DOCSLIB.ORG

The Hourglass

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Hourglass Home Search Collections Journals About Contact us My IOPscience The hourglass This content has been downloaded from IOPscience. Please scroll down to see the full text. 1993 Phys. Educ. 28 117 (http://iopscience.iop.org/0031-9120/28/2/010) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 166.111.44.118 This content was downloaded on 26/11/2014 at 13:37 Please note that terms and conditions apply. The hourglass CAJames, TA Yates, M E R Walford and D F Gibbs The flow of sand within an hourglass (a conical out the offices of the king and the meditations of hopper In faa) has been Shrdled using coloured the devout. The hourglass was used for timing the sand as a tracer material and gel-fixing to reveal two- and the four-hour watches (the periods of the distributions. A video was made of the flow, duty) on board a ship at sea, which apparently it seen through a glass plate. did quite adequately despite the ship's motion. Sermons too, on spacious Sundays, were once timed by the glass: a particularly humane measure An hourglass, an extinct and charming timepiece, if visible to the congregation, as well as to the is shown in figure 1. It is a closed flask consisting vicar. A somewhat hectic application of the hour- of two pear-shaped glass bulbs joined tip to tip glass principle involved a miniature threeminute with a small interconnectinghole. Fine, dry sand is glass, used to time divisions in the House of Lords; sealed inside. The quantity is carefully selected so the cry 'the sands are running out' would summon that it runs under gravity from one bulb to the tardy Lords to cast their votes before chamber other in a time interval approximating one hour. doors were locked as the last grains fell. Even more The infant offspring of the hourglass, the sand-in- miniature was a glass tbat ran for 28 seconds and glass egg-timer, is still often to be found in the was used to determine a ship's speed through the kitchen, for it is quick to operate and easy to clean. water: a mariner threw overboard, as the glass was Here is a pretty, end-of-term, egg-timer problem: turned, a log to which was attached a string in 'I have a double egg-timer. It has a thresminute which knots were tied every 47' 3" (14.39 m). The and a five-minute glass mounted in the one frame, number of knots that ran through the sailor's such that either or both can be inverted. That is fingers as the sand ran through the glass was taken handy because I like a soft-boiled egg and my wife as the ship's speed in 'knots'. A knot is still used to a hard-boiled one. My brother prefers a four- express the speed of a ship at sea although the minute egg when he visits; can we time his egg with ship's log is now mechanized. A knot is one our egg-timer? More generally, can any eccentric nautical mile per hour (1.852 kilometres per hour). (but integer) preference in the matter of egg- boiling be accommodated?' Watching the sand flow History The rate at which sand flows in an hourglass is fairly constant, unlike the flow of water in a clep- It seems that the hourglass was invented in the sydra, which decreases as the head of water falls. 15th century. Being reputedly of superior precision We found that to enquire why this is the case and certainly convenient in use, it rapidly super- made an interesting project. However, whether seded both the Roman water clock (the clqpsydra) we reached a satisfactory conclusion is open to and the graduated candle, once used to measure question. Simple measurements were made on the repeat- ability of the interval timed by an egg-timer and Mlchael WaHord has been a Lecturer in Physics at on how it was altered by being whirled around Bristol University since 1870. He previously lectured in the head, effectively increasing 'g'. We became Rhodesia (as it was then) and Barbados. His research interested in watching the flow of the sand and so has included radio echo-sounding through ice, ice we attempted to make visible the Bow wifhin the physics, rock magnetism and oceanography. Catherine James and Tim Yams graduaied in Physlcs from Bristol hourglass. For this purpose, rather than destroy in 1992, and David Glbbs recently retired from the an hourglass, we used a conical filter funnel. We Physics Department at Bristol University. shortened the stem and filled the funnel with he, Particularly interesting is the initial motion of the sand after the hole is opened. Movement