HYDROMECHANICS HYTHE
HYDROMEDUSAE I
HYDROMETER IAMBIC
HYDROPATHY IAMBLICHUS (Greek philosopher)
HYDROPHOBIA IAMBLICHUS (Greek romance writer)
HYDROSPHERE IANNINA
HYDROSTATICS IAPETUS
HYDROXYLAMINE IAPYDES
HYDROZOA IATROCHEMISTRY
HYENA IAZYGES
HYÈRES IBADAN
HYGIEIA IBAGUÉ
HYGIENE IBARRA
HYGINUS (eighth pope) IBERIANS
HYGINUS (Latin writer) IBEX
HYGINUS, GAIUS JULIUS IBIS
HYGROMETER IBLIS
HYKSOS IBN 'ABD RABBIHI
HYLAS IBN 'ARABI
HYLOZOISM IBN ATHIR
HYMEN IBN BATUTA
HYMENOPTERA IBN DURAID
HYMETTUS IBN FARADI
HYMNS IBN FARID
HYPAETHROS IBN GABIROL
HYPALLAGE IBN HAUKAL
HYPATIA IBN HAZM
HYPERBATON IBN HISHAM
HYPERBOLA IBN ISHAQ
HYPERBOLE IBN JUBAIR
HYPERBOREANS IBN KHALDUN
HYPEREIDES IBN KHALLIKAN
HYPERION IBN QUTAIBA
HYPERSTHENE IBN SA'D
HYPERTROPHY IBN TIBBON
HYPNOTISM IBN TUFAIL
HYPOCAUST IBN USAIBI'A
HYPOCHONDRIASIS IBO
HYPOCRISY IBRAHIM AL-MAUSILI
HYPOSTASIS IBRAHIM PASHA
HYPOSTYLE IBSEN, HENRIK
HYPOSULPHITE OF SODA IBYCUS
HYPOTHEC ICA
HYPOTHESIS ICE
HYPOTRACHELIUM ICEBERG
HYPSOMETER ICELAND
HYRACOIDEA ICELAND MOSS
HYRCANIA ICE-PLANT
HYRCANUS ICE-YACHTING
HYSSOP I-CH'ANG
HYSTASPES ICHNEUMON
HYSTERESIS ICHNEUMON-FLY
HYSTERIA ICHNOGRAPHY
HYSTERON-PROTERON
HYDROMECHANICS ([Greek: hydromêchanika]), the science of the mechanics
of water and fluids in general, including _hydrostatics_ or the
mathematical theory of fluids in equilibrium, and _hydromechanics_, the
theory of fluids in motion. The practical application of hydromechanics
forms the province of hydraulics (q.v.).
_Historical._--The fundamental principles of hydrostatics were first
given by Archimedes in his work [Greek: Peri tôn ochoumenôn], or _De
iis quae vehuntur in humido_, about 250 B.C., and were afterwards
applied to experiments by Marino Ghetaldi (1566-1627) in his _Promotus
Archimedes_ (1603). Archimedes maintained that each particle of a
fluid mass, when in equilibrium, is equally pressed in every
direction; and he inquired into the conditions according to which a
solid body floating in a fluid should assume and preserve a position
of equilibrium.
In the Greek school at Alexandria, which flourished under the auspices
of the Ptolemies, the first attempts were made at the construction of
hydraulic machinery, and about 120 B.C. the fountain of compression,
the siphon, and the forcing-pump were invented by Ctesibius and Hero.
The siphon is a simple instrument; but the forcing-pump is a
complicated invention, which could scarcely have been expected in the
infancy of hydraulics. It was probably suggested to Ctesibius by the
_Egyptian Wheel_ or _Noria_, which was common at that time, and which
was a kind of chain pump, consisting of a number of earthen pots
carried round by a wheel. In some of these machines the pots have a
valve in the bottom which enables them to descend without much
resistance, and diminishes greatly the load upon the wheel; and, if we
suppose that this valve was introduced so early as the time of
Ctesibius, it is not difficult to perceive how such a machine might
have led to the invention of the forcing-pump.
Notwithstanding these inventions of the Alexandrian school, its
attention does not seem to have been directed to the motion of fluids;
and the first attempt to investigate this subject was made by Sextus
Julius Frontinus, inspector of the public fountains at Rome in the
reigns of Nerva and Trajan. In his work _De aquaeductibus urbis Romae
commentarius_, he considers the methods which were at that time
employed for ascertaining the quantity of water discharged from
ajutages, and the mode of distributing the waters of an aqueduct or a
fountain. He remarked that the flow of water from an orifice depends
not only on the magnitude of the orifice itself, but also on the
height of the water in the reservoir; and that a pipe employed to
carry off a portion of water from an aqueduct should, as circumstances
required, have a position more or less inclined to the original
direction of the current. But as he was unacquainted with the law of
the velocities of running water as depending upon the depth of the
orifice, the want of precision which appears in his results is not
surprising.
