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5487 results in Thermal-fluids engineering

Page 82 of 275

  • 1 - Introduction

  • Roger C. Baker
  • Book:
    Flow Measurement Handbook
    Published online:
    05 August 2016
    Print publication:
    25 August 2016, pp 1-26
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  • Summary

    Initial Considerations

    Some years ago at Cranfield, where we had set up a flow rig for testing the effect of upstream pipe fittings on certain flowmeters, a group of senior Frenchmen was being shown around and visited this rig. The leader of the French party recalled a similar occasion in France when visiting such a rig. The story goes something like this.

    A bucket at the end of a pipe seemed particularly out of keeping with the remaining high-tech rig. When someone questioned the bucket's function, it was explained that the bucket was used to measure the flow rate. Not to give the wrong impression in the future, the bucket was exchanged for a shiny, new, high-tech flowmeter. In due course, another party visited the rig and observed the flowmeter with approval. “And how do you calibrate the flowmeter?” one visitor asked. The engineer responsible for the rig then produced the old bucket!

    This book sets out to guide those who need to make decisions about whether to use a shiny flowmeter, an old bucket, nothing at all or a combination of these! It also provides information for those whose business is the design, manufacture or marketing of flowmeters. I hope it will, therefore, be of value to a wide variety of people, both in industry and in the science base, who range across the whole spectrum from research and development through manufacturing and marketing. In my earlier book on flow measurement (Baker 1988a/1989, 2002b, 2003), I provided a brief statement on each flowmeter to help the uninitiated. This book attempts to give a much more thorough review of published literature and industrial practice.

    This first chapter covers various general points that do not fit comfortably elsewhere. In particular, it reviews guidance on the accuracy of flowmeters (or calibration facilities).

    The second chapter reviews briefly some essentials of fluid mechanics necessary for reading this book. The reader will find a fuller treatment in Baker (1996), which also has a list of books for further reading.

    A discussion of how to select a flowmeter is attempted in Chapter 3, and some indication of the variety of calibration methods is given in Chapter 4, before going in detail in Chapters 5–20 into the various high- (and low-) tech meters available.

  • 6 - Venturi Meter and Standard Nozzles

  • Roger C. Baker
  • Book:
    Flow Measurement Handbook
    Published online:
    05 August 2016
    Print publication:
    25 August 2016, pp 163-176

  • Summary

    Introduction

    In this chapter, we are concerned with devices defined in international standard documents. Among these, the Venturi meter is one of the oldest industrial methods of measuring flow, although other methods may be more common. Chapter 8 deals with other devices such as variable area meters, target meters, averaging pitot tubes, Dall meters, V-cone meters and other Venturi, nozzle and orifice-like devices.

    As in the case of the orifice plate, the reader should have access to a copy of the latest version of the ISO standard (5167). I have refrained from repeating information that should be obtained from the standard, and include only the minimum information to provide an understanding of the discharge coefficients, the likely uncertainty of the various devices and the type of material from which they may be constructed. There is a growing interest in the use of some of these devices for difficult metering tasks and a re-evaluation of their behaviour. Recent publications are briefly reviewed in Appendix 6.A.

    Spink (1978) suggested that a standard orifice should be used unless:

    1. • The velocity is such as to require the value of β to exceed 0.75: if higher differential pressure or larger pipe is not possible, he suggested considering a flow nozzle.

    2. • The fluid contains a second phase of some sort – particulate, bubble or droplet – in suspension: either a Venturi or a flow nozzle with vertically downward flow, an eccentric or segmental orifice, or a different type of device such as a target meter or electromagnetic flowmeter should be considered.

    3. • The fluid is very viscous or results in low Reynolds number flows: the meters already mentioned may be suitable, or a quadrant or semi-circular orifice may be worth considering.

    4. • The flow is very low and the fluid very clean: an integral orifice or a small calibrated meter run may be appropriate.

    5. • Pumping costs are a major consideration: in which case go to a lower-loss device.

    If a liquid or a gas flows down a pipe of decreasing cross-section, the velocity (provided, in the case of a gas, that it is below the speed of sound) increases as the area decreases, and the pressure also decreases with the increase in velocity. This behaviour allows the measurement of the change in pressure as a means of obtaining the flow rate in the duct.

