Hydraulics, notwithstanding its ancient origins, is very young as a discipline. It has been founding and consolidating its scientific bases onIy for the last three centuries as pure science, like mechanics, and its application to engineering. The «discovery» of basic principles, the fundamentals of hydraulic science, required many efforts throughout the 17th and 18th century.

1. From the «Architecture hydraulique»
to the «Science des ingénieurs»: Hydrostatics
and Hydrodynamics in the XIXth century
L' ARCHITECTURE HYDRAULlQUE: THE FIRST
STUDIES ON RUNNING WATER AND THE FOUNDATION
OF HYDRAULlCS
Hydraulics, notwithstanding its ancient ongms, is
very young as a discipline. lt has been founding and
consolidating its scientific bases on Iy for the last three
centuries as pure science, like mechanics, and its
application to engineering. The «discovery» of basic
principIes, the fundamentals of hydraulic science,
required many efforts throughout the 17th and 8th
century.
The first phase of deve10pment is the great season
of experimental hydraulics during the Renaissance,
especially in Italy, thanks to the contribution
of Leonardo da Vinci (1452-1519), Girolamo
Cardano (1501-1576), Giovan Battista Benedetti
(1530-1590), Bernardino Baldi (1553-1617) and
others. Only with the school of Galileo Galilei and his
pupils, like Evangelista Torricelli (1608-1647) and
Benedetto Castelli (1577- 1643), with his treatise
Delta misura delte acque correnti COn measuring
running water') published in 1628, the road to the
great treatises on hydraulics of the 17th and 18th
centuries was opened. In this field of studies
the treatise of Carlo Fontana (1634-1714) «On
measuring running water» (Fontana 1696) played a
great importance role.
In 1644 Torricel!i, an Italian scientist, published in
Florence 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 law
stated that the velocity of water efflux from an orifice
in the bottom of a tank is proportional to the square of
height 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 heavy
body, 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 is
commonly written as v = V2ih. This law wil! be
thourougly explained, with the utmost accuracy, by
Daniel Bernoul!i (1700-1782), in the first half of the
18th 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! over
Europe 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 Isaac
Newton (1642-1727) with his studies on fluid
mechanics and, on a more experimentallevel, Pierre
Varignon (1654-1722) on motion and the
measurement of running water.
Mariotte's treatise on running waters and fluid
bodies (Mariotte 1686) -published two years after
his 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.

2. 636
UTILlSSIMO TRA TT: TO,
D f. L 1.'
ACQUE CORREN TI
D!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 IGNAZIO
D A l! S T R 1 A
R!'.
J) R o ~I A X l. ~o.
t;-..,,-,,j.
--
Figure 1
Caria Fontana: Trattato dell'acque correnti (1696)
even compressible, on the measurement of running
water, on the trajectory of ]iquid particIes, on water' s
distribution and finally on the resistance of water
pipes under water pressure. Mariotte started fram
Torricelli' s eff]ux principIe and he verified his
theories in several experiments by means of
ingenious mechanism.
Concurrent]y, in Ita]y, Domenico Guglielmini
(1655-] 710), and considered the founder of ]talian
school of hydraulics, published very important
treatises on hydrau]ics, the measurement of running
water (Gug]ielmini ]690), and the motion of water
rivers (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 the
first scientist who showed the existence of a uniform
M. Corradi
state of equilibrium between running water on
incIined 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 in
hydraulic sciences, particu]arIy hydrostatics. His
treatise on the equilibrium of liquids, pub]ished
posthumous]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 the
same water depth. In a fluid the hydrastatic pressure
is the same in all directions which are starting fram
the centre of water particIe. This important
contribution of Pasea] bridges dynamics of rigid
bodies and fIuid dynamics.
Moreover, we remember Newton's fundamenta]
contributions on bodies immersed in fIuids or liquidsa

