Physics
Fluid Flow
Fluid flow refers to the movement of liquids or gases through a system or medium. It is characterized by the continuous deformation of the fluid, with the velocity and pressure varying at different points within the flow. Understanding fluid flow is crucial in various fields, including engineering, environmental science, and medicine, as it impacts the design and operation of systems and processes.
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8 Key excerpts on "Fluid Flow"
eBook - PDF- J. A. Blom(Author)
- 2003(Publication Date)
- CRC Press(Publisher)
2 Physics of Fluid Transport in Tubes In both the respiratory and the circulatory systems, transport — of gas and blood, respectively — is through tubes. We therefore need to study the transport phenomena in tubes more closely. Fluid dynamics is the branch of science which attempts to understand — and from understanding comes the possibility of prediction — fluids and their behavior. From a fluid dynamics point of view, gases and liquids are both fluids; the only difference between gases and liquids is that their properties (density, for example) have different numerical values. 2.1. FLUID DYNAMICS We first need to introduce some terms. A flow line (or streamline) is the path that a hypothetical small particle would follow if one lets it go somewhere in the flow. The flow velocity is the velocity that this hypothetical particle would have; the flow velocity can be different from position to position and can change in time as well. Flow is laminar when all flow lines are (almost) parallel (Figure 2.1a); the word lamina actually means “layer” or “sheet,” and thus refers to a surface rather than a line. A flow profile is a two- or three-dimensional plot of flow velocities; Figure 2.1b, for example, shows that when a solid object is placed near the Fluid Flow, it influences the velocity profile in such a way that the fluid velocity decreases near the surface of the object and becomes zero at the surface. Flow is turbulent when the flow lines are not (almost) parallel anymore but intermix (Figure 2.1c). a) b) c) Laminar Flow in Free Space V = V free V = 0 Figure 2.1. Laminar flow in free space has parallel flow lines with equal velocities (a). Velo-cities are zero at a wall (b). At high flows, flow lines are not parallel anymore but show tur-bulence (c). Pressure is created due to the (nearly) elastic collisions of the molecules of the fluid with the surface of a body (e.g., a pressure transducer).
eBook - PDF- C. A. Brebbia, A. J. Ferrante(Authors)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
Chapter 2 Basic concepts of fluids in movement 2.1 Introduction The basic concepts of fluid dynamics will be reviewed in this chapter, in order to study their application for the solution of engineering problems. For this the fluid is considered to be incompressible. Two types of Fluid Flows are found in practice, known as turbulent flows and laminar flows. In turbulent flows the fluid particles follow irregular paths and the velocities, at a given point, change with time. The instantaneous velocity v can be decomposed into a constant mean velocity component v, and a variable velocity component t/, such that v = v + v' (2.1) The distribution of velocities between two plates, for turbulent flow, is depicted in Figure 2.1(a). The particles are subjected not only to axial but also to transverse velocities. For laminar flow between two plates, the fluid particles, not being subjected to transverse velocities, follow rectilinear paths (Figure 2.1(b)). If a colour dye is injected as a tracer the result will be a thin rectilinear line for laminar flow, while for turbulent flow the colour will be rapidly dispersed in the fluid. Laminar flows exist for low velocity and high viscosity fluids. The theory describing laminar flow is mathematically very well developed. That is not the case for turbulent flow, however, which is still a largely unknown area for research. Figure 2.1 (a) Turbulent and (b) laminar flow 15 16 Basic concepts of fluids in movement Flows can also be classified as rotational or irrotational. In a rotational flow the fluid particles will possess a non-zero angular velocity, while for irrotational flows that velocity component will be null. In Figure 2.2 we illustrate both types of flow, by defining an infinitesimal particle of dimension dxdy, and studying the rotation of the axes. Figure 2.2(a) shows a flow where velocities in the horizontal direction are constant for any given height, but there is a vertical velocity gradient.
eBook - PDF- Robert Resnick, David Halliday, Kenneth S. Krane(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
351 FLUID DYNAMICS W e now turn from fluid statics to the dynamics of fluids in motion. We use familiar concepts to analyze fluid dynamics, including Newton’s laws of motion and the conservation of energy. In this chapter we apply these principles to fluids, which are described using variables such as pressure and density that we introduced in Chapter 15. We begin with a simplified model of Fluid Flow, in which we ignore dissipative forces. This approach is similar to our previous study of particle dynamics, in which we at first ignored dissipative (frictional) forces. An advantage of this approach is that it permits an analysis in terms of conservation of mechanical energy, as we did in Chapter 12 in the case of particles. Later in this chapter we give a brief description of the interesting and unusual results that occur in real fluids when dissipative forces, called viscous forces, are taken into account. 16-1 GENERAL CONCEPTS OF Fluid Flow One way of describing the motion of a fluid is to divide the fluid into infinitesimal volume elements, which we may call fluid particles, and to follow the motion of each particle. If we knew the forces acting on each fluid particle, we could then solve for the positions and velocities of each particle as functions of the time. This procedure, which is a direct generalization of particle mechanics, was first developed by Joseph Louis Lagrange (1736 – 1813). Because the number of fluid particles is generally very large, using this method is a formidable task. There is a different treatment, developed by Leonhard Euler (1707 – 1783), that is more convenient for most pur- poses. In it we give up the attempt to specify the history of each fluid particle and instead specify the density and the velocity of the fluid at each point in space at each instant of time.
