to reject), and on his own website (with noreviewing at all!). Particularly in the latter case, the author con-sidered that it was important to get the material into print and tolet the world review it, according to principles of the free mar-ket. He cannot understand why some people denigrate researchthat has not been peer reviewed when peer reviewing can be sobadly and unfairly done.

At this point it should be noted that the present editor andan associate editor of the Journal of Hydraulic Research, withrather more experience than this author, both disagree, and theymaintain that peer review is highly necessary to guard againstinferior work being submitted.

The author maintains his stand, however, as he has seen somevery bad work published that did survive the peer review pro-cess. He has long maintained the cynical view that the quality ofa paper is proportional to the difficulty in getting it published.

As peer reviewing depends on the people chosen by edi-tors and associate editors, it also depends on those editors andassociate editors. While some associate editors and editors havenot taken their honorary “jobs” (maybe therein lies the prob-lem) seriously enough and showed laziness, gullibility and littleimagination in interpreting reviews, there are those who havetaken their responsibilities seriously, and have been very good,which will be acknowledged in the next section.

To counterbalance the bitter comments of the author (whohas not been an associate editor or editor), here we should con-sider the view from the other side, from the associate editor,J. Aberle, who reviewed this paper:

. . . before working as an Associate Editor I probably wouldhave been supportive. However, my experiences now tell methat some researchers (thankfully not all!) are too convincedby themselves and if one dares criticising them (also in a verymoderate way) one is sometimes accused of being ignorant etc.

One can just imagine the abuse from authors that the gentle“etc.” at the end represented.

Here, however, attention must be drawn to the importantpaper already cited near the beginning of this paper. Koutsoyian-nis et al. (2016), eight editors of hydrology journals, made a

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number of criticisms of the peer review process as well as otheraspects of the process of publishing, plus suggestions to improvethe process of peer review. Making such suggestions mighthave the same problems as any system of rules, guidelines, orCommandments for people to behave morally and reasonably:they can and often are ignored. However, the recognition of theproblem is important and a good start.

5 Hydraulics science – some solutions

5.1 The importance of a journal editor and associate editors

When the author was doing his doctoral research, in about 1970,he heard G.K. Batchelor, the head of department and founderand editor of the Journal of Fluid Mechanics for 40 years, say“no piece of research is complete until it has appeared in print”.This meant that the writing-up process is important, provid-ing discipline and time for thought and reflection, but also thepeer review process is important, providing feedback, criticismsand suggestions and maybe corrections, and that the process ofeditorship was most important, where a scholar in the field col-lates the contributions of the referees and the possibly-outragedauthors and reconciles and negotiates with both sides, hopefullycoming to a Solomonic decision.

It seems, to this author, that the quality of peer reviewing, solamented above, depends almost completely on the journal edi-tor. It is he/she who chooses associate editors and referees, it ishe/she who reads the subsequent reviews, or reads the associateeditor’s report, or doesn’t read either, and writes their report,accepting or rejecting or requiring resubmission. The editor ispivotal. To do her/his (or hers and his, in one contemporarycase) tasks properly is a huge commitment to the science andthe journal. One has the example of G.K. Batchelor and otherscurrently who have taken and are taking their onerous task seri-ously, and raised the level and quality of science through theirefforts.

5.2 Making hydraulics science and research more open

What can we do to make research more open, both to those whodo it and to those who use it? We have the technological solutionat our fingertips – the World Wide Web, to which many peoplein the world have access, even in a world where most resourcesare unequally distributed. At the moment we are not using theresources that are available to us in the form of the Web as wellas we might, and there is a lack of serious venues for criticaldebate.

5.2.1 Conferences

Conferences, despite the best intentions of the IAHR, are expen-sive, prohibitively so for many people, again leading to thehegemony of the wealthy. It would seem to be a very goodsolution to consider some form of electronic conferencing. Thetechnology must be rapidly changing: a number of solutions and

technologies can be found by searching on the Web using termssuch as “electronic conferencing”, “web conferencing”, “webseminars”, “webinars”, “webcasts”, etc. There would seem tobe many benefits here for many people and organizations aroundthe world. And the earth’s atmosphere.

