Pipe flow: a gateway to turbulence
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Pipe flow: a gateway to turbulence Michael Eckert1 Received: 14 August 2020 © The Author(s) 2020
Abstract Pipe flow has been a challenge that gave rise to investigations on turbulence—long before turbulence was discerned as a research problem in its own right. The discharge of water from elevated reservoirs through long conduits such as for the fountains at Versailles suggested investigations about the resistance in relation to the different diameters and lengths of the pipes as well as the speed of flow. Despite numerous measurements of hydraulic engineers, the data could not be reproduced by a commonly accepted formula, not to mention a theoretical derivation. The resistance of air flow in long pipes for the supply of blast furnaces or mine air appeared even more inaccessible to rational elaboration. In the nineteenth century, it became gradually clear that there were two modes of pipe flow, laminar and turbulent. While the former could be accommodated under the roof of hydrodynamic theory, the latter proved elusive. When the wealth of turbulent pipe flow data in smooth tubes was displayed as a function of the Reynolds number, the empirically observed friction factor served as a guide for the search of a fundamental law about turbulent skin friction. By 1930, a logarithmic “wall law” seemed to resolve this quest. Yet pipe flow has not been exhausted as a research subject. It still ranks high on the agenda of turbulence research—both the transition from laminar to turbulent flow and fully developed turbulence at very large Reynolds numbers. Abbreviations DMA Deutsches Museum, Archiv, München GALCIT Guggenheim Aeronautical Laboratory of the California Institute of Technology GOAR Göttinger Archiv des Deutschen Zentrums für Luft- und Raumfahrt MPGA Max-Planck-Gesellschaft, Archiv, Berlin NACA National Advisory Committee for Aeronautics
Communicated by Olivier Darrigol.
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Michael Eckert [email protected] Deutsches Museum, Museumsinsel 1, 80538 Munich, Germany
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M. Eckert
ZAMM
Zeitschrift für Angewandte Mathematik und Mechanik
1 Introduction Turbulence emerged as a research field in its own right only in the twentieth century. Turbulent pipe flow, on the other side, has been observed much earlier by practitioners concerned with the design of water conduits. Pipe flow became the subject of hydraulics, a science as old as civilization. For centuries, pipe flow and hydraulics were almost synonymous. The word “hydraulics” amalgamates the Greek words for water (hydor) and pipe (aulos). For our ancestors in antiquity, hydraulics involved practical experience with pipe flow in conduits for water supply and in sophisticated devices such as water clocks or water organs (Rouse and Ince 1957, Chapters 1–3). Prior to the seventeenth century, however, there is no evidence of systematic pipe flow investigations, not to speak of turbulence. There are other empirical gateways to turbulence, such as the wake of bodies moving through water and air, jets, atmospheric turbulence, etc., but pipe flow deserves part
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