eBook - PDF- John Ward-Smith(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
The flow is steady and continuous, that is, the rate at which mass enters the region considered equals that at which mass leaves the region and neither varies with time. 2. Conditions at any point between the inlet and outlet sections 1 and 2 do not vary with time. 100 The principles governing fluids in motion 3. Heat and shaft work are transferred to or from the fluid at a constant net rate. 4. Quantities are uniform over the inlet and outlet cross-sections 1 and 2. 5. Energy due to electricity, magnetism, surface tension or nuclear reaction is absent. If energy due to any of these phenomena is, in fact, involved, appropriate additional terms will appear in the equations. No assumptions are made about details of the flow pattern between inlet and outlet and no assumption is made about the presence or absence of fric-tion between inlet and outlet. The restrictions of assumptions 1 and 2 may in practice be slightly relaxed. Fluctuations in conditions are permissible if they occur through a definite cycle so that identical conditions are again reached periodically. This happens in fluid machinery operating at constant speed and torque. Flow in the neighbourhood of the moving blades or pistons of the machine is cyclic rather than absolutely steady. In other words, the con-ditions at any particular point in the fluid vary with time in a manner that is regularly repeated at a certain frequency. In such a case the equation may be used to relate values of the quantities averaged over a time considerably longer than the period of one cycle. In practice, assumption 4 is never completely justified, since viscous forces cause the velocity to fall rapidly to zero at a solid boundary. Thermodynamic properties may also vary somewhat over the cross-section. To allow for these effects, appropriate correction factors may be introduced – for example, the kinetic energy correction factor α we shall mention in Section 3.5.3 .
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
A tiny variation in one factor has an exaggerated (or nonlinear) effect on 454 Chapter 12 | Fluid Dynamics and Its Biological and Medical Applications This OpenStax book is available for free at http://cnx.org/content/col11406/1.9 the flow. Phenomena as disparate as turbulence, the orbit of Pluto, and the onset of irregular heartbeats are chaotic and can be analyzed with similar techniques. 12.6 Motion of an Object in a Viscous Fluid A moving object in a viscous fluid is equivalent to a stationary object in a flowing fluid stream. (For example, when you ride a bicycle at 10 m/s in still air, you feel the air in your face exactly as if you were stationary in a 10-m/s wind.) Flow of the stationary fluid around a moving object may be laminar, turbulent, or a combination of the two. Just as with flow in tubes, it is possible to predict when a moving object creates turbulence. We use another form of the Reynolds number N′ R , defined for an object moving in a fluid to be (12.55) N′ R = ρvL η (object in fluid), where L is a characteristic length of the object (a sphere’s diameter, for example), ρ the fluid density, η its viscosity, and v the object’s speed in the fluid. If N′ R is less than about 1, flow around the object can be laminar, particularly if the object has a smooth shape. The transition to turbulent flow occurs for N′ R between 1 and about 10, depending on surface roughness and so on. Depending on the surface, there can be a turbulent wake behind the object with some laminar flow over its surface. For an N′ R between 10 and 10 6 , the flow may be either laminar or turbulent and may oscillate between the two. For N′ R greater than about 10 6 , the flow is entirely turbulent, even at the surface of the object. (See Figure 12.18.) Laminar flow occurs mostly when the objects in the fluid are small, such as raindrops, pollen, and blood cells in plasma.