A simple immediate partial solution would be to makethe proceedings of IAHR Congresses freely available. How-ever currently they too are expensive. For example, five yearsafter the conference, the Proceedings of the 34th IAHR WorldCongress in Brisbane in 2011 are on sale for e160. Simi-larly, e250 for the 35th Congress in Chengdu in 2013, ande100 for the 36th Congress in The Hague in 2015. To manypeople such prices are out of the question. The benefit ofhaving those results available to the whole community must out-weigh the cost of foregoing sales of what is probably a smallnumber.

5.2.2 Open Access publication of research

There are a number of ways of making access to research resultsmore open. It has been said that compared with the film andmusic industries, with many illegal sharing websites, academiahas been slow to take advantage of the internet to covertlyshare publications. There are, apparently, sharing platforms withmany documents online for free; however, these are still mostlyunknown. More legally, in May 2016, the European Commis-sioner for Research and Innovation has ordered that by 2020 allresults of research supported by public and public-private fundsbe freely available to and reusable by anyone.

There is an Open Access movement which aims to makeacademic papers freely accessible on the internet, to download,share, rework and process the data with the user’s own software.Many researchers are sympathetic in principle but remain sus-picious of innovation, particularly since the academic rewardsystem is dependent on measures that count publications inestablished journals.

Generally speaking we might abandon the process of peerreview, and rely on the Free Market of Ideas. Some possible spe-cific innovations that could be considered by the IAHR and thehydraulics community include the following. They are generallyranked in decreasing order of openness of access:

• A possible model is the electronic journal of the EuropeanGeosciences Union, Hydrology and Earth System Sciences.This is “an international two-stage open-access journal”,where an editor considers the basic suitability, and if acceptedit is first published on the Web in a discussion version ofthe journal, when it is open for public discussion and ref-erees’ reviews and for authors’ responses. Then the editoreither accepts the manuscript, possibly with revisions, or not.In any case, all versions and discussions remain available tothe public. There are article processing charges of e75 perpage if submitted in LATEX, ande90 if submitted in MS Word,plus German taxes of 19% (paying for two pages would cost

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more than some of the IAHR Congress proceedings men-tioned above!). The pricing structure means that it is not reallyopen access. The author has a slight concern, given his earlierscepticism about too much publishing in hydrology, that thisjournal might encourage it – from those with money.

• The existing IAHR Rivers-list is a moderated community sitefor rivers, as a means of circulating information among riverspecialists about jobs, discussions on specific research prob-lems, announcements of courses, etc. All submissions must bepre-approved before they are posted by the person in charge.Recently, however, there has been little appearing to do withresearch itself. This could be expanded.

• Relatively small contributions, such as recipes, formulae, use-ful tips, or practical results, perhaps less than one or two pageseach, could be published in a journal or on a website. Thesepublications would be open to discussion and might have agreater degree of moderation.

• Some form of free-access moderated discussion could beimplemented, as in modern online newspapers, where anyonecan submit, but a moderator checks to guard against abuse,and removes if necessary. Often sites such as those for LATEXor C and C++ programming have such an arrangement. Theyseem to function well.

• An alternative is an open repository of electronic preprints,known as e-prints, such as arXiv (http://arxiv.org/), inphysics, mathematics, computer science, quantitative biology,quantitative finance and statistics. In fact, physics includes asection on fluid dynamics. The site can be accessed online,whether to upload or download. On that site, almost allthe papers are self-archived, usually for review before theyare published in peer-reviewed journals. Physics and mathe-matics journals routinely accept manuscripts that have beenposted to such preprint servers. Although arXiv is not peerreviewed, a collection of moderators for each area reviewthe submissions. A majority of the e-prints are also sub-mitted to journals for publication (some journals downloadsubmissions directly from arXiv), but some work, includingsome very influential papers, remain purely as e-prints andare never published in a peer-reviewed journal.

5.3 Making hydraulics science and practice more open

In view of those suggestions, the next question that might beasked is: where can one get help with a better/simpler/modernmethod in daily practice? The answer is actually very difficult togive. Most hydraulics or open-channel textbooks are really verysimilar and often just repeat each other. A mechanical engineerfriend of the author’s tells the story of visiting a well-knownwriter of fluid mechanics books (whose name has fortunatelybeen forgotten), where in his office he had a long desk with fivefluid mechanics books side-by-side, held open by a long woodenrod extending the length of the desk, while he, on a chair withwheels, moved along the desk, assimilating the work of each forhis own next book.