is confined to a narrow vertical column above the hole and slightly wider than it. The motion is initiated at the hole, and from there a well defined interface between static and falling sand can be seen shooting rapidly upwards. It can be regarded as a kind of kinematic shock front across which a phase change from static to fluid phases occurs. The sand grains are not in free fall within the falling column hut collide with each other, giving rise to a kind of viscosity within the fluid sand mass, just as the molecules of a gas produce viscosity in a gas by their mutual collisions. Once the column is established, it continues to flow. It gradually broadens laterally, narrowing towards the base, and a conical pit appears in the upper, horizontal, surface of the sand. Avalanches of sand of various scale sizes can be seen cascading down the free surface of the pit, which grows larger therefore, whilst keeping a roughly constant semi-angle. The avalanching material feeds the ~~ central vertical column which, as figure 2 shows, Flgunl. An hourglass. becomes flared at the top. The remainder of the sand in the glass remains static until the surface pit has grown so large that it touches the edge of the dry, graded white sand into which bands of simi- funnel. A change then occurs in the behaviour of larly graded dark sand were carefully laid. The the sand: the previously static material surround- sand was allowed to flow out for a period of time, ing the flowing column starts slowly to sink. As it then it was stopped and its distribution was 'fixed' by pouring in a solution of gelatin. When this set the cast could be removed, sectioned and the dist,.ibution of coloured sand exa,,,ined to reveal Figure 2. Asand cast showing how initially horizontal marked layers of sand are distorted by the flow. The something Of the (figure The resuks motion 2)' upper, wnical mass of dark sand was carefully poured were interesting, so we made a video recording of in after the flow experiment was stopped but prior to the the motion in the following Way: a semi-fwd is addition ofthe casting agent (gelatin solution),which prepared by dividing a funnel into two equal would otherwise have disturbed the distribution of halves by a vertical cut and cementing one half to a interest. sheet of glass. This semi-funnel is filled with sand containing markers just as before, but this time the flow can be seen through the glass from beginning to end and can be recorded using the video camera. It is important to ascertain whether the flow seen in this way is essentially similar to that which happens inside the complete funnel. It was indeed found that the pattern of flow did not differ greatly from that observed in the dismted cast. Also a sand-cast made in the semi-funnel looked similar on internal vertical surfaces and on the exposed flat face. We conclude from this that the video record does provide reliable information as to the flow regimes within a funnel. A centimetre scale and clock were included in the field of view of the camera so that, in playback mode, we were able to stop the video and make measurements on a single frade or measure displacements between frames. 118 does so it must contract radially, but it does this Osbome Reynolds, better known for his studies keeping the coloured bands within it flat and of the onset of turbulence in flowing fluids, horizontal. The faster flowing vertical column of observed in 1885 that the initiation of flow in sand sand now &cremes in diameter until eventually all is always accompanied by a dilation, for the grains the sand has run o.ut. in static sand are packed closely together and no All of this is very pretty to watch, especially motion is possible without at least some elbow when run backwards, but what is the physics room, so to speak. Reynolds described the follow- involved? ing simple demonstration of dilation: a balloon is filled with sand and water and a glass tube is inserted into the neck in such a way that the water level can be seen in the tube. When the balloon is The physics of flowing sand given a sharp squeeze the water level goes down because of dilation of the sand-water mixture. The problem of understanding flow in granular Dilation also occurs in our hourglass: as the initial and in powdery materials is a subtle one. It has shock front passes upwards, the state of the sand exercised scientists for many years and continues changes from static to fluid and the specific volume to do so (Hill and Wu 1992).