eBook - PDFComputational Fluid Dynamics and Energy Modelling in Buildings
Fundamentals and Applications
- Parham A. Mirzaei(Author)
- 2022(Publication Date)
- Wiley-Blackwell(Publisher)
78 2 An Overview on Fundamentals of Fluid Mechanics in Buildings 2.8 Internal Flow Internal flow is related to the fluid motion in the closed conduits such as pipes and ducts while in most of the cases the flowing fluid is assumed to be incompressible. In general, internal flows can be explained as the circulation of fluid by a pressure gradient imposed through a conduit. It is a valid assumption to neglect the impact of gravity in most of the case studies for further simplification of the analysis. Figure 2.17 shows a Fluid Flow in an internal flow. A common classification of internal flows is based on the flow being laminar, transient, or turbulent, depending on the Reynolds number of the conduit calculated using its characteristic length. Each of the mentioned regimes demonstrates different flow mechanism. In a laminar flow, we expect the fluid par- ticles to move in a direction parallel to the conduit’s direction while mixing between layers of fluid perpendicular to the flow direction is barely expected to occur. In a transitional regime, an irregular mixing starts between layers of fluid in the normal to the flow direction while this random and irregular motion is highly intensified in a turbulent regime. Figure 2.28 demonstrates the development of the boundary layer within a conduit in a uniform internal flow. As it can be clearly observed, the boundary layer continues to grow on the conduit’s surfaces. The structure of a boundary layer will be explained in more details in the following sections. The region outside of the boundary can be assumed as the irro- tational and inviscid flow. Nonetheless, this region diminishes after a certain distance from the entrance of a conduit, which is called the hydrodynamic entrance region.
- Robert W. Fox, Alan T. McDonald, John W. Mitchell(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
One-, Two-, and Three-Dimensional Flows A flow is classified as one-, two-, or three-dimensional depending on the number of space coordinates required to specify the velocity field. Equation 2.5 indicates that the velocity field may be a function of three space coordinates and time. Such a flow field is termed three-dimensional because the velocity at any point in the flow field depends on the three coordinates required to locate the point in space. Although most flow fields are inherently three-dimensional, analysis based on fewer dimensions is frequently appropriate. Consider, for example, the steady flow through a long straight pipe that has a divergent section, as shown in Fig. 2.2. In this example, we are using cylindrical coordinates r, θ, x . We will learn in Chapter 8 that under certain circumstances the velocity distribution may be described by u = u max 1 − r R 2 2 7 This is shown on the left of Fig. 2.2. The velocity u r is a function of only one coordinate, and so the flow is one-dimensional. On the other hand, in the diverging section, the velocity decreases in the x direction, and the flow becomes two-dimensional: u = u r, x . As you might suspect, the complexity of analysis increases considerably with the number of dimen- sions of the flow field. For many problems encountered in engineering, a one-dimensional analysis is adequate to provide approximate solutions of engineering accuracy. Since all fluids satisfying the continuum assumption must have zero relative velocity at a solid sur- face (to satisfy the no-slip condition), most flows are inherently two- or three-dimensional. To simplify the analysis it is often convenient to use the notion of uniform flow at a given cross section. In a flow that 18 Chapter 2 Fundamental Concepts is uniform at a given cross section, the velocity is constant across any section normal to the flow. Under this assumption, the two-dimensional flow of Fig. 2.2 is modeled as the flow shown in Fig. 2.3. In the flow of Fig.
eBook - PDFMEMS
Introduction and Fundamentals
- Mohamed Gad-el-Hak, Frank Kreith, Roop L. Mahajan(Authors)
- 2005(Publication Date)
- CRC Press(Publisher)
For macroscopically unsteady flows, ensemble averaging of many independent Monte Carlo simulations is carried out to obtain the final results within a prescribed statistical accuracy. 4.8 Liquid Flows From the continuum point of view, liquids and gases are both fluids obeying the same equations of motion. For incompressible flows, for example, the Reynolds number is the primary dimensionless param-eter that determines the nature of the flow field. True, water, for example, has density and viscosity that are respectively three orders and two orders of magnitude higher than those for air, but if the Reynolds num-ber and geometry are matched, liquid and gas flows should be identical. 10 For MEMS applications, how-ever, we anticipate the possibility of nonequilibrium flow conditions and the consequent invalidity of the Navier–Stokes equations and the no-slip boundary conditions. Such circumstances can best be researched using the molecular approach. We discussed this for gases earlier and will give the corresponding argu-ments for liquids in the present section. The literature on non-Newtonian fluids in general and polymers in particular is vast (for example, the bibliographic survey by Nadolink and Haigh, 1995, cites over 4,900 references on polymer drag reduction alone) and provides a rich source of information on the molecu-lar approach for liquid flows. Solids, liquids, and gases are distinguished merely by the degree of proximity and the intensity of motions of their constituent molecules. In solids, the molecules are packed closely and confined, each hemmed in by its neighbors [Chapman and Cowling, 1970]. Only rarely would one solid molecule slip from its neigh-bors to join a new set. As the solid is heated, molecular motion becomes more violent, and a slight ther-mal expansion takes place. At a certain temperature that depends on ambient pressure, sufficiently intense motion of the molecules enables them to pass freely from one set of neighbors to another.
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