3. From the «Architecture hydraulique» to the «Science des ingénieurs» 637
A
[!]
J L
: :;,.o
J
'-:":'" F(;
[jlJ
r~n.. ~.::::.. ::;;::D J~l :..)1
G Hh
'J
Z
..
r
A
B C'
A
J4.
:::::::~~:.:~::.
':::::::f""::::'.
Figure 2
From Mariotte's treatise (1686)
and his studies on water jets, wave-motion,
viscosity' s coefficients, About viscosity Newton
established that tangential stresses in a viscous fluid
are proportional to the relative velocity of fluid in
adjacent parts. In an endJess cylinder rotating on its
own axis with constant angular velocity, fluids
velocity changes in inverse proprotion to the radial
distance measured from the axis. Thus, Newton
rejected Descartes' theory on vortex.
In 1725 the treatise of Pierre Varignon on water
motion and running water measurement was
published posthumous. From this point of view, this
treatise focused on the mechanistic aspects of the
problem rather than to the fluids behaviour. Varignon
analysed the Torricelli's problem: the discharge of a
liquid 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 Nouvelle
hydraulique. In this work Bernoulli indicated his
point of view of Newton's theory about the shape of
a stream of water discharged from a cataract. In this
subject Bernoulli caJled attention to the error in
Newton cataract theory, as this hypotheses required a
zero 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 empirical
sciences. It was only with the coming of differential
and integral calculus, in the 17th century, that the
principIes of the motion of fluids were established
and hydraulics raised to the same level of the other
mechanical sciences.

4. I
I~
:l- 1 L
L
G- .JC
I
A. H B
!7lr. ;7.
638
«
.
~
Figure 3
Velocity 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 energy
loss, hydraulics machine, air motion, fluids motion
etc. This compendium of Bernoulli studies showed
Bernoulli concern with theoretical principIes and
application of the progress in hydraulics, and
particularly in hydrostatics and hydrodynamics
aspects. Por example, we remember that Bernoulli
was the first scientist to use the piezometer to
calculate the water pipes pressure. This work is a
cornerstones of modern hydraulics, in that it is the
definition of the fundamental relationship between
the speed of an element in a liquid mass and its
relative loado In this important work Daniel Bernoulli
defined the basis of modern hydraulics.
What is significant is the demonstration of his
theorem, based on the energetic principIes by
Christiaan Huygens (1629-1695) and Gottfried
Wilhelm Leibniz (1646-1716), which establishes that
in a perfect liquid, in stationery motion, the sum of
position, pressure and kinetic energy of each particle
is constant during the whole trajectory, which
confirms the principIe of energy conservation.
R.
e E G F 1)
Figure 4
Newton' s original concept of orifice discharge
2. THE BEGINNING m' THEORETlC HYDRODYNAMICS
The beginning of theoretic hydrodynamics dates back
to 1738, Daniel Bernoulli published the treatise on
hydrodynamics (see: Hydrodynamica, 1738). The
Figure 5
Water eftlux from an orifice by BernoulJi

5. From the «Architecture hydraulique» to the "Science des ingénieurs» 639
9i.1'.7.3
'A
e
J.
i'~J,
Figure6
The first idea of the piezometer by Daniel Bernoulli
In formula: S + P- +
2
V2
= consto (Bernoulli's
y g
Theorem), where S is the height 01' generic water
particle on his trajectory; p is the liquid pressure; y is
the specific weight 01'liquid; Vis the water velocity;
g is the acceleration due to gravity
Bernoulli's work opened up the road to important
developments in hydraulics by scientist like Jean-
Baptiste Le Rond d'Alembert (1717-1783), with his
studies on hydrodynamics and tluid mechanics,
Leonhard Euler (1707-1783), Pierre-Simon, Marquis
de Laplace (1749-1827), Alexis-Claude Clairaut
(1713-]765) and many others.
During few years numerous treatise had been
published and this scientific literature granted to this
discipline the role 01' mechanics science instead 01'
empirical arto For this reason we make a concise
compendium 01'most significant researches.
In ]744 d' Alembert published his Traité de
l' equilihre et du mouvement des fluides on
hydrodynamics and fluid mechanics. In the opinion 01'
this French scientist hydrodynamics (and then
hydraulics) must be founded on experimental
observations; converse]y, solid mechanics can be
founded on the basis 01'metaphysical principies. The
problem related to the fluid motion and t1uid
resistance were complex; they can be misinterpreted
by the Philosophes a notions incomplettes -as stated
by Leibniz-, but also the scientists with a propensity
to give a philosophical halo with metaphysical
peculiarity to mechanics principies used in this
particular field. The problem -certainly a
comp]icated one- dated back to the problem 01'
conservation of live forces which Daniel Bemoulli
assumed as principie although d' Alembert deduced it
by his «principie».
Three years later, in 1747, the Berlin Academy set
a prize competition on this topic and the winner was
d' Alembert with his essay Réflexions sur la cause
générale des vents. This results was strongly
criticised 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 the
mathematical problem, but in this work was showed
important results introducing aerodynamics studies.
AIso in 1750 the Berlin Academy promoted another
prize competition more related to the subject of
hydrodynamics 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 his
hydrodynamics «parado x» (or «d' Alembert's
paradox»). This paradox stated that a body moving in
a perfect t1uid or if it is possible to state a related
motion between fluid and body, the resultant 01' the
whole t1uid pressure acting on body is equal to zero.
This result, in conflict with experience, depends on
the hypotheses 01' a fluid without adhesion and
viscosity and that the body is acting through an ideal
homogeneous weightless fluido
The next step was the publication 01' Euler's
Principia (Principia motus jluidorum) in 1755; this
work is the benchmark for al! scientists of tluid
mechanics and hydrodynamics. In this fundamental
book Euler defines his equation of continuity for a
fluido This equation translates in mathematical form
the physical principIe 01'mas s conservation, by using
potential functions for an incompressible fluido By
using this equation it is possible obtain the equation
describing the motion 01' a fluid, even if -as Euler
himself remarked- «it still impossible to have a
complete knowledge 01' t1uid motion not for
inadequacy 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