Load more

Recommended publications
  • Hourglass User and Installation Guide About This Manual
    HourGlass Usage and Installation Guide Version7Release1 GC27-4557-00 Note Before using this information and the product it supports, be sure to read the general information under “Notices” on page 103. First Edition (December 2013) This edition applies to Version 7 Release 1 Mod 0 of IBM® HourGlass (program number 5655-U59) and to all subsequent releases and modifications until otherwise indicated in new editions. Order publications through your IBM representative or the IBM branch office serving your locality. Publications are not stocked at the address given below. IBM welcomes your comments. For information on how to send comments, see “How to send your comments to IBM” on page vii. © Copyright IBM Corporation 1992, 2013. US Government Users Restricted Rights – Use, duplication or disclosure restricted by GSA ADP Schedule Contract with IBM Corp. Contents About this manual ..........v Using the CICS Audit Trail Facility ......34 Organization ..............v Using HourGlass with IMS message regions . 34 Summary of amendments for Version 7.1 .....v HourGlass IOPCB Support ........34 Running the HourGlass IMS IVP ......35 How to send your comments to IBM . vii Using HourGlass with DB2 applications .....36 Using HourGlass with the STCK instruction . 36 If you have a technical problem .......vii Method 1 (re-assemble) .........37 Method 2 (patch load module) .......37 Chapter 1. Introduction ........1 Using the HourGlass Audit Trail Facility ....37 Setting the date and time values ........3 Understanding HourGlass precedence rules . 38 Introducing
    [Show full text]
  • “The Hourglass”
    Grand Lodge of Wisconsin – Masonic Study Series Volume 2, issue 5 November 2016 “The Hourglass” Lodge Presentation: The following short article is written with the intention to be read within an open Lodge, or in fellowship, to all the members in attendance. This article is appropriate to be presented to all Master Masons . Master Masons should be invited to attend the meeting where this is presented. Following this article is a list of discussion questions which should be presented following the presentation of the article. The Hourglass “Dost thou love life? Then squander not time, for that is the stuff that life is made of.” – Ben Franklin “The hourglass is an emblem of human life. Behold! How swiftly the sands run, and how rapidly our lives are drawing to a close.” The hourglass works on the same principle as the clepsydra, or “water clock”, which has been around since 1500 AD. There are the two vessels, and in the case of the clepsydra, there was a certain amount of water that flowed at a specific rate from the top to bottom. According to the Guiness book of records, the first hourglass, or sand clock, is said to have been invented by a French monk called Liutprand in the 8th century AD. Water clocks and pendulum clocks couldn’t be used on ships because they needed to be steady to work accurately. Sand clocks, or “hour glasses” could be suspended from a rope or string and would not be as affected by the moving ship. For this reason, “sand clocks” were in fairly high demand in the shipping industry back in the day.
    [Show full text]
  • The Quantum Hourglass
    The Quantum Hourglass Approaching time measurement with Quantum Information Theory Paul Erker Master Thesis, ETH Z¨urich September 30, 2014 Abstract In this thesis a general non-relativistic operational model for quan- tum clocks called quantum hourglass is devised. Taking results from the field of Quantum Information Theory the limitations of such time measurement devices are explored in different physical and information- theoretic scenarios. It will be shown for certain cases that the time resolution of the quantum hourglass is limited by its power consump- tion. Supervisors: Prof. Dr. Renato Renner Dr. Yeong-Cherng Liang and Sandra Rankovi´c 1 Contents 1 The Past 3 2 The Context 6 2.1 Margolus-Levitin bound . 8 2.1.1 A generalized bound . 10 2.1.2 The adiabatic case . 12 2.2 Communication rate vs power consumption . 13 3 Quantum Hourglass 16 3.1 Time resolution . 19 3.2 The hourglass as a quantum computer . 20 3.2.1 CNOT hourglass . 21 3.2.2 SWAP hourglass - quantum logic clock . 23 3.2.3 Algorithmic hourglass - Mesoscopic implementation . 25 3.3 Thermal hourglass . 26 3.4 de Broglie hourglass . 33 3.5 Relativistic considerations . 36 4 Synchronization and Causality 39 5 The Future 43 6 Conclusion 49 7 Acknowledgements 50 8 References 51 2 1 The Past "Time is what the constant flow of bits of sand in an hourglass measures,"one says. Akimasa Miyake [1] Time enters Quantum Theory in manifold ways. Since the early days of quantum theory this led to heated discussions about its nature. In a letter Heisenberg wrote to Pauli in November 1925, he commented: Your problem of the time sequence plays, of course, a fundamen- tal role, and I had figured out for my own private use (Hausge- brauch) something about it.
    [Show full text]
  • The Sundial Use the Sun 52
    H The sundial Use the Sun 52 time learning outcomes materials needed 55 minutes, To: • 12 large stones spread across • know that you can tell • scissors two days the time using a sundial • glue • tell the time using the Sun • a stick around • discover that long ago 150 centimetres long it was much more difficult • a large protractor to tell the time than it is • a marker pen today • a compass to tell where North is end product • optional: • a small sundial indoors extra small stones • a large sundial outdoors Preparation For the activity The large sundial you will need a playing field that is in sunlight most of the day. What time is it? 5 min. Ask if any of the children is wearing a watch. Why is it handy to have a watch? Explain that 600 years ago nobody had a watch. Ask how the people back then Tip. Long ago people knew what time it was. Before the mechanical clock was invented, people some- also used other times used the sun to tell the time. They did this using a sundial. devices to tell the time, such Have any children ever seen a sundial? Do they know how it works? Explain that as the hourglass. a sundial has a stick or pointer that makes a shadow. This is called the gno- Lesson 50 shows mon. It is important that in the Northern hemisphere the gnomon always points how to make an North, or you will not be able to read the sundial. Explain that the Earth turns hourglass and use on its axis.
