LEONARDIAN FLUID MECHANICS “LIBRO DELL’ACQUA” ENZO MACAGNO IIHR Monograph No. 120 Iowa Institute of Hydraulic Research The University of Iowa College of Engineering Iowa City, Iowa 52242-1585 February 2000 LEONARDIAN FLUID MECHANICS "LIBRO DELL’ACQUA” II ENZO MACAGNO Sponsored by National Science Foundation and National Endowment for the Humanities IIHR Monograph No. 120 Iowa Institute of Hydraulic Research The University of Iowa College of Engineering Iowa City, Iowa 52242-1585 FEBRUARY 2000 i Effetto delle mje regole Se ttu mj diciessi che partorisschano queste tue regole a che sono lor bone io ti rispondo eh elle tengon 1 briglia all ingegnieri inuestigatora a non si lasiare promettere a sse medesimo o a d altri cose inpossibili e ffarsi tenere matto o givntatore. CA 922R c. 1493-5 ii TABLE OF CONTENTS INTRODUCTION.........................................................................................1-5 THE NEVER COMPLETED BOOKS.........................................................6-16 REMARKS ON VARIOUS BOOKS....................................................... 17-31 THE BOOK ON WATER AND FLOW SCIENCE....................................32-39 REMARKS ON LEONARDO’S DYNAMICS...........................................40-45 IMAGINING THE PROEM TO THE "LIBRO DELL'ACQUA"........... 46-67 HYDROSTATICS IN THE "LIBRO DELL ACQUA".............................. 68-71 BIBLIOGRAPHY.......................................................................................72-83 LIBRO DELL’ACQUA. PROEMJO..................................................... 1-53 LIBRO DELL'ACQUA. IDROSTATICA.............................................1-67 iii INTRODUCTION Perhaps, of those who have written about Leonardo da Vinci, the only one to have had a life somewhat similar to his was Vasari. I feel compelled to say that I have studied Leonardo's manuscripts because of an irresistible drive to do it, but I admit that, as many others, having lived not only in different times but having had such a difference in the formative and in the productive years, I may be blind to many things that were natural and logical part of his work and his personality. In this kind of research, to avoid blind spots much work needs to be done. The study of the history before and during Leonardo's times may help to interpret and evaluate his work, but one should always be careful because history is written in other times, sometimes centuries after the events, and usually by people with an agenda of their own. If the historian is Italian one usually can expect a certain bias, sometimes over critical, sometimes over appreciative, while if the historian is non-Italian he will have one of a great variety of other biases many times due to lack of direct knowledge of the writings of Leonardo and other documents in Italian . If there is something I have in common with Leonardo is a deep interest in flow phenomena, the dominant theme of my life as a research engineer and a physicist and as a man deeply interested in the representative arts. I truly believe that flow is the most original subject in Leonardo's writings. All that is in fact the main justification for me to dare to interpret his work in such an area. Of all the publications I have read dealing with Leonardo as a student of flow, only those of Giacomelli and Arredi seem to have similar motivations. 1 I have studied Leonardo's manuscripts in its original form. This is intrinsically important, but it is also absolutely necessary because the notebooks are full of drawings. One must read drawings and text together as Leonardo left them. Occasionally, when in doubt about a passage's meaning, I have consulted - with scant success - available transcriptions and translations. I cannot conceive studying Leonardo without knowing Italian. Italian and two other languages from Italy were the ones I spoke during the first seven years of my life for the simple reason of having being bom to Italian parents natives of different regions. In the course of my life, I learnt other languages but continued to use and study Italian languages to this day. I consider always very important to gain the most direct access to Leonardo's mind. Fortunately the documents I work with were written by him and there seem to be no modifications. There is a difference between studying, for instance , the writings of classic Greek authors and those of Leonardo, because both his texts and figures are surely in the original form, while the others are not. Most of the notebooks have been transcribed and translated and anthologized. We know, however, that translations are never without flaws; the reality is that most translations are rather poor. I believe that a scholar should never descend to use translations in his research work. And in fact, even work that is not scholarly like biographies based loosely on Leonardo's life or personality (what used to be to called in Spanish, "biograffas noveladas"), are bound to be too much off the mark if the author does not know Italian and Italy. Of course, I am speaking of necessary, but