From the «Architecture hydraulique»to the «Science des ingénieurs»: Hydrostatics

and Hydrodynamics in the XIXth century

L' ARCHITECTURE HYDRAULlQUE: THE FIRSTSTUDIES ON RUNNING WATER AND THE FOUNDATION

OF HYDRAULlCS

Hydraulics, notwithstanding its ancient ongms, isvery young as a discipline. lt has been founding and

consolidating its scientific bases on Iy for the last threecenturies as pure science, like mechanics, and itsapplication to engineering. The «discovery» of basicprincipIes, the fundamentals of hydraulic science,

required many efforts throughout the 17th and \8thcentury.

The first phase of deve10pment is the great seasonof experimental hydraulics during the Renaissance,especially in Italy, thanks to the contributionof Leonardo da Vinci (1452-1519), GirolamoCardano (1501-1576), Giovan Battista Benedetti(1530-1590), Bernardino Baldi (1553-1617) and

others. Only with the school of Galileo Galilei and hispupils, like Evangelista Torricelli (1608-1647) and

Benedetto Castelli (1577- 1643), with his treatiseDelta misura delte acque correnti COn measuringrunning water') published in 1628, the road to thegreat treatises on hydraulics of the 17th and 18th

centuries was opened. In this field of studies

the treatise of Carlo Fontana (1634-1714) «Onmeasuring running water» (Fontana 1696) played agreat importance role.

In 1644 Torricel!i, an Italian scientist, published inFlorence De motu Aquarum (Torricelli 1644). In this

book, he set the !aw bearing his name: the first public

Massimo Corradi

announcement of his water efflux principIe. This lawstated that the velocity of water efflux from an orificein the bottom of a tank is proportional to the square ofheight from the surface of the water to the bottom of

the tank. In other words, this velocity is equal to«liquids (velocity) which issue with violence have at

the point of issue the same velocity which any heavybody, or any drop of the same liquid, it were to fal!

from the upper surface ofthe liquid to the orifice from

which it issues» (Rouse and Ince 1963, 62). It iscommonly written as v = V2ih. This law wil! bethourougly explained, with the utmost accuracy, by

Daniel Bernoul!i (1700-1782), in the first half of the18th century, by means of differential and integral

calculus.In the 17th century the studies on hydraulics were

no longer limited to ltaly but they spread al! overEurope thanks to the work of Simon Stevin(1548-1620), Edmé Mariotte (1620-1684) -who is

considered the father of the experimental method-Marin Mersenne (\588-1648), Blaise Pascal(1623-1662) -who was the most important scientist

of the century in hydraulic science- and also IsaacNewton (1642-1727) with his studies on fluidmechanics and, on a more experimentallevel, PierreVarignon (1654-1722) on motion and the

measurement of running water.

Mariotte's treatise on running waters and fluidbodies (Mariotte 1686) -published two years afterhis death- led the research on fluid and liquid

properties, on the equilibrium of heavy fluid bodies,

Proceedings of the First International Congress on Construction History, Madrid, 20th-24th January 2003, ed. S. Huerta, Madrid: I. Juan de Herrera, SEdHC, ETSAM, A. E. Benvenuto, COAM, F. Dragados, 2003.

636

UTILlSSIMO TRA TT:\ TO,

D f. L 1.'

ACQUE CORREN TID!V!~O 1:-: rRE LlliRL

H ,\!. c.\y

.\ t t r 11.

e A R L o F o N T A N A.r o

ALLA SA<;RA. E ¡lEAL ~!AEST.\'

DI GIUSEPPE IGNAZIOD A l! S T R 1 A

R!'. J) R o ~I A X l. ~o.

t;-..,,-,,\\j\.

--Figure 1Caria Fontana: Trattato dell'acque correnti (1696)

even compressible, on the measurement of runningwater, on the trajectory of ]iquid particIes, on water' s

distribution and finally on the resistance of waterpipes under water pressure. Mariotte started fram

Torricelli' s eff]ux principIe and he verified histheories in several experiments by means ofingenious mechanism.