  • 20 - Coriolis Flowmeters

  • Roger C. Baker
  • Book:
    Flow Measurement Handbook
    Published online:
    05 August 2016
    Print publication:
    25 August 2016, pp 560-602

  • Summary

    Introduction

    This is one of the most important meter developments, and its application is impinging on many areas of industry. Its importance has been recognised by the national and international advisory bodies (see Mandrup-Jensen 1990 for an early description of work in Denmark on pattern approval and ISO developments).

    Background

    Plache (1977) makes the interesting point that mass cannot be measured without applying a force on the system and then measuring the resulting acceleration. This is a point which the present author has long considered a possible requirement and it is certainly supported in the Coriolis meter.

    Possibly the first application of the Coriolis effect for mass flow measurement was proposed by Li and Lee (1953) [but see Wang and Baker (2014) for other possible contenders for the original concept]. The meter is shown in Figure 20.1. The T-piece flow tube rotated with the outer casing and was linked to it by a torque tube. As the flow increased, so the T-piece experienced a displacing torque due to the Coriolis acceleration and this was measured from the displacement of the T-piece relative to the main body.

    In the Li and Lee meter the liquid was forced to move radially and therefore a force was applied to it through the tube. This force in turn was balanced by an equal and opposite one applied by the liquid to the tube. The force caused the tube to twist and the small relative rotation was sensed to obtain the mass flow rate.

    It is interesting to note that Stoll (1978) made no mention of the technology which was to revolutionise mass flow measurement. Medlock (1989) referred to several designs which, although not identified as dependent on the Coriolis effect, have a very similar basis. Macdonald (1983) described a vibrating vane flowmeter. Vsesojuzny (1976) described a vibrating nozzle flowmeter (Figure 20.2) [cf. Hemp's (1994b) work on vibrating elements]. Finnof et al. (1976) described a vibrating tube flowmeter (Figure 20.3).

    Tucker and Hayes (1982) analysed the error in oil flow rate for a vibrating pendulum two-phase flowmeter invented by Rivkin (1978) and its suitability for North American oil well applications. Reimann, John and Muller (1982) tested a True Mass FlowMeter (TMFM) on a steam-water loop.

  • 7 - Critical Flow Venturi Nozzle

  • Roger C. Baker
  • Book:
    Flow Measurement Handbook
    Published online:
    05 August 2016
    Print publication:
    25 August 2016, pp 177-194

  • Summary

    Introduction

    This meter makes use of a fascinating effect which occurs when gas flows at very high velocity through a nozzle. As the gas is sucked through the nozzle the velocity increases as the cross-section of the nozzle passage decreases towards the throat. At the throat the maximum velocity which can be achieved is sonic – the speed of sound. Downstream of the throat, the velocity will either fall again returning to subsonic, or will rise and become supersonic. In normal operation of the nozzle, the supersonic region is likely to be small, and to be followed by a shock wave which stands across the divergent portion of the nozzle, and causes the gas velocity to drop, very suddenly, from supersonic to subsonic. The existence of the shock wave does not mean that one will hear a “sonic boom”! Such booms are usually caused by moving shock waves carried forward by high-speed aircraft.

    The fascinating effect of sonic conditions at the throat is that changes in the flow downstream of the throat have no effect on conditions upstream. The sonic or critical or choked condition, as it is called, appears to block any information which is trying to penetrate upstream. A simple picture of this is that the messengers carrying such information travel at the speed of sound, and so they are unable to make any headway over the fast-flowing gas stream.

    Two important effects of this are that:

    1. i) the mass flow rate is a function of the gas properties, the upstream stagnation temperature and pressure and the area of the throat, provided that the nozzle is actually running at critical conditions (which can be ascertained by checking the downstream pressure);

    2. ii) the nozzle acts as a flow controller, creating steady conditions upstream even though conditions downstream are unsteady.

    Figure 2.6(a) shows a simple illustration of a convergent-divergent nozzle with a throttle valve downstream. Figure 2.6(b) shows the variation of pressure through the nozzle, and the critical flow conditions are those bounded by curves c and i for which the flow becomes sonic at the throat.