6. 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 Simon
Laplace (1749-1827) introduced his Laplacian
operator -in his Mécanique céleste published in five
vo1umes starting from 1799 to 1825- to study
problems related to hydrodynamics. His studies on
wave-motion and tides, in addition to those on
capillarity, are very important to develop
hydrodynamics. Considering applicatory point of
view, Franz Joseph von Gerstner (1756-1832)
increased these studies. He also studied hydraulic
machines, dams, water motion in channels and wave-
motion [Gerstner, 1788].
To synthetize: the indefinite equations of
equilibrium 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 related
to area unit. If the liquid is incompressible, then it is
possible 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 vector
force is applied F, p and are respectively the pressure
and density in the same point at the time t.
To establish kinetic state oí' a fluid, or the velocity
assumed by fluid particles when through a
determinated 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 +
dP
v =F -
k
. Thls
equation shows the absolute form of Euler' equation
(Marcolongo 1904).
3. ApPLIED HYDRAULlCS
The 18th and the 19th centuries were also the
centuries of experimental hydraulics. Experimenters
played a crucial role in the development of applied
hydraulics. The aim of this essay is follow the same
route that leaded from theoretical hydrostatics and
hydrodynamics to applied hydraulics during the 19th
M. Corradi
century. In ltaly and France scientists of hydraulics
opened up the road to the application of the Science
de Ingénieurs. in France we remember the important
contributions 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 Louis
Georges 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 for
his studies about the reinforcement oí' St. Peter' s
Dome in Rome (Benvenuto 1991)- studied so me
problems related to water efflux from an orifice and
then he stated the weir laws (Poleni 1717), De Regi
focused on the measurement oí' running water (De
Regi 1764), while the Barnabite Frisi devoted his life
to study river hydraulics (Frisi, 1770; Frisi 1777).
Figure 7
Poleni: De Motu Aquae Mixto (1717)