Benedetto Castelli (1577-1644), and Evangelista Torricelli
(1608-1647), two of the disciples of Galileo, applied the discoveries
of their master to the science of hydrodynamics. In 1628 Castelli
published a small work, _Della misura dell' acque correnti_, in which
he satisfactorily explained several phenomena in the motion of fluids
in rivers and canals; but he committed a great paralogism in supposing
the velocity of the water proportional to the depth of the orifice
below the surface of the vessel. Torricelli, observing that in a jet
where the water rushed through a small ajutage it rose to nearly the
same height with the reservoir from which it was supplied, imagined
that it ought to move with the same velocity as if it had fallen
through that height by the force of gravity, and hence he deduced the
proposition that the velocities of liquids are as the square root of
the head, apart from the resistance of the air and the friction of the
orifice. This theorem was published in 1643, at the end of his
treatise _De motu gravium projectorum_, and it was confirmed by the
experiments of Raffaello Magiotti on the quantities of water
discharged from different ajutages under different pressures (1648).
In the hands of Blaise Pascal (1623-1662) hydrostatics assumed the
dignity of a science, and in a treatise on the equilibrium of liquids
(_Sur l'équilibre des liqueurs_), found among his manuscripts after
his death and published in 1663, the laws of the equilibrium of
liquids were demonstrated in the most simple manner, and amply
confirmed by experiments.
The theorem of Torricelli was employed by many succeeding writers, but
particularly by Edmé Mariotte (1620-1684), whose _Traité du mouvement
des eaux_, published after his death in the year 1686, is founded on a
great variety of well-conducted experiments on the motion of fluids,
performed at Versailles and Chantilly. In the discussion of some
points he committed considerable mistakes. Others he treated very
superficially, and in none of his experiments apparently did he attend
to the diminution of efflux arising from the contraction of the liquid
vein, when the orifice is merely a perforation in a thin plate; but he
appears to have been the first who attempted to ascribe the
discrepancy between theory and experiment to the retardation of the
water's velocity through friction. His contemporary Domenico
Guglielmini (1655-1710), who was inspector of the rivers and canals at
Bologna, had ascribed this diminution of velocity in rivers to
transverse motions arising from inequalities in their bottom. But as
Mariotte observed similar obstructions even in glass pipes where no
transverse currents could exist, the cause assigned by Guglielmini
seemed destitute of foundation. The French philosopher, therefore,
regarded these obstructions as the effects of friction. He supposed
that the filaments of water which graze along the sides of the pipe
lose a portion of their velocity; that the contiguous filaments,
having on this account a greater velocity, rub upon the former, and
suffer a diminution of their celerity; and that the other filaments
are affected with similar retardations proportional to their distance
from the axis of the pipe. In this way the medium velocity of the
current may be diminished, and consequently the quantity of water
discharged in a given time must, from the effects of friction, be
considerably less than that which is computed from theory.
The effects of friction and viscosity in diminishing the velocity of
running water were noticed in the _Principia_ of Sir Isaac Newton, who
threw much light upon several branches of hydromechanics. At a time
when the Cartesian system of vortices universally prevailed, he found
it necessary to investigate that hypothesis, and in the course of his
investigations he showed that the velocity of any stratum of the
vortex is an arithmetical mean between the velocities of the strata
which enclose it; and from this it evidently follows that the velocity
of a filament of water moving in a pipe is an arithmetical mean
between the velocities of the filaments which surround it. Taking
advantage of these results, Henri Pitot (1695-1771) afterwards showed
that the retardations arising from friction are inversely as the
diameters of the pipes in which the fluid moves. The attention of
Newton was also directed to the discharge of water from orifices in
the bottom of vessels. He supposed a cylindrical vessel full of water
to be perforated in its bottom with a small hole by which the water
escaped, and the vessel to be supplied with water in such a manner
that it always remained full at the same height. He then supposed this
cylindrical column of water to be divided into two parts,--the first,
which he called the "cataract," being an hyperboloid generated by the
revolution of an hyperbola of the fifth degree around the axis of the
cylinder which should pass through the orifice, and the second the
remainder of the water in the cylindrical vessel. He considered the
horizontal strata of this hyperboloid as always in motion, while the
remainder of the water was in a state of rest, and imagined that there
was a kind of cataract in the middle of the fluid. When the results of
this theory were compared with the quantity of water actually
discharged, Newton concluded that the velocity with which the water
issued from the orifice was equal to that which a falling body would
receive by descending through half the height of water in the
reservoir. This conclusion, however, is absolutely irreconcilable with
the known fact that jets of water rise nearly to the same height as
their reservoirs, and Newton seems to have been aware of this
objection. Accordingly, in the second edition of his _Principia_,
which appeared in 1713, he reconsidered his theory. He had discovered
a contraction in the vein of fluid (_vena contracta_) which issued
from the orifice, and found that, at the distance of about a diameter
of the aperture, the section of the vein was contracted in the
subduplicate ratio of two to one. He regarded, therefore, the section
of the contracted vein as the true orifice from which the discharge of
water ought to be deduced, and the velocity of the effluent water as
due to the whole height of water in the reservoir; and by this means
his theory became more conformable to the results of experience,
though still open to serious objections. Newton was also the first to
investigate the difficult subject of the motion of waves (q.v.).