  • 4 - Calibration

  • Roger C. Baker
  • Book:
    Flow Measurement Handbook
    Published online:
    05 August 2016
    Print publication:
    25 August 2016, pp 67-115

  • Summary

    Introduction

    The object of calibration is to benchmark a flowmeter to an absolute datum. Just as a benchmark tells us how a particular geographical point compares in height with sea level datum, so a calibration of a flowmeter tells us how the signal from the flowmeter compares with the absolute standard of a national laboratory. The analogy is not perfect at this stage. The national laboratory standard must also be compared with other more fundamental measures of time and mass, and it will be essential to check and compare different national standards in different countries from time to time.

    There is a desire to reference back to fundamental measurements such as mass, length and time. Thus if we can measure mass flow on a calibration facility by using fundamental measurements of mass and time, this will bring us nearer to the absolute values than, say, obtaining the volume of a calibration vessel by using weighed volumes of water and deducing the volume from the density. The first is more correctly termed primary calibration, whereas the second fails strictly to achieve this. It is likely that the final accuracy will reflect this. Liquid calibration facilities can achieve a rather higher accuracy than is possible for most of the gas calibration facilities. In part, this difference will result from the lower density and the increased difficulties of handling a gas.

    The result of a calibration will be both a comparison with the national standard and also a range within which the reading is likely to lie.

    Calibration Considerations

    Figure 4.1 shows three different approaches to obtaining the data. Although the selection of calibration points and their optimum distribution over the range is not obvious, most of the reference books seem to omit any comment on this. Figure 4.1(a) records data at one flow rate. This might be appropriate if the flowmeter were expected to operate at one rate. It shows the fact that there is variation with time to which the repeatability refers. Such a plot might be used to compare the calibration facility itself with other facilities or to test the consistency of diverter operation. Figure 4.1(b) is probably the most usual plot. Here a number of points have been taken over the full range of the flowmeter.

  • 1 - Properties, dimensions, and scales

  • from Part I - Use of experimental data
  • William M. Deen, Massachusetts Institute of Technology
  • Book:
    Introduction to Chemical Engineering Fluid Mechanics
    Published online:
    28 May 2018
    Print publication:
    15 August 2016, pp 3-29

  • Summary

    INTRODUCTION

    Fluids, including both gases and liquids, are materials that deform continuously when subjected to shearing forces. If a flowing fluid contains a dye or other tracer, the labeled region tends to change shape from instant to instant. The viscosity of a fluid is a reflection of its resistance to such deformations. This chapter begins with definitions of viscosity and three other material properties that are important in fluid mechanics, namely density, kinematic viscosity, and surface tension. Representative values of each are presented, and some of the differences between Newtonian and non-Newtonian fluids are described.

    Physical quantities have dimensions, such as mass (M), length (L), and time (T). The concepts of mass, length, and time are more fundamental than the units in a particular system of measurement, such as the kilogram (kg), meter (m), and second (s) that underlie the SI system. To have general validity, a physical relationship must be independent of the observer, including the observer's choice of units. That can be achieved by making each variable or parameter in an equation dimensionless, which means that the physical quantities are grouped in such a way that their dimensions cancel. Dimensionless parameters are ratios, and often the numerator and denominator are each the scale of a variable. A scale is the maximum value of something, such as a velocity or force. Thus, the numerical value of such a group reveals how two things compare, and thereby offers insight into what is important in the process or phenomenon under consideration and what might be negligible. Several dimensionless groups that arise in fluid mechanics are discussed.

    Dimensional analysis, the last major topic of the chapter, provides a systematic way to identify the dimensionless groups that are involved in something of interest. In addition to yielding relationships that are more universal, grouping quantities in this manner minimizes the number of independent variables. This greatly facilitates the design of experiments and interpretation of data, as discussed here and explored further in Chapters 2 and 3.

    FLUID PROPERTIES

    Viscosity

    A definition of viscosity is provided by the idealized experiment in Fig. 1.1. Imagine that a fluid fills a space of thickness H between parallel plates, each of which has an area A. Suppose that the upper plate is pulled to the right (in the x direction) at a constant velocity U, while the lower one is held in place.

