Reynolds Experiment

7 Key excerpts on "Reynolds Experiment"

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  Introduction to Thermal and Fluid Engineering

  • Allan D. Kraus, James R. Welty, Abdul Aziz(Authors)
  • 2011(Publication Date)
  • CRC Press

    (Publisher)

  This behavior was clearly due to the orderly character of laminar flow in the first case and the chaotic nature of tur-bulent flow in the latter case. It was clear, in Reynolds’ experiment, that the transition from laminar to turbulent flow was velocity dependent. In investigating other variables affecting this transition, he found that pipe diameter, fluid density, and fluid viscosity were also important. The combination of these four variables into a dimensionless parameter produced the Reynolds number Re = ˆ Vd (16.1) named in honor of the British engineer, Sir Osborne Reynolds, whose experiment first demonstrated its importance. The Reynolds number is often specified on the basis of the length dimension employed. For example, when the Reynolds number is based on the diameter, Re d is often used; when a length or a length coordinate is employed, we frequently see the Reynolds number indicated by Re L or Re x . The transition from laminar to turbulent flow in a pipe is generally agreed to occur at a value of Re equal to 2300. Below this value, the flow is definitely laminar. For carefully controlled experiments, laminar flow has been reported for values of Re as high as 40,000. However, at high values of Re, a slight disturbance will cause the flow to become turbulent. Laminar flows at a Reynolds number above 2300 are therefore unstable and this value, 2300, is the generally accepted value for the critical Reynolds number for pipe flow. Laminar Turbulent Pipe Smooth, Well-rounded Entrance (a) (b) Dye Dye Streak D FIGURE 16.1 (a) Features of the Reynolds’ experiment and (b) flow behaviors. Viscous Flow 505 16.3 Fluid Drag In Example 15.1, in the preceding chapter, we used dimensional analysis to determine that the effects of flow normal to a cylinder are related by two parameters 1 = F / d 2 ˆ V 2 and 2 = d ˆ V The second of these dimensionless quantities, 2 , is observed to be 1/Re or we could simply use Re, which is the better-accepted dimensionless form.

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  Investigation of High Reynolds Number Pipe Flow

  • (Author)
  • 2015(Publication Date)
  • Cuvillier Verlag

    (Publisher)

  (c) Turbulent structures in pipe flow. Figure 2.2: Experimental results performed by Reynolds [85] in 1883. From [85]. water after a certain distance from the entrance. The result is completely filled tube, which is schematically depicted in Figure 2.2b. A steady increase in the velocity up to the maximum caused the mixing point to move upstream, but it never reached the inlet of the tube. These observations together with his theoretical considerations gave scien-tists the understanding of the commonly known laminar and turbulent flow. Another fundamental result from this simple but at the same time very effective experiment is the observed relation between the inertial and viscous force, which is since then well-known as the Reynolds number Re = inertialforce viscousforce = ρ L c U c μ = L c U c ν , where L c is a characteristic length, U c is a characteristic velocity, ρ is the density of the working fluid, μ is the dynamic viscosity and ν = μ / ρ -the kinematic viscosity of the working fluid. This non-dimensional relation gives scientist the possibility to investigate pipe flow under different conditions, and compare the results, anyway. A detailed literature review on the historic development of pipe flow is among others presented by Zagarola [108]. In the following chapter the focus is on some selected references, which are confined through different ranges in the Reynolds number. Dieses Werk ist copyrightgeschützt und darf in keiner Form vervielfältigt werden noch an Dritte weitergegeben werden. Es g ilt nur für den persönlichen Gebrauch. 2 Literature Review 12 2.1 The Onset of Sustained Turbulence From theory we know that pipe flow is linear stable and hence laminar. Contrarily, in most practical and experimental applications the turbulent flow state is achieved even for lower Reynolds numbers. This is a well-known paradox, which is the subject of various experiments and numerical analysis during the last decade.

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  Fundamentals of Momentum, Heat, and Mass Transfer

  • James Welty, Gregory L. Rorrer, David G. Foster(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  Water was allowed to flow through a transparent pipe, as shown, at a rate controlled by a valve. A dye having the same specific gravity as water was introduced at the pipe opening and its pattern observed for progressively larger flow rates of water. At low rates of flow, the dye pattern was regular and formed a single line of color as shown in Figure 12.1(a). At high flow rates, however, the dye became dispersed throughout the pipe (a) Re < 2300 (b) Re > 2300 Water Water Dye Dye Valve Valve Figure 12.1 Reynolds’s experiment. 129 cross section because of the very irregular fluid motion. The difference in the appearance of the dye streak was, of course, due to the orderly nature of laminar flow in the first case and to the fluctuating character of turbulent flow in the latter case. The transition from laminar to turbulent flow in pipes is thus a function of the fluid velocity. Actually, Reynolds found that fluid velocity was the only one variable determining the nature of pipe flow, the others being pipe diameter, fluid density, and fluid viscosity. These four variables, combined into the single dimensionless parameter Re Dρ μ (12-1) form the Reynolds number, symbolized Re, in honor of Osborne Reynolds and his important contributions to fluid mechanics. For flow in circular pipes, it is found that below a value for Reynolds number of 2300, the flow is laminar. Above this value the flow may be laminar as well, and indeed, laminar flow has been observed for Reynolds numbers as high as 40,000 in experiments wherein external disturbances were minimized. Above a Reynolds number of 2300, small disturbances will cause a transition to turbulent flow, whereas below this value distur- bances are damped out and laminar flow prevails. The critical Reynolds number for pipe flow thus is 2300. ▶ 12.2 DRAG Reynolds’s experiment clearly demonstrated the two different regimes of flow: laminar and turbulent.

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  The John Zink Hamworthy Combustion Handbook

  Volume 1 - Fundamentals

  • Charles E. Baukal Jr.(Author)
  • 2012(Publication Date)
  • CRC Press

    (Publisher)

  A famil-iar example demonstrating laminar and turbulent flow regimes is shown in Figure 9.7. In Figure 9.7, smoke rises from soldering iron in a room of still air. Notice the smoke initially rises up in a fine line and flows smoothly (laminar) for a distance of about 6 in. When the smoke line rises up some distance, it suddenly transitions into a chaotic motion (turbulent). Turbulent flows are easier to find than laminar flows; for example, flow from volcanoes, wind, rivers, and exhaust from a jet engines are all turbulent. From his experiments, Reynolds made a famous dis-covery. He found that below a certain velocity, the flow always became laminar. As the velocity was increased, turbulent flow could always be achieved. In addition, Temperature (°C) 1 × 10 –5 1 × 10 –4 1 × 10 –3 1 × 10 –2 1 × 10 –1 1.0 Dynamic viscosity, μ (N-s/m 2 ) 120 100 80 60 40 20 0 –20 Methane Kerosene SAE10W-30 oil Castor oil Glycerin SAE 10 W oil Octane Heptane Air Carbon dioxide Hydrogen Water FIGURE 9.3 Dynamic viscosity as a function of temperature for various fluids. 236 The John Zink Hamworthy Combustion Handbook Reynolds was able to generalize his results into a non-dimensional parameter, which today is known as the Reynolds number, Re. It is defined as follows: Re = VD ν (9.10) where V is the velocity in the pipe D is the pipe diameter ν is the kinematic viscosity As a practical matter, pipe flows having a Reynolds number less than 2300 are laminar, and flows having a Reynolds number greater than 4000 are turbulent. In addition to determining the type of flow, Reynolds numbers have been proven to also scale the intensity of turbulence in a flow. That is, higher Reynolds numbers result in greater vortex generation and faster mixing rates. As a result, Reynolds number calculations are very common in the petrochemical industry. They are used to scale flow coefficients, friction factors, heat transfer rates, and mass transfer rates.

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  Automotive Aerodynamics

  • Joseph Katz(Author)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  Fig. 1.7 ) is discussed briefly in the next section.

  4.6 High Reynolds Number Flows and Turbulence

  The concept of laminar and turbulent flows, as was mentioned briefly in Section 1.5.2 , was investigated by Osborne Reynolds during the late nineteenth century. In his experiments (circa 1883) he demonstrated that laminar flow transitions to turbulent flow when a nondimensional number (the Reynolds number) is reached. Because the next two chapters will focus on this high Reynolds number flow region, the subject of turbulent flow is revisited here briefly. For this discussion, consider a velocity-measuring probe that is inserted into the turbulent free-stream (as in Fig. 1.7 ) and the momentary velocity is recorded. Although the average speed is in one direction only, small fluctuations in the other directions can be detected, as well. As an example, Fig. 4.4 shows the time dependent recording of the momentary velocity in the x direction.

  Figure 4.4

  Fluctuation of the u velocity component over time (t) and the average velocity

  Based on the data in Fig. 4.4 the average velocity for the time period between t1 and t2 is defined as

  (4.21)

  and the momentary velocity vector will have components in all directions (u′, v′, w′)

  (4.22)

  and the average velocity is in one direction only

  This short introduction suggests that turbulent flows are time dependent and three-dimensional! This feature significantly complicates the fluid mechanic model and usually average flow based models are used. The next question is related to how, and under which conditions does turbulence evolve? Usually strong shear conditions near solid surface or in open jets can lead to turbulence, but most laminar flows may turn turbulent if the Reynolds number is increased (up to a point called the transition point). The original Reynolds Experiment (in 1883) suggested that transition from laminar to turbulent flow inside a smooth pipe occurs at about Re = 2000. For external flows over streamlined shapes, such as airfoils, transition occurs at much higher Reynolds numbers (e.g., Re = 105 –107

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  Fluid Mechanics for Civil Engineers

  SI edition

  • N.B. Webber(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  78 The experiments, which were necessarily of somewhat limited scope and accuracy, tended to indicate that the head loss was proportional to V raised to a power which was near to 2. On the assumption then that r 0 = cF 2, Eq. (5.8) becomes Apjw — 4cV2ALfpgD. Putting A = 8 c/p and integrating along the pipe we obtain h{ = XLV2/2gD , which is in the desired form. It also follows from Eqs. (5.7) and (5.8) that THE CONTRIBUTION OF OSBORNE REYNOLDS §5.4 It was realised at an early stage that the friction factor varied not only with the roughness of the pipe walls but also with the diameter and velocity. This indicated that A was not a simple coefficient, as once supposed, but an overall coefficient, which had to represent the com-bined effect of several variables. Furthermore hf was not dependent on the square of F but on F raised to some slightly lesser power. 5.4 The Contribution of Osborne Reynolds 5.4.1 Dye Experiments Osborne Reynolds1 in his classic experiments at Manchester University demonstrated most effectively the characteristics of laminar and turbu-lent flow. He showed that, under suitable conditions, the two types of flow could be made to occur in the one pipe. His apparatus was ex-tremely simple and consisted essentially of a glass tube through which water could be passed at varying velocities. Provision was made for the insertion of a thin jet of aniline dye into the stream of water at the upstream end. Commencing with a very low water velocity, it was found that the dye remained intact in the form of a thin slender thread extending the whole length of the tube as in Fig. 5.2(a). This indicated that the particles of liquid were moving in straight parallel paths and that the flow was therefore laminar. The velocity of the water was then gradually increased and at a certain point the thread broke up, as in Fig.

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  Fluid and Particle Mechanics

  Chemical Engineering Division

  • S. J. Michell, M. Perry(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  The work has since become famous for the formulation of a parameter now bearing his name. The parameter takes the form of a dimehsionless group of terms and is defined by Re = ^ l ( U3) where the symbols v, , and μ refer .to fluid in flow through a pipe of diameter D, while Re is the symbol usually given to the so defined parameter, and named the Reynolds number. The formulation contained in eq. (1.13) is the outcome of the most successful correlation of experimental data in a long series of attempts to produce a means of predicting the nature of flow in pipes, and—as will be shown later—in other confinements as well. The significance of the correlation may be appreciated from the fact that—among other things—it enables us to draw a demarcation line between the laminar and non-lami-nar pattern of flow, a distinction of particular interest in the mathematical analysis of flow phenomena. Experimental evidence led Reynolds to the specification of a useful number, later called the critical number, for the dimensionless group to mark the dividing line between the two patterns of flow. He gave 1400 as 22 FLUID AND PARTICLE MECHANICS his first value, but later corrected this figure to between 1900 and 2000. The latter has since been accepted as the upper limit for laminar flow, and the velocity corresponding to a Reynolds number of 2000 has been specified as the critical velocity. The present-day approach to the Reynolds number, as a criterion of the nature of flow, is more conventional than realistic. Although there is strong evidence that flow in pipes is always laminar for Reynolds numbers up to 2000, there is also a great deal of evidence that fully turbu-lent flow may not develop until this number exceeds 10,000. It will be recalled at this stage that this kind of flow is characterised by a chaotic movement of fluid particles as distinct from an orderly movement, char-acteristic of laminar flow.

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