    [Show full text]
  • The Hourglass Model Revisited
    Department: Affective Computing and Sentiment Analysis Editor: Erik Cambria, Nanyang Technological University The Hourglass Model Revisited Yosephine Susanto Bee Chin Ng Nanyang Technological University Nanyang Technological University Andrew G. Livingstone Erik Cambria University of Exeter Nanyang Technological University Abstract—Recent developments in the field of AI have fostered multidisciplinary research in various disciplines, including computer science, linguistics, and psychology. Intelligence, in fact, is much more than just IQ: it comprises many other kinds of intelligence, including physical intelligence, cultural intelligence, linguistic intelligence, and emotional intelligence (EQ).Whiletraditionalclassificationtasksand standard phenomena in computer science are easy to define, however, emotions are still a rather mysterious subject of study. That is why so many different emotion classifications have been proposed in theliteratureandthereisstillnocommon agreement on a universal emotion categorization model. In this article, we revisit the Hourglass of Emotions, an emotion categorization model optimized for polarity detection, based on some recent empirical evidence in the context of sentiment analysis. This new model does not claim to offer the ultimate emotion categorization but it proves the most effective for the task of sentiment analysis. & IN 1872, CHARLES Darwin was one of the first always been a big challenge for the research scientists to argue that all humans, and even ani- community.2;3 To date, in fact, there are still mals, show emotions through remarkably simi- active debates on whether some basic emotions, lar behaviors.1 Since then, there has been broad e.g., surprise,4 should be defined as emotions at consensus on how and why emotions have all. In this work, we do not aim to initiate any new evolved in most creatures.
    [Show full text]
  • The Dynamics of Granular Flow in an Hourglass
    Original papers Granular Matter 3, 151–164 c Springer-Verlag 2001 ! The dynamics of granular flow in an hourglass Christian T. Veje, P. Dimon Abstract We present experimental investigations of flow [2–5]. Traditionally, an hourglass consists of two glass am- in an hourglass with a slowly narrowing elongated stem. poules, partly filled with grains, connected by a small hole The primary concern is the interaction between grains in the stem. Typically, ballotini (small glass beads), sand, and air. For large grains the flow is steady. For smaller marble powder, and even crushed egg shells have been grains we find a relaxation oscillation (ticking) due to the used as the granular material [1]. Recently, the hourglass counterflow of air, as previously reported by Wu et al. has become a source of interest to the physics communi- [Phys. Rev. Lett. 71, 1363 (1993)]. In addition, we find ty as a convenient simple system to investigate granular that the air/grain interface in the stem is either stationary flows [1,6–10]. or propagating depending on the average grain diameter. The flow of granular materials has been found to ex- In particular, a propagating interface results in power-law hibit a wide range of different phenomena. In particular, relaxation, as opposed to exponential relaxation for a sta- density waves and shock waves are common in dry granu- tionary interface. We present a simple model to explain lar flows. Density patterns due to rupture zones as grains this effect. We also investigate the long-time properties of flow through hoppers have been observed using X-ray the relaxation flow and find, contrary to expectations, that imaging [11–13].
