Physics
Compressibility
Compressibility is a measure of how much a substance's volume decreases under pressure. It is the reciprocal of the substance's bulk modulus, which is a measure of its resistance to compression. Compressibility is an important property in the study of fluids and gases.
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10 Key excerpts on "Compressibility"
eBook - ePubFrom Deep Sea to Laboratory 3
From Tait's Work on the Compressibility of Seawater to Equations-of-State for Liquids
- Frederic Aitken, Jean-Numa Foulc(Authors)
- 2019(Publication Date)
- Wiley-ISTE(Publisher)
1.2. Concepts of CompressibilityCompressibility is a general property of a material that causes anything to reduce its volume under the effect of pressure. This property is characterized by coefficients that can be different depending on the material concerned (gas, liquid or solid). In the case of a liquid (usually a state of matter that cannot withstand static shear stress without flow), the only modulus that can be defined is its modulus of elasticity in volume κ, also called the tangent modulus in volume.A specific volume V of liquid that is subjected to a hydrostatic pressure variation ΔP = P – P0 (P is the applied pressure and P0 the reference pressure) undergoes a volume decrease equal to ΔV; its deformation in volume is: -ΔV/V. The modulus of elasticity in volume is then, by definition:[1.3]The reference pressure P0 is often taken as 1 atmosphere. In practice, since the pressures applied to measure the Compressibility of liquids are much higher than 1 atm, the pressure variation is considered to be equal to the pressure applied (i.e. ΔP = P).The value of the module κ depends on the speed at which pressure variations occur. If the pressure is applied slowly, the liquid will remain at a constant temperature and, under these conditions, we will have an isothermal module κT . If the pressure variations are so rapid that there can be practically no heat exchange between the liquid and its environment, then we will have an adiabatic module κS
eBook - PDF- Ronald K. McLaughlin, R. Craig McLean, W. John Bonthron(Authors)
- 2016(Publication Date)
- Butterworth-Heinemann(Publisher)
In addition, vaporisa-tion effects are displayed in liquids which have a free surface. These three important characteristics will now be reviewed briefly. 1.2.2 Compressibility All fluids may be compressed by the application of pressure forces. The degree of Compressibility of a fluid is characterised by 1 1 2 The Fundamentals of Fluid Flow defining the bulk modulus V K E = -Ap — ΔΙ/' (1.1) Here Ap represents the increase in pressure necessary to decrease a given volume V' by the amount-ΔΙ/'. All liquids have a high value of bulk modulus and are compressible only to a small extent. For example, the bulk modulus of water is quoted as 20.085 x 10 5 kN/m 2 , and thus a decrease of only 0.2% in a given volume requires a pressure increase of In the study of fluid mechanics it is necessary to make the dis-tinction between flows in which Compressibility effects may be ignored and flows in which they require to be taken into account. As the change in the density of a liquid with an increase in pres-sure is small even for very large pressure changes, the density of a liquid is consequently taken as constant in most flow situations. The analysis of problems involving liquids is thereby greatly sim-plified. Some exceptions to this general simplification do exist however, and in certain special flow problems the Compressibility of liquids is an important factor—as in the case of water-hammer, where the fluid is subjected to a very high rate of velocity change. Unlike liquids, gases are highly compressible. However, in flows where a gas is subjected to relatively small changes in pres-sure (e.g. ventilation and air conditioning systems), the corres-pondingly small density variations are generally ignored and the gas is treated as an incompressible fluid. On the other hand, in high-speed flows, where the fluid velocity approaches that at which sound is propagated through the medium, Compressibility effects become important and must be taken into account.
eBook - PDF- E. Shashi Menon(Author)
- 2005(Publication Date)
- CRC Press(Publisher)
1 CHAPTER 1 Gas Properties In this chapter we will discuss the properties of gases that influence gas flow through a pipeline. We will explore the relationship of pressure, volume, and temperature of a gas and how the gas properties such as density, viscosity, and Compressibility change with the temperature and pressure. Starting with the ideal or perfect gases that obey the ideal gas equation, we will examine how real gases differ from ideal gases. The concept of Compressibility factor, or gas deviation factor, will be intro-duced and methods of calculating the Compressibility factor using some popular graphical correlation and calculation methods explained. The properties of a mixture of gases will be discussed, and how these are calculated will be covered. Under-standing the gas properties is an important first step toward analysis of gas pipeline hydraulics. A fluid can be a liquid or a gas. Liquids are generally considered almost incom-pressible. A gas is classified as a homogenous fluid with low density and viscosity. It expands to fill the vessel that contains the gas. The molecules that constitute the gas are spaced farther apart in comparison with a liquid and, therefore, a slight change in pressure affects the density of gas more than that of a liquid. Gases, therefore, have higher Compressibility than liquids. This implies that gas properties such as density, viscosity, and Compressibility factor change with pressure. 1.1 MASS AND WEIGHT Mass is the quantity of matter in a substance. It is sometimes used interchangeably with weight. Strictly speaking, mass is a scalar quantity, whereas weight is a force and, therefore, a vector quantity. Mass is independent of the geographic location, whereas weight depends upon the acceleration due to gravity and, therefore, varies slightly with geographic location. Mass is measured in slugs in the U.S. Customary System (USCS) of units and kilograms (kg) in Systeme International (SI) units.
eBook - PDFIntroduction to Fluid Dynamics
Understanding Fundamental Physics
- Young J. Moon(Author)
- 2022(Publication Date)
- Wiley(Publisher)
267 8 Compressible Flows 8.1 Compressibility of Fluids 8.1.1 Wave Propagation The concept of Compressibility is explained with a tube filled with a stationary compressible fluid of density 𝜌 0 , pressure p 0 , and temperature T 0 . If the fluid is suddenly moved by a massless piston that accelerates from 0 to du with an infinitesimally small force dF, what will happen to the fluid? The fluid column in the tube is not moