DANIEL BERNOULLI'S
This is another work with a
long history, which I will put in place here gradually as my own translation, that
you can read if you are not familiar with it already; at present we content
ourselves with the first two section of a work that will take some time to
translate in its entirety. Section I is mainly historical, while section II
delves into some of D. B.'s previous research into the shapes of bodies
distended by certain forces, and in fact he finishes off as it were some of the
questions handled by his uncle James and father John regarding sails filled
with water, surface tension as he understood it, and finally begins his work on
the pressure of flowing water, which he appears to be the first to realize to
be different from the static pressure of a fluid at rest. Since writing the
above some 6 months have passed, and we are now nearing the end of the translation,
which has been a rather onerous task.
References :
1. Anmerkungen
zu Daniel Bernoulli's Hydrodynamicae. K. Flierl : Publications of the Research
Institute of the
2. Translation
of the Hydrodynamicae into English by Thomas Carmody and Helmut Kobus.
Most of the early works mentioned in the text are available at the e-rara website
3. Die Werke von Daniel Bernoulli. Hydrodynamicae, edited by P. Radelet-de-Grave
and D. Speiser (Birkhäuser)
Volume 5. Notes originally in Russian by G.H. Mikhailov translated into English by Prof. R. Radox,
4. An Idiot's Fugitive Essays on Science, by C. Truesdell. This is a fascinating book, so good in fact that my local university library has had its copy stolen! Some commentary is made on the Hydrodynamicae, as well as criticism of the above translation by Carmody and Kobus ; this translation is unusual in that some parts where the Latin is difficult have been correctly translated, while other parts where the flow of Bernoulli's thoughts has been lost, are essentially nonsense.
5. Landmark Writings in Western
Mathematics, (Elsevier) editor Grattan-Guinness : Chapter 9 is
devoted to Mikhailov's discussion of
the Hydrodynamicae, although understandably he
concentrates on the Bernoulli Effect found in a later chapter.
6. Gravitational oscillations of a liquid column in a pipe; Lorenceau et al., PHYSICS OF FLUIDS VOLUME 14, NUMBER 6, June 2002;
A modern development following Section VII, Part II initially.
7. The Vortex Theory of Planetary Motion ; E.J. Aiton; An interesting book documenting the decline and fall of DeCartes vortex theory; initially D. Bernoulli, following in his father’s footsteps, accepted this theory, but as he matured as a scientist, he grew away from this theory and turned instead to the Newtonian viewpoint. These matters are discussed in Ch. 11.
CONTENTS
Click here for Section. I :
Which is the introduction, and contains various matters to be considered
initially.
Here Daniel Bernoulli sets out
an apparently rapidly written introduction to his book, in which he summarizes
the contents of the following sections, adding various observations that have
occurred to him since writing the following sections. This work is the basis of
the modern science of hydrodynamics, though some of the concepts are presented
in a state of still being evolved, such as that of pressure.
Click here for
Section. II : Which
discusses the equilibrium of fluids at rest, both within themselves, as well as
related to other causes.
Here Daniel Bernoulli sets the
stage for his work, discussing initially an antiquated account of surface
tension due to John Bernoulli, following which he delves into the shapes of
bladders filled with water, and investigates the action of surface forces
acting either normal to the surface or vertically downwards. This work involves
a number of references to a previous work on such surfaces, that I have
translated below, and which is called here CP1728, from the Comm. of the
Click here for CP1728 : A General Method : For
determining the curvature of a string extended by the forces observed to be
acting among themselves, according to some law, together with the
solution of certain new problems pertaining to that.
Click here for Section. III : Concerning the
velocities of fluids flowing from some kind of
vessel through an opening of any kind.
Here Daniel Bernoulli sets the
to work, and presents a fairly comprehensive account of what he has thought
out; for us perhaps the phrases potential ascent and actual descent indicates
the origin of potential energy in the development of energy conservation,
viewed from the light of fluid dynamics, where speeds and accelerations of
water in pipes can be measured by little more than a clock and a bucket. This
is a long and quite demanding section, thought the mathematics is essentially
simple. I have used the results of K. Flierl extensively.
Click here for
Section. IV : Concerned
with the various times, which are desired in the efflux of the water.
In this section an attempt is made
to calculate the times required to empty or change the level of the water
in cylindrical vessels under various
conditions, such as from a simple opening in or near the base, pipes of various
kinds inserted into the opening; these theoretical times are compared with 12
experimental times presented at the end of the section. The start of the flow
in an experiment is known to differ from the steady decline in the level that
follows ; an attempt is made to quantify this amount and to compare it with experimental
values.
Click here for
Section. V : Concerning
the motion of water from vessels being filled constantly.
In this section two different
ways are evaluated whereby a vessel can be kept filled with water while it
flows out through an orifice lower down; these result in the solution of
differential equations, relying on the methods of Section III. Bernoulli is
frustrated because some of the phenomena he discusses, such as leaping
fountains, are of a transient nature, and changes happened faster than could be
recorded at the time.
Click here for
Section. VI : Concerning
fluids not flowing out, or, moving
within the walls of the vessels.
In this section fluids are
considered either flowing indefinitely along a conical tube, or oscillating in
an isochronous manner in a U-tube; the theoretical models agree with the
experiments presented.
Click here for Section. VII : Concerning
the motion of water through submerged vessels, where it is shown by examples,
either how significantly useful the principle of the conservation of living
forces shall be, or as in these cases in which a certain amount is agreed to be
lost from these continually.
This section investigates the oscillations performed by a column of
water in a cylinder kept steady and erect in a large reservoir; the column is
released from rest either above or below the level of the outer surface, and
the heights and depths of the subsequent oscillations examined using the
conservation of the vis viva principle.
It is of special interest as the mass oscillating is not conserved. The theoretical models agree with the experiments presented
Click here for Section VIII : Concerning the
motion both of homogeneous as well as heterogeneous fluids through vessels of
irregular construction divided up into several parts, where the individual
phenomena of the trajectories of the fluids through a number of openings may be
explained and a part of the motion may be absorbed continually from the theory
of living forces; and with the general rules for the motions of the fluids
defined everywhere.
Click here for Section IX :
Concerning the motion of fluids which are not ejected by their own weight but
by certain other forces, and which concern hydraulic machines, especially where
the highest degree of perfection of the same can be given, and how they can be perfected further both
by the mechanics of solids as well as of fluids.
Click here for Section X :
Concerning the properties and motions of elastic fluids, but especially
those of air.
This is a fascinating chapter, in which Daniel Bernoulli
presents his ideas about gases, and essentially introduces the beginnings of
the kinetic theory of gases. There is a lot in the section, and if you are a physicist,
then you would probably gain something by reading it; a number of ideas are
presented here in a rudimentary form that went on to be developed further both
here in later chapters, and by others; the previous reviewers K.F. and G.H.M have made valiant
efforts to come to grips with this work, occasionally have made mistakes
themselves, misunderstood each other occasionally, and as no doubt I have done
as well. Most of the trouble lies around the refraction by the atmosphere,
which was presented originally with a wrong formula but correct tables.
Click here for Section XI : Concerning fluids acting
in a vortex, also those which may be contained in moving vessels. This is a
relatively short chapter, in which Bernoulli tries to reconcile the vortex
theory of planetary motion with Newton’s Law of gravitation, as well as
presenting the theory of fluid vortices, and some interesting experiments
involving fluids in accelerating frames of reference.
Click here for
Section XII : Which presents the static properties of moving fluids,
what I call static-hydraulics.
The theorems presented here are hence of a
time independent nature, and relate to the conservation of vis
viva, or in modern terms, the conservation of the total potential &
kinetic energy of water in an experiment. Thus, the rudiments of what is now
known as the Bernoulli Principle are presented here; the missing ingredient
being the idea of streamlines, later introduced by Euler in his Neue Gründsatze der Artellerie, along which lines the sum of these
energies is considered to be conserved. The experiments presented at the end
validate the theory mainly.
Click here for Section XIII : Concerning the reaction of fluids flowing out of vessels, and with the impulse of the same after they have flowed out, on planes which they meet.
This is the final chapter to the book, which became a sort of guiding light for further research; many of principles so dear to physicists can be found here in embryonic form. The business of investigating the action: reaction properties of a jet of water flowing out from a vessel are discussed and based on experiment. The final part investigates an unusual mode of propulsion for ships involving the discharge of water from a cistern, which is interesting for the light it sheds on how Bernoulli went about his calculations, if nothing else.
Ian
Bruce. 1st Sept., 2014 latest revision.
Copyright : I reserve the right to publish this translated work in book form.
You are not given permission to sell all or any part of this translation as an
e-book. However, if you are a student, teacher, or just someone with an
interest, you can copy part or all of the work for legitimate personal or
educational uses. See note on the index page. Please feel free to contact me if
you wish by clicking on my name here, especially if you have any relevant
comments or concerns.