    [Show full text]
  • Lunar Distances Final
    A (NOT SO) BRIEF HISTORY OF LUNAR DISTANCES: LUNAR LONGITUDE DETERMINATION AT SEA BEFORE THE CHRONOMETER Richard de Grijs Department of Physics and Astronomy, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia Email: [email protected] Abstract: Longitude determination at sea gained increasing commercial importance in the late Middle Ages, spawned by a commensurate increase in long-distance merchant shipping activity. Prior to the successful development of an accurate marine timepiece in the late-eighteenth century, marine navigators relied predominantly on the Moon for their time and longitude determinations. Lunar eclipses had been used for relative position determinations since Antiquity, but their rare occurrences precludes their routine use as reliable way markers. Measuring lunar distances, using the projected positions on the sky of the Moon and bright reference objects—the Sun or one or more bright stars—became the method of choice. It gained in profile and importance through the British Board of Longitude’s endorsement in 1765 of the establishment of a Nautical Almanac. Numerous ‘projectors’ jumped onto the bandwagon, leading to a proliferation of lunar ephemeris tables. Chronometers became both more affordable and more commonplace by the mid-nineteenth century, signaling the beginning of the end for the lunar distance method as a means to determine one’s longitude at sea. Keywords: lunar eclipses, lunar distance method, longitude determination, almanacs, ephemeris tables 1 THE MOON AS A RELIABLE GUIDE FOR NAVIGATION As European nations increasingly ventured beyond their home waters from the late Middle Ages onwards, developing the means to determine one’s position at sea, out of view of familiar shorelines, became an increasingly pressing problem.
    [Show full text]
  • Hourglass User and Installation Guide About This Manual
    HourGlass Usage and Installation Guide Version 6 Release 1 SC23-8561-01 Note! Before using this information and the product it supports, be sure to read the general information under “Notices” on page 97. Third Edition (May 2012) This edition applies to Version 6 Release 1 Mod 0 of IBM® HourGlass (program number 5655-U42) and to all subsequent releases and modifications until otherwise indicated in new editions. Order publications through your IBM representative or the IBM branch office serving your locality. Publications are not stocked at the address given below. IBM welcomes your comments. For information on how to send comments, see “How to send your comments to IBM” on page vii. © Copyright IBM Corporation 1992, 2012. US Government Users Restricted Rights – Use, duplication or disclosure restricted by GSA ADP Schedule Contract with IBM Corp. Contents About this manual ..........v Using the CICS Settings Control Facility ....30 Organization ..............v Using the CICS Audit Trail Facility ......31 Summary of amendments for Version 6.1 Usage and Using HourGlass with IMS message regions . 31 Installation Guide refresh ..........v HourGlass IOPCB Support ........31 Summary of amendments for Version 6.1 ....vi || Running the HourGlass IMS IVP ......31 Using HourGlass with DB2 applications .....32 How to send your comments to IBM . vii Using HourGlass with the STCK instruction . 33 Method 1 (re-assemble) .........33 If you have a technical problem .......vii Method 2 (patch load module) .......33 Using the HourGlass Audit Trail Facility ....34 Chapter 1. Introduction ........1 Understanding HourGlass precedence rules . 35 Setting the date and time values ........2 || Introducing the HourGlass Repository ......3 Chapter 4.
    [Show full text]
  • Inside the Orion Nebula
    AMATEUR ASTRONOMERS DEEP-SKY OBSERVING find the Orion Nebula (M42) irresistible. It’s large, bright, On a brisk winter night, the Orion Nebula beckons astronomers and detailed. Las Vegas astro- and observers alike. ⁄⁄⁄ BY RAYMOND SHUBINSKI photographer George Gre- aney shot it with his 6-inch Astro-Physics EDF apochro- matic refractor at f/7. This image is a digital composite of two 45-minute exposures on hypered 120-format View the sky’s Kodak PPF Pro 400 film. greatest nebula is composed of hundreds of billions of stars The Orion Nebula (M42) is so named and massive amounts of gas and dust. Our because it lies within Orion the Hunter, a constellation that solar system resides in the Perseus arm, dominates the winter sky. To find the nebula, look below about two-thirds of the way out from the galactic center. Orion’s belt where his sword hangs. Your eyes alone will see Our earthbound view is rather different. the center star as fuzzy. Binoculars help, but also reveal more On a clear summer night in the Northern Hemisphere, the glow of the Milky Way fuzz. Look through a telescope, however, Stellar neighborhood stretches from Cassiopeia in the northeast and you’ll never forget it. For here lies one The Orion Nebula’s position in our galaxy to Scorpius in the south. From this vantage of the showpiece celestial objects — a stel- is well known. If we could view the Milky point, we’re looking along the galaxy’s rim. lar nursery that, after being observed for Way from above, it would appear as a vast Toward Scorpius is the central part of the hundreds of years, still has a lot to reveal.