Concurrent]y, in Ita]y, Domenico Guglielmini

(1655-] 710), and considered the founder of ]talian

school of hydraulics, published very importanttreatises on hydrau]ics, the measurement of runningwater (Gug]ielmini ]690), and the motion of waterrivers (Gug]ie]mini ] 697). In this ]ast field,Gug]ielmini takes again specu]ative ideas from

Castelli and TorriceIli, and somehow he established

the basics of fluvial hydrau]ics. Guglielmini was thefirst scientist who showed the existence of a uniform

M. Corradi

state of equilibrium between running water onincIined p]ane (which increases his velocity) and the

riverbed' s active resistance.In the midd]e of 17th century Blaise Pasea]

(1632-1662) was the most important scientist inhydraulic sciences, particu]arIy hydrostatics. His

treatise on the equilibrium of liquids, pub]ishedposthumous]y in 1663, extends Stevin's ana]ysis and

experiments. The most notable theory in his book is

the concept of constant hydrastatic pressure at thesame water depth. In a fluid the hydrastatic pressureis the same in all directions which are starting framthe centre of water particIe. This importantcontribution of Pasea] bridges dynamics of rigidbodies and fIuid dynamics.

Moreover, we remember Newton's fundamenta]contributions on bodies immersed in fIuids or liquidsa

From the «Architecture hydraulique» to the «Science des ingénieurs» 637

A

[!]J L

: :;,.oJ'-:":'" F(;

[jlJr~n.. \~.::::. . ::;;::D J~l :..)1

G Hh'JZ

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r

A

B C'

A

J4.:::::::~~:.:~::.

':::::::f""::::'.

Figure 2From Mariotte's treatise (1686)

and his studies on water jets, wave-motion,viscosity' s coefficients, About viscosity Newtonestablished that tangential stresses in a viscous fluidare proportional to the relative velocity of fluid inadjacent parts. In an endJess cylinder rotating on itsown axis with constant angular velocity, fluidsvelocity changes in inverse proprotion to the radial

distance measured from the axis. Thus, Newtonrejected Descartes' theory on vortex.

In 1725 the treatise of Pierre Varignon on watermotion and running water measurement waspublished posthumous. From this point of view, this

treatise focused on the mechanistic aspects of theproblem rather than to the fluids behaviour. Varignonanalysed the Torricelli's problem: the discharge of aliquid from an orifice. But, as Newton, he obtained

the same wrong result about the coefficient which is

a velocity multiplier of liquid' s eft1ux.

M.

[tJ

p

¡,

--<T

A few years later, in 1743, Johann Bernoulli(1667-1748) published a treatise entitled Nouvellehydraulique. In this work Bernoulli indicated hispoint of view of Newton's theory about the shape of

a stream of water discharged from a cataract. In thissubject Bernoulli caJled attention to the error in

Newton cataract theory, as this hypotheses required azero pressure -which was physically impossible-throughout the zone of contact between the cataract

and the stagnant water around it.We have to remember though that for the whole of

the 16th, and part of the 17th century as we]],hydraulics has been confined to the empiricalsciences. It was only with the coming of differentialand integral calculus, in the 17th century, that theprincipIes of the motion of fluids were established

and hydraulics raised to the same level of the other

mechanical sciences.

II~

:l- 1 LL

G- .JCI

A. H B!7lr. ;7.

638

«

.~

Figure 3Velocity distribution around a rotating cylinder by Newton

M. Corradi

A..

author gives a simple explanation of the probJems

related to the static balance of fluids, efflux velocity,liquids oscilJation, energy saving principIe or energyloss, hydraulics machine, air motion, fluids motion

etc. This compendium of Bernoulli studies showedBernoulli concern with theoretical principIes andapplication of the progress in hydraulics, andparticularly in hydrostatics and hydrodynamicsaspects. Por example, we remember that Bernoulli

was the first scientist to use the piezometer tocalculate the water pipes pressure. This work is acornerstones of modern hydraulics, in that it is thedefinition of the fundamental relationship betweenthe speed of an element in a liquid mass and itsrelative loado In this important work Daniel Bernoullidefined the basis of modern hydraulics.

What is significant is the demonstration of histheorem, based on the energetic principIes by

Christiaan Huygens (1629-1695) and GottfriedWilhelm Leibniz (1646-1716), which establishes thatin a perfect liquid, in stationery motion, the sum ofposition, pressure and kinetic energy of each particle

is constant during the whole trajectory, whichconfirms the principIe of energy conservation.