5.3.1 Open access repository of knowledge

Research results are usually too complicated or expensive orare difficult to find, especially if they are published in journalswithout open access, even in this era of the Web. The researchthat is published in journals advances the science of hydraulics.It is specialized and advanced, and because of that it is nowrather difficult to read many articles. That is not the fault of thejournal, as it is not its task to ensure that all readers can under-stand everything. A more general question is for practitioners:how should hydraulic knowledge be applied beyond that whichwe learnt in university or college? How can our knowledge beupdated, going from the known to the unknown? To solve theproblem of updating knowledge, the author recommends a web-site such as that suggested above for research – in the form ofa free-access moderated repository with discussions, again asin modern online newspapers, possibly containing material of atextbook or lecture note nature, or methods and approaches ofinterest. The free market of students and practitioners might bevery grateful.

5.3.2 Some suggestions for individual hydraulicians

Part of the problem of hydraulics is ourselves – there is notmuch of a culture of questioning. We all have a tendency toreject things beyond our comfort zone. What advice might theauthor give to his younger colleagues about the generation anduse of hydraulics science and knowledge? At the risk of sound-ing pompous and self-righteous and possibly trivial, he suggeststhe following:

• Believe nothing that you were taught or that you read. Con-sider that anything might be wrong. Remember Popperiandisproof.

• Is there a more scientific way of doing it based on rationalmechanics?

• Is there a better and maybe simpler way of doing it?• Is there a more modern way of doing it?• Do you understand what you are doing?• What does it mean physically?• Can you explain it to colleagues?• Make your own approximation, maybe a series with one or

two terms.• How well do you know the input parameters – if not well, is

it worth pursuing a complicated method?• Remember that “Small is Beautiful”.• And, if you were publishing a new idea, remember that what

was once derided and scorned might later be accepted as com-mon knowledge, which is how the author thinks as the concisemessage of Kuhn’s ideas. You might, however, say that youdo not have that long to wait!

• If one were tempted to publish quickly and lightly, rememberthe advice of P.B. Medawar:

Any scientist of any age who wants to make important dis-coveries must study important problems. Dull or pifflingproblems yield dull or piffling answers. It is not enough that

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a problem should be “interesting” – The problem must besuch that it matters what the answer is – whether to sciencegenerally or to mankind.

The present author in about 1973 in London saw Medawargive a lecture in which he used that quotation, which, at leastthe italicized part, again, lodged in the author’s brain. Until hefound it on the Web when writing this, the author had remem-bered it as “Dull or piffling problems yield dull or pifflingpapers”, and he had usually tried to avoid that mistake. Pub-lishing cheaply gives cheap publications.A concrete example of that, viewed from a different angle,is the story recounted by a former young and ambitious col-league of the author. He was visiting and being entertained inthe faculty club at the California Institute of Technology:

Young visitor: “How many research papers are necessary tobecome a full professor at Caltech?”Full professor at Caltech: “One.”

6 Conclusions

A number of assertions, recommendations, and conclusionshave been made. Greater use of scientific methods and think-ing has been recommended, rather than those of traditionalempiricism. Using rational methods makes testing, examinationand extension to other research easier. A greater recognitionis desirable that we are usually modelling problems approxi-mately. This is where some of the charms of our special subjectlie. Accordingly there should be a greater sense of criticismand questioning, and disproof if necessary, as well as a greaterreadiness for changing paradigms. In this way, it is hoped thathydraulic research might be rejuvenated, particularly at the sim-pler end, by making entry and participation easier. To help withthis it is necessary for people working in hydraulics to haveaccess to recent research and practical developments and toshare in them. The technology, in the form of the Web, is inplace. The will to change is also now in place, to bring aboutopen access to research results and hopefully to a greater inter-activeness in the culture. Because of the relatively inexpensivenature of Web access to research and conferences, we standat an almost historic moment to bring about real changes anda democratization and internationalization of our field. Insti-tutional steps should be taken to bring about accessibility byelectronic means, so that all hydraulicians in the world canshare.

Acknowledgements

The author thanks the Editor, V.I. Nikora and Associate Edi-tor, J. Aberle, for much inspiration and intellectual and practicalassistance.

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