by no means sufficient conditions. Even to penetrate with some depth in the world of Leonardo's notes and drawings on flow, one is never enough submerged into the world in which he lived. One thing I know well is that, due to the kind of documents available, the work I am doing is one of exegesis. Flow, as a phenomenon, is everywhere in nature. As a concept, it is one of the dominant traits of Leonardo da Vinci's mind; in fact, it pervades all his life and work. 2 Just like in the rivers and the seas of our planet one finds a physically present, usually observable, immense variety of flow patterns, an equally immense variety of dynamic patterns of flux and reflux is present in all the thoughts that come from him. In flow phenomena, shape is constantly changing and substance is constantly diffused and mixed, and undergoing reactions. For Leonardo, shape is something that is constantly fluent even when it achieves a final state, as he retires his hand to do something else, and we are left with a drawing or a painting, or one of his thoughts, full of flowing suggestions. Whatever we observe that comes from Leonardo, one faces something that conveys always a sense of flow, and more than that, of diffusive reacting flow to use a metaphor with modem fluid mechanics gist. What I mean is that flow in the abstractions of some hydromechanicians may be without transport and chemical phenomena, but it is never so in nature, and never sopn Leonardo's mind. This is so because a deep and a vivid sense of kinematicity impregnates all his work from art to zoology. What I am trying to explain is the feeling that one has when contemplating the work of some artists, like van Gogh's later paintings, so full of suggestions of motion, in spite of just being the completely static reality of some apparently excessive paint applied to canvases about a century ago. The scientific study of flow phenomena is relatively recent. The reader must realize that without a well established mathematical kinematics it is not possible to describe flows with any accuracy. I believe that regarding flow studies, Leonardo was probably better armed than most people alive today, outside fluid-mechanicists, because he made some remarkable inroads into kinematics which were not seen again for a long time after him [Macagno 1992a, 1995b]. To understand the slow progress of the mathematical descriptions of flow kinematics we may use a rather revealing feature: the study of deformations in the close neighborhood of a point. Even in turbulent flow, what seems a region very small compared with man's scaleps enormous relative to a region with still many molecules, and for such a neighborhood, kinematics of the continuum is valid and 3 the tensor of strain can be simply described [Aris 1962]. While mathematical descriptions of simple velocity fields was attained rather easily after vectorial calculus was available, there was not much progress concerning the theory of deformations, until it could be cast in terms of tensorial calculus. On the other hand, accurate experimental study of flows requires techniques of visualization and measurement which only became available about the same time that tensorial calculus provided a clear understanding of flow properties. In a purely geometrical way and with simple flow visualizations, Leonardo was able to gain a preview of such studies, but several centuries separate such views from the achievements that were actually effected only in the twentieth century, in the science of flow and transport phenomena. To be sure, we do not want to depict Leonardo's science of flow as a precursor of the modem science of flow, but to really comprehend what he accomplished and he failed to achieve, it is necessary and unavoidable to do the historical study with full knowledge of the contemporary knowledge in this field. This approach seems to disturb some historians of science, but we should not worry about that because they are uneasy simply because they lack the necessary scientific background that should be part of their training for the chosen profession. I cannot deprive myself from using all my knowledge, because of the weakness in the curriculum of other students of Leonardo's science of flow. It is remarkable that different topics in such a science require all a tensorial approach to be well understood. In addition to the strains around a point, we need tensors for good understanding of stresses (which include pressure as a particular case) and the correlations in turbulence. Within Leonardo's studies of flow phenomena none was second to his interest in water, and one of the books, to which he dedicated much time and work, was the one he expected to be a treatise on water science and technology. To work effectively in the composition of the "Libro dell'Acqua" one must first realize that such a book, that was 4 never put together by Leonardo da Vinci, is in fact part of a vast body of study and work, which is his lifelong investigation of flow in its many aspects, in science and engineering in art and technology.