R.

e E G F 1)

Figure 4Newton' s original concept of orifice discharge

2. THE BEGINNING m' THEORETlC HYDRODYNAMICS

The beginning of theoretic hydrodynamics dates backto 1738, Daniel Bernoulli published the treatise onhydrodynamics (see: Hydrodynamica, 1738). The

Figure 5Water eftlux from an orifice by BernoulJi

From the «Architecture hydraulique» to the "Science des ingénieurs» 639

9i.1'.7.3'A

e

J.

i'~J ,

Figure6The first idea of the piezometer by Daniel Bernoulli

In formula: S + P- +2

V2= consto (Bernoulli'sy g

Theorem), where S is the height 01' generic waterparticle on his trajectory; p is the liquid pressure; y isthe specific weight 01' liquid; Vis the water velocity;g is the acceleration due to gravity

Bernoulli's work opened up the road to importantdevelopments in hydraulics by scientist like Jean-Baptiste Le Rond d'Alembert (1717-1783), with hisstudies on hydrodynamics and tluid mechanics,Leonhard Euler (1707-1783), Pierre-Simon, Marquisde Laplace (1749-1827), Alexis-Claude Clairaut(1713-]765) and many others.

During few years numerous treatise had beenpublished and this scientific literature granted to thisdiscipline the role 01' mechanics science instead 01'empirical arto For this reason we make a concisecompendium 01' most significant researches.

In ] 744 d' Alembert published his Traité de

l' equilihre et du mouvement des fluides onhydrodynamics and fluid mechanics. In the opinion 01'

this French scientist hydrodynamics (and thenhydraulics) must be founded on experimentalobservations; converse]y, solid mechanics can befounded on the basis 01' metaphysical principies. Theproblem related to the fluid motion and t1uid

resistance were complex; they can be misinterpretedby the Philosophes a notions incomplettes -as statedby Leibniz-, but also the scientists with a propensity

to give a philosophical halo with metaphysical

peculiarity to mechanics principies used in thisparticular field. The problem -certainly acomp]icated one- dated back to the problem 01'

conservation of live forces which Daniel Bemoulli

assumed as principie although d' Alembert deduced itby his «principie».

Three years later, in 1747, the Berlin Academy seta prize competition on this topic and the winner was

d' Alembert with his essay Réflexions sur la causegénérale des vents. This results was stronglycriticised by Daniel Bernoulli: he named the winner a«good mathematician» but a «very poor physicist». In

fact, the prize was assigned with merit: the

d'Alembert's work doesn't solve thourougly themathematical problem, but in this work was showedimportant results introducing aerodynamics studies.AIso in 1750 the Berlin Academy promoted anotherprize competition more related to the subject ofhydrodynamics and the theory of t1uid resistance, but

no memoirs was deserved the prize.In 1752 d' Alembert published in Paris his

fundamental work Essai d'une nouvelle théorie de

la résistance des fluides where he introduced hishydrodynamics «parado x» (or «d' Alembert'sparadox»). This paradox stated that a body moving in

a perfect t1uid or if it is possible to state a relatedmotion between fluid and body, the resultant 01' thewhole t1uid pressure acting on body is equal to zero.This result, in conflict with experience, depends onthe hypotheses 01' a fluid without adhesion andviscosity and that the body is acting through an ideal

homogeneous weightless fluidoThe next step was the publication 01' Euler's

Principia (Principia motus jluidorum) in 1755; thiswork is the benchmark for al! scientists of tluidmechanics and hydrodynamics. In this fundamentalbook Euler defines his equation of continuity for afluido This equation translates in mathematical formthe physical principIe 01'mas s conservation, by usingpotential functions for an incompressible fluido Byusing this equation it is possible obtain the equation

describing the motion 01' a fluid, even if -as Eulerhimself remarked- «it still impossible to have acomplete knowledge 01' t1uid motion not forinadequacy of principIes, but for lack 01' instruments

in mathematical analysis » (Euler 1755).There is a great difficulty: it is the mathematical

integration 01' differential equations to partial

derivative which describes the motion of generic

640

fluid, as later remarked by Joseph-Louis Lagrange(1736-1813) in his Méchanique analytique(Lagrange 1788, 436]. Finally, it is important to

remember Laplace' contribution. Pierre SimonLaplace (1749-1827) introduced his Laplacianoperator -in his Mécanique céleste published in five

vo1umes starting from 1799 to 1825- to studyproblems related to hydrodynamics. His studies on

wave-motion and tides, in addition to those oncapillarity, are very important to develop

hydrodynamics. Considering applicatory point ofview, Franz Joseph von Gerstner (1756-1832)

increased these studies. He also studied hydraulicmachines, dams, water motion in channels and wave-motion [Gerstner, 1788].