In 1738 Daniel Bernoulli (1700-1782) published his _Hydrodynamica seu
de viribus et motibus fluidorum commentarii_. His theory of the motion
of fluids, the germ of which was first published in his memoir
entitled _Theoria nova de motu aquarum per canales quocunque
fluentes_, communicated to the Academy of St Petersburg as early as
1726, was founded on two suppositions, which appeared to him
conformable to experience. He supposed that the surface of the fluid,
contained in a vessel which is emptying itself by an orifice, remains
always horizontal; and, if the fluid mass is conceived to be divided
into an infinite number of horizontal strata of the same bulk, that
these strata remain contiguous to each other, and that all their
points descend vertically, with velocities inversely proportional to
their breadth, or to the horizontal sections of the reservoir. In
order to determine the motion of each stratum, he employed the
principle of the _conservatio virium vivarum_, and obtained very
elegant solutions. But in the absence of a general demonstration of
that principle, his results did not command the confidence which they
would otherwise have deserved, and it became desirable to have a
theory more certain, and depending solely on the fundamental laws of
mechanics. Colin Maclaurin (1698-1746) and John Bernoulli (1667-1748),
who were of this opinion, resolved the problem by more direct methods,
the one in his _Fluxions_, published in 1742, and the other in his
_Hydraulica nunc primum detecta, et demonstrata directe ex fundamentis
pure mechanicis_, which forms the fourth volume of his works. The
method employed by Maclaurin has been thought not sufficiently
rigorous; and that of John Bernoulli is, in the opinion of Lagrange,
defective in clearness and precision. The theory of Daniel Bernoulli
was opposed also by Jean le Rond d'Alembert. When generalizing the
theory of pendulums of Jacob Bernoulli (1654-1705) he discovered a
principle of dynamics so simple and general that it reduced the laws
of the motions of bodies to that of their equilibrium. He applied this
principle to the motion of fluids, and gave a specimen of its
application at the end of his _Dynamics_ in 1743. It was more fully
developed in his _Traité des fluides_, published in 1744, in which he
gave simple and elegant solutions of problems relating to the
equilibrium and motion of fluids. He made use of the same suppositions
as Daniel Bernoulli, though his calculus was established in a very
different manner. He considered, at every instant, the actual motion
of a stratum as composed of a motion which it had in the preceding
instant and of a motion which it had lost; and the laws of equilibrium
between the motions lost furnished him with equations representing the
motion of the fluid. It remained a desideratum to express by equations
the motion of a particle of the fluid in any assigned direction. These
equations were found by d'Alembert from two principles--that a
rectangular canal, taken in a mass of fluid in equilibrium, is itself
in equilibrium, and that a portion of the fluid, in passing from one
place to another, preserves the same volume when the fluid is
incompressible, or dilates itself according to a given law when the
fluid is elastic. His ingenious method, published in 1752, in his
_Essai sur la résistance des fluides_, was brought to perfection in
his _Opuscules mathématiques_, and was adopted by Leonhard Euler.
The resolution of the questions concerning the motion of fluids was
effected by means of Euler's partial differential coefficients. This
calculus was first applied to the motion of water by d'Alembert, and
enabled both him and Euler to represent the theory of fluids in
formulae restricted by no particular hypothesis.