    [Show full text]
  • The Weight of Time Ian H
    Note The Weight of Time Ian H. Redmount, Department of Science and Mathematics, Parks College of Engineering and Aviation, Saint Louis University, St. Louis, MO 63156; and Richard H. Price, Department of Physics, University of Utah, Salt Lake City, UT 84112 s physics teachers, we are impulse is equal to the always on the lookout for net change in momen- Aproblems that can illustrate tum of the system dur- the sometimes subtle implications of ing the time interval. physical laws, particularly problems We can apply this to the that can be concisely stated and easi- interval that starts just ly visualized. One such problem is before the sand begins remarkable for the way it illustrates to flow, and ends just several fundamental principles of after it stops flowing. At mechanics. It is a wonderful problem both these endpoints the for stimulating discussion, even system has no momen- among students who have had only tum, so the change in an introduction to mechanics. momentum—and thus Fig. 1. Three types of hourglasses for which calculations are Suppose we have an old-fashioned the impulse—are zero. done: (a) cylindrical “egg timer” type, (b) spherical vessel type, hourglass, like any of those pictured in This means that the and (c) conical hourglass. Fig. 1, and suppose that it has been sit- average force on the hourglass-and- tem is moving downward at constant ting inactive on a perfect and perfectly sand system is zero. There are only velocity, then there is no net force sensitive scale which reads exactly two forces acting on the system.
    [Show full text]
  • Clock Hour: Time to Learn
    Clock Hour: Time to Learn Seconds : Minutes : Hours Origin of Time The mathematician and astronomer Theodosius of Bithynia (ca. 160 BCE- ca. 100 BCE ) is said to have invented a universal sundial that could be used anywhere on Earth. The Romans adopted the Greek sundials, and the first record of a sun-dial in Rome is 293 BC according to Pliny. Origin of Time An hourglass keeping track of elapsed time. The hourglass was one of the earlier timekeeping devices and has become a symbol of the concept of time Origin of Time The first mechanical clock was made in 723 A.D. by a monk and mathematician I-Hsing. It was an astronomical clock and he called it the "Water Driven Spherical Birds-Eye-View Map of The Heavens." Origin of Time A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element. The advantage of a pendulum for timekeeping is that it is a harmonic oscillator; it swings back and forth in a precise time interval dependent on its length, and resists swinging at other rates. From its invention in 1656 by Christiaan Huygens until the 1930s, the pendulum clock was the world's most precise timekeeper, accounting for its widespread use. Time is Money!!! What is Controlled by Time? What is Controlled by Time? What is Controlled by Time? And of Course……… Education!! Carnegie Unit (Clockhours) • If you earned a high school diploma, or a certificate from a technical school, or any degree from any college or university in the United States, you served your time.
    [Show full text]
  • Pressure and Motion of Dry Sand – Translation of Hagen's Paper From
    Granular Matter manuscript No. (will be inserted by the editor) Brian P. Tighe · Matthias Sperl Pressure and Motion of Dry Sand – Translation of Hagen’s Paper from 1852 August 24, 2018 Abstract In a remarkable paper from 1852, Gotthilf Hein- particle diameter, which is consistent with more recent mea- rich Ludwig Hagen measured and explained two fundamen- surements. tal aspects of granular matter: The first effect is the satura- Hagen’s work lays out the basis of the so-called hour- tion of pressure with depth in a static granular system con- glass theory where the flow of granular material is found to fined by silo walls – generally known as the Janssen effect. be independent of the filling height in the container, thus al- The second part of his paper describes the dynamics ob- lowing the measure of time with an hourglass [7, sec 10.4]. served during the flow out of the container – today often Later work both confirms and extends Hagen’s early analy- called the Beverloo law – and forms the foundation of the sis [9]. More recently, a lot of work has been devoted to un- hourglass theory. The following is a translation of the origi- derstanding the fundamental differences between fluid and nal German paper from 1852. granular flows [10]. While on the level of the individual grains the probability of arching at the opening is a matter of current investigations [11], Hagen provides a successful route to a continuum description of the flow by the rescaling 1 Introduction of the diameter of the opening. Gotthilf Heinrich Ludwig Hagen is most renowned for his contributions to the study on laminar flow in pipes; his mea- 2 Gotthilf Heinrich Ludwig Hagen, Pressure and Motion surements published in 1839 studied what is now well-known of Dry Sand, 19th January 1852 as the (Hagen-)Poiseuille law [1, 2].
    [Show full text]