To synthetize: the indefinite equations ofequilibrium in a generic fluid are: kF = grad(p),

where F is the vector force referred to the mass unit,

k is the liquid density, p the specific pressure relatedto area unit. If the liquid is incompressible, then it ispossible write that p = f(k). The equations of fluid

motion, obtained from d' Alembert' principie, are:

( dv ) ak .k F -ctt =grad(p),p =f(k),

a/+ dlv(kv) = O.The

last equation is named continuity equation, and it

assumes the next form~~

+ k div(v) =O where vis the

velocity of a single fluid particle P where the vectorforce is applied F, p and are respectively the pressureand density in the same point at the time t.

To establish kinetic state oí' a fluid, or the velocityassumed by fluid particles when through adeterminated fixed point in the fluid mass, it is

.bl

.h

dv av (dV ) Th.

pOSSI e to wnte t at: dt =a¡ +dP

v. en IS

av (dV ) grad(p).easy to have that at +

dPv = F -

k. Thls

equation shows the absolute form of Euler' equation(Marcolongo 1904).

3. ApPLIED HYDRAULlCS

The 18th and the 19th centuries were also thecenturies of experimental hydraulics. Experimentersplayed a crucial role in the development of appliedhydraulics. The aim of this essay is follow the same

route that leaded from theoretical hydrostatics andhydrodynamics to applied hydraulics during the 19th

M. Corradi

century. In ltaly and France scientists of hydraulicsopened up the road to the application of the Science

de Ingénieurs. in France we remember the importantcontributions of Bernard Forest de Belidor(1697 -1761), Gaspard-Fran¡;ois-Clair- Marie Le

Riche de Prony (1755-1839), Antoine Chézy(1718-1798), Pierre-Simon Girard (1765-1836),

Jean-Charles Borda (1733-1799), Pierre LouisGeorges Du Buat (1734-1809), and others.

In Italy we remember Giovanni Poleni(1683-1781), Francesco Maria De Regi (1720-1794)

and Father Barnabite Paolo Frisi (1728-1784).Giovanni Poleni -may be best remembered well forhis studies about the reinforcement oí' St. Peter' sDome in Rome (Benvenuto 1991)- studied so meproblems related to water efflux from an orifice and

then he stated the weir laws (Poleni 1717), De Regifocused on the measurement oí' running water (DeRegi 1764), while the Barnabite Frisi devoted his life

to study river hydraulics (Frisi, 1770; Frisi 1777).

Figure 7Poleni: De Motu Aquae Mixto (1717)

From the «Architecture hydraulique» to the «5Óence des ingénieurs» 641

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Figure 8Belictor: L 'Architecture Hydraulique (1737-39)

As the Ita]ian Schoo] of experimenta] hydrau]icswe remember a great number of scientists and amongthem we mention Ottaviano Cametti (1711-] 789)(Cametti ]777) and Nicco]o Carletti (II ha]f of 17th)

(Carletti ]780)< In this scientific context, it' s veryimportant to remember the researches of JacopoRiccati (1676-1754) on the prablem «to determinethe force caused by tluid bodies crashing into solidbodies» (Riccati 1742) or, also, his studies «on the]aws of tluid resistance to delay the motion of so]id

bodies» (Riccati ]722)< The Guglielmini' s works andhis «Epistola hydrostatica» (Guglie]mini ] 731)written by Domenico Guglie]mini (1655-1710) in173] ha ve to be remembered. And we also remind

Anton-Maria Lorgna (1735-1796) and his researcheson running waters (Lorgna ]777), Antonio Rocchi(1724-1780) and his studies on measurement of

bodies velocity and strength in motion and hisapplication to hydrostatic prob]ems (Rocchi 1775),Gregorio Fontana (1735-1805) and his dissertationupon hydrodynamics, on the motion of a body in a

resistant medium, on the waterproof of channels(Fontana 1802), on the water pressure in motion intovessels, tubes and pipes, on the effect of centrifuge

force on tluid motion (Fontana] 803), and the maturestudies carried out by Louis Lagrange at the earlyeighties of 18th century (Lagrange 1781; Lagrange]781-85). Finally, we have to mention the translationof Hydrodynamics treatise of abbé Charles Bossut(1730-]814) by Gregorio Fontana (Fontana 1785) in]785.