One of the most successful labourers in the science of hydrodynamics
at this period was Pierre Louis Georges Dubuat (1734-1809). Following
in the steps of the Abbé Charles Bossut (_Nouvelles Experiences sur la
résistance des fluides_, 1777), he published, in 1786, a revised
edition of his _Principes d'hydraulique_, which contains a
satisfactory theory of the motion of fluids, founded solely upon
experiments. Dubuat considered that if water were a perfect fluid, and
the channels in which it flowed infinitely smooth, its motion would be
continually accelerated, like that of bodies descending in an inclined
plane. But as the motion of rivers is not continually accelerated, and
soon arrives at a state of uniformity, it is evident that the
viscosity of the water, and the friction of the channel in which it
descends, must equal the accelerating force. Dubuat, therefore,
assumed it as a proposition of fundamental importance that, when water
flows in any channel or bed, the accelerating force which obliges it
to move is equal to the sum of all the resistances which it meets
with, whether they arise from its own viscosity or from the friction
of its bed. This principle was employed by him in the first edition of
his work, which appeared in 1779. The theory contained in that edition
was founded on the experiments of others, but he soon saw that a
theory so new, and leading to results so different from the ordinary
theory, should be founded on new experiments more direct than the
former, and he was employed in the performance of these from 1780 to
1783. The experiments of Bossut were made only on pipes of a moderate
declivity, but Dubuat used declivities of every kind, and made his
experiments upon channels of various sizes.
The theory of running water was greatly advanced by the researches of
Gaspard Riche de Prony (1755-1839). From a collection of the best
experiments by previous workers he selected eighty-two (fifty-one on
the velocity of water in conduit pipes, and thirty-one on its velocity
in open canals); and, discussing these on physical and mechanical
principles, he succeeded in drawing up general formulae, which
afforded a simple expression for the velocity of running water.
J. A. Eytelwein (1764-1848) of Berlin, who published in 1801 a
valuable compendium of hydraulics entitled _Handbuch der Mechanik und
der Hydraulik_, investigated the subject of the discharge of water by
compound pipes, the motions of jets and their impulses against plane
and oblique surfaces; and he showed theoretically that a water-wheel
will have its maximum effect when its circumference moves with half
the velocity of the stream.
J. N. P. Hachette (1769-1834) in 1816-1817 published memoirs
containing the results of experiments on the spouting of fluids and
the discharge of vessels. His object was to measure the contracted
part of a fluid vein, to examine the phenomena attendant on additional
tubes, and to investigate the form of the fluid vein and the results
obtained when different forms of orifices are employed. Extensive
experiments on the discharge of water from orifices (_Expériences
hydrauliques_, Paris, 1832) were conducted under the direction of the
French government by J. V. Poncelet (1788-1867) and J. A. Lesbros
(1790-1860). P. P. Boileau (1811-1891) discussed their results and
added experiments of his own (_Traité de la mésure des eaux
courantes_, Paris, 1854). K. R. Bornemann re-examined all these
results with great care, and gave formulae expressing the variation of
the coefficients of discharge in different conditions (_Civil
Ingénieur_, 1880). Julius Weisbach (1806-1871) also made many
experimental investigations on the discharge of fluids. The
experiments of J. B. Francis (_Lowell Hydraulic Experiments_, Boston,
Mass., 1855) led him to propose variations in the accepted formulae
for the discharge over weirs, and a generation later a very complete
investigation of this subject was carried out by H. Bazin. An
elaborate inquiry on the flow of water in pipes and channels was
conducted by H. G. P. Darcy (1803-1858) and continued by H. Bazin, at
the expense of the French government (_Recherches hydrauliques_,
Paris, 1866). German engineers have also devoted special attention to
the measurement of the flow in rivers; the _Beiträge zur Hydrographie
des Königreiches Böhmen_ (Prague, 1872-1875) of A. R. Harlacher
(1842-1890) contained valuable measurements of this kind, together
with a comparison of the experimental results with the formulae of
flow that had been proposed up to the date of its publication, and
important data were yielded by the gaugings of the Mississippi made
for the United States government by A. A. Humphreys and H. L. Abbot,
by Robert Gordon's gaugings of the Irrawaddy, and by Allen J. C.
Cunningham's experiments on the Ganges canal. The friction of water,
investigated for slow speeds by Coulomb, was measured for higher
speeds by William Froude (1810-1879), whose work is of great value in
the theory of ship resistance (_Brit. Assoc. Report._, 1869), and
stream line motion was studied by Professor Osborne Reynolds and by
Professor H. S. Hele Shaw. (X.)