  • 4 - Fluid statics: pressure, gravity, and surface tension

  • from Part II - Fundamentals of fluid dynamics
  • William M. Deen, Massachusetts Institute of Technology
  • Book:
    Introduction to Chemical Engineering Fluid Mechanics
    Published online:
    28 May 2018
    Print publication:
    15 August 2016, pp 85-109

  • Summary

    INTRODUCTION

    In a static fluid, gravity causes the pressure to increase with depth. Pressures at fluid–fluid interfaces may be influenced also by surface tension. Both kinds of pressure variation have numerous practical consequences, as will be discussed in this chapter. An advantage of beginning a more detailed analysis of fluid mechanics with statics is that viscous stresses, which are the most difficult conceptually and mathematically, are absent in fluids at rest. Thus, we can concentrate first on pressure, gravity, and surface tension, and return later to a more general and precise description of viscous stresses. Quantifying momentum changes within fluids also can be deferred. Viscous stresses and inertia are considered in detail in Chapter 6.

    This chapter begins the use of vector notation, and it is suggested that the reader review certain parts of the appendix before proceeding. Needed particularly is familiarity with vector representation (Section A.2), vector dot products (Section A.3), the gradient operator (Section A.4), and cylindrical and spherical coordinates (last part of Section A.5).

    PRESSURE IN STATIC FLUIDS

    Properties of pressure

    Pressure is a force per unit area, making it a type of stress. It has three properties, whether or not there is flow.

  • (i) Pressure forces only act normal to (perpendicular to) surfaces.

  • (ii) Positive pressures are compressive (rather than tensile). In other words, pressure pushes on (rather than pulls on) a surface.

  • (iii) Pressure is isotropic. That is, the pressure P has a single value at any point in a fluid, and tends to act equally in all directions.

    • Properties (i) and (ii) provide a mechanical definition of pressure and establish the direction of pressure forces when P > 0. Property (iii) is a consequence of (i), as shown at the end of this section. If (i) and (iii) seem contradictory, keep in mind that the pressure itself is a scalar, whereas the pressure force acting on a surface is a vector. The orientation of the surface determines the direction of the force vector, but not the value of P.

    Static pressure equation

    A differential equation that describes pressure variations in a static fluid will be derived using a force balance on the small fluid cube in Fig. 4.1.

  • 12 - Pipe flow: entrance effects, fittings, and compressibility

  • from Part IV - Macroscopic analysis
  • William M. Deen, Massachusetts Institute of Technology
  • Book:
    Introduction to Chemical Engineering Fluid Mechanics
    Published online:
    28 May 2018
    Print publication:
    15 August 2016, pp 322-361

  • Summary

    INTRODUCTION

    The calculation of pressure drops and flow rates for fully developed flow in various kinds of conduits was discussed in Chapter 2. The resistance to such flows is due to a wall shear stress τ w that is independent of conduit length, and it was seen that information on τ w could be correlated in terms of the friction factor f. All that is needed for design calculations involving incompressible flow in long pipes is fluid property data and plots or formulas for f. However, any system that distributes a fluid to multiple locations, whether in an oil refinery, a microfluidic device, or the body, consists of conduits of finite length that are connected to ones of different size and to tanks or other dissimilar elements. Additional flow resistances arise from sudden changes in diameter or the presence of valves and fittings. Although the additional resistances are negligible in some systems, in others their total exceeds that from plain sections of pipe. Tube inlets coincide with abrupt reductions in diameter and create entrance regions where the flow adjusts to the new cross-section. The resistance there exceeds that for fully developed flow, as detailed in Section 12.2. Section 12.3 extends the discussion of “other” resistances to pipe fittings and valves and includes basic information on pumps, thereby providing a foundation for practical designs.

    Our default assumption for all flow regimes and geometries has been that the fluid density is constant. Assuming a gas to be incompressible is satisfactory if, as is often the case, the change in pressure is a small fraction of the absolute pressure. Gas flows in very long pipes or at velocities comparable to the speed of sound are exceptions, and are the focus of Sections 12.4 and 12.5, respectively. Introduced there are some of the distinctive features of compressible flow, including how “choking” limits flow rates through pipes or nozzles.

    ENTRANCE EFFECTS

    Entrance length

    Something we have not yet accounted for in calculations is that the velocity profile in a tube or other conduit becomes fully developed only after a certain distance from the inlet. An inlet typically involves a sudden reduction in cross-sectional area, as at position 1 in Fig. 12.1. The radius ratio will be denoted as β = R/R0. For a pipe connected to a large tank, β is practically zero.

Page 82 of 275