7. From the «Architecture hydraulique» to the «5Óence des ingénieurs» 641
}I>,
<>
Figure 8
Belictor: L 'Architecture Hydraulique (1737-39)
As the Ita]ian Schoo] of experimenta] hydrau]ics
we remember a great number of scientists and among
them 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 very
important to remember the researches of Jacopo
Riccati (1676-1754) on the prablem «to determine
the force caused by tluid bodies crashing into solid
bodies» (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 and
his «Epistola hydrostatica» (Guglie]mini ]731)
written by Domenico Guglie]mini (1655-1710) in
173] ha ve to be remembered. And we also remind
Anton-Maria Lorgna (1735-1796) and his researches
on running waters (Lorgna ]777), Antonio Rocchi
(1724-1780) and his studies on measurement of
bodies velocity and strength in motion and his
application to hydrostatic prob]ems (Rocchi 1775),
Gregorio Fontana (1735-1805) and his dissertation
upon hydrodynamics, on the motion of a body in a
resistant medium, on the waterproof of channels
(Fontana 1802), on the water pressure in motion into
vessels, tubes and pipes, on the effect of centrifuge
force on tluid motion (Fontana] 803), and the mature
studies carried out by Louis Lagrange at the early
eighties of 18th century (Lagrange 1781; Lagrange
]781-85). Finally, we have to mention the translation
of Hydrodynamics treatise of abbé Charles Bossut
(1730-]814) by Gregorio Fontana (Fontana 1785) in
]785.
In France, after the important studies begun by
Mariotte 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), who
published an important encyclopaedic treatise on
Architecture hydraulique (2 volumes in 4 tomes)
where he thouroughly investigate on subjects related
to 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 a
challange for many other scientists who obtained a
]arge number of interesting resuJts. Henri de Pitot
(1695-1771) invented an instrument to measure
running water; Antoine Chézy (17] 8-] 798)
expressed a mathematica] formula for the evaluation
of water ve]ocity in a channel under constant running
water. This formula is still in use in applied
hydraulics< John Smeaton (1724-1792), a famous
English engineer, was invo]ved in experimental
hydraulics; Charles Borda (1733-1799) carried out
severa] laboratory tests on tluid resistance and on
liquids' eftlux fram one or more orifices in a vessel.
Charles Bossut (1730-] 814) conducted extensive
studies on hydrodynamics (Bossut ]775) and on
experimental hydraulics (Bossut 1795); Pierre Louis
Georges Du Buat (1734-1809) studied various
phenomena re]ated to tluid motion through pipes and
channe]s and so he described veIocity of water eftlux
fram an orifice, pipes resistance under constant
pressure and then he deve]oped a semi-empirical
method to evaluate channe]s' cross section in
accordance with Chézy' theory< Finally, we mention
the contributions of Giovanni Battista Venturi

8. 642
'~~
'.
In
Figure9
Le Chevalier Morland. Elevation des eaux , . . (1685)
(1746-1822) and Reinhard Woltman (1757-1837)
with their studies on measurement of pipes resistance
under pressure and their researches on water motion
in tubes and channe1s (Rouse and luce 1954).
4. NEW TRENDS IN HYDRAULICS
By the end of the 18thcentury and the beginning of the
19thcentury, a 1arge number of studies and researches
on hydrau1ics (hydrostatics and hydrodynamics) was
carried out. This trend was set with an imposing
amount of treatise, books, critical essays on various
topics related with hydraulics and its applications to
engineering. The work of Pons-Joseph Bernard
(1748-1816) on Principes d'Hydraulique (Bernard
1787), 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 new
trend in hydrau1ics scientific community. The Prony's
Nouvelle Architecture Hydraulique (Prony 1790-96)
so as the Belidor' s Architecture hydraulique (Belidor
1737-53) were the basis of applied hydraulics in
engineering (Belidor 1729). They had a great
diffusion in scientific community and in practical
engineering as well. They turned theories from
Bernoulli, Bossut, d' Alembert, Euler, Lagrange into
M. Corradi
construction of machinery and instruments to convey
water in rivers, channels, tubes, pipes, etc. It is a
revival 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, but
this is another story.
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AA. VV. 1765-1774 (2"0 ed.). Raccolla d'autori che
trallano del moto dell'acque. 9 vols. Firenze: nella
Stamperia di Sua Altezza Reale, Gaetano Cambiagi
Stampator Granduca]e.
Alembert, Jean-Baptiste Le Rond d'. 1743 (2"" ed. 1758).
Traité de Dynamique . . . . Nouvelle Edition, revue &fort
augmentée par l'Auteur. Paris: David.
Alembert, Jean-Baptiste Le Rond d'. 1744. Traité de
l'équilibre et du mouvement des fluides. Pour Servir de
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Alembert, Jean-Baptiste Le Rond d'. 1752. Essai d'une
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Alembert, Jean-Baptiste Le Rond d'. 1770. Traité de
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Chézy, Amoine de. 1775. Mémoire sur la vitesse de l'eau
conduite dans une rigole donnée. 1775.
C]airaut, A]exis-Claude. 1743. Théorie de la figure de la
terre tirée des principes de I'hydrodynamique. Paris:
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