In France, after the important studies begun byMariotte and le Chevalier Samuel Morland(1625-1695) (Mor]and 1685), we remember the

scientific work of C]aude Antoine Couplet(1642-] 722) on the resistance of pipes subject to

great pressure, and then the very editorial effort of

Bernard Forest de Belidor (1693-] 761), whopublished an important encyclopaedic treatise on

Architecture hydraulique (2 volumes in 4 tomes)where he thouroughly investigate on subjects relatedto hydraulic engineering and construction machinery(hydrauJic whee], watermill, windmin, suction pump,

water pump, hydrauJic pump, vessels, tubes, pipes,and others topics as mari time construction as weirs,dams, channels, river ports, and others).

The difficult field of mechanica] science was achallange for many other scientists who obtained a]arge number of interesting resuJts. Henri de Pitot

(1695-1771) invented an instrument to measurerunning water; Antoine Chézy (17] 8-] 798)expressed a mathematica] formula for the evaluationof water ve]ocity in a channel under constant runningwater. This formula is still in use in appliedhydraulics< John Smeaton (1724-1792), a famousEnglish engineer, was invo]ved in experimentalhydraulics; Charles Borda (1733-1799) carried outsevera] laboratory tests on tluid resistance and on

liquids' eftlux fram one or more orifices in a vessel.Charles Bossut (1730-] 814) conducted extensivestudies on hydrodynamics (Bossut ]775) and on

experimental hydraulics (Bossut 1795); Pierre LouisGeorges Du Buat (1734-1809) studied variousphenomena re]ated to tluid motion through pipes andchanne]s and so he described veIocity of water eftlux

fram an orifice, pipes resistance under constantpressure and then he deve]oped a semi-empiricalmethod to evaluate channe]s' cross section in

accordance with Chézy' theory< Finally, we mention

the contributions of Giovanni Battista Venturi

642

'\~~

'.In

Figure9Le Chevalier Morland. Elevation des eaux , . . (1685)

(1746-1822) and Reinhard Woltman (1757-1837)

with their studies on measurement of pipes resistanceunder pressure and their researches on water motionin tubes and channe1s (Rouse and luce 1954).

4. NEW TRENDS IN HYDRAULICS

By the end of the 18thcentury and the beginning of the19th century, a 1arge number of studies and researches

on hydrau1ics (hydrostatics and hydrodynamics) wascarried out. This trend was set with an imposingamount of treatise, books, critical essays on varioustopics related with hydraulics and its applications toengineering. The work of Pons-Joseph Bernard(1748-1816) on Principes d'Hydraulique (Bernard1787), the treatises of Gaspard-Clair-Fran¡;ois-Marie

Le Riche, Baron de Prony (1755-1839) on

L'ecoulement des jluides incompressibiles [Prony,1790-96]. on the Jaugeage des eaux courantes[Prony, 1802], or on the Théorie des Eaux Courantes(Prony 1804), the essay of Pierre-Simon Girard

(1765-1836) on the Mouvement des eaux courantes

(Girard 1804), or the critica1 review of Du Buat's

treatise by Fran¡;ois-Michel Lecreulx (1729-1812)(Lecreulx 1809) are an anticipation of the publishing

revolution which enhanced the diffusion 01' the newtrend in hydrau1ics scientific community. The Prony'sNouvelle Architecture Hydraulique (Prony 1790-96)so as the Belidor' s Architecture hydraulique (Belidor1737-53) were the basis of applied hydraulics inengineering (Belidor 1729). They had a great

diffusion in scientific community and in practicalengineering as well. They turned theories fromBernoulli, Bossut, d' Alembert, Euler, Lagrange into

M. Corradi

construction of machinery and instruments to conveywater in rivers, channels, tubes, pipes, etc. It is arevival of app1ied hydrostatic and hydrodynamics,glorys 1'or Italy and France in the Renaissance.

The 1'olJowing century will be the century 01'theoretical hydrodynamics or t1uid mechanics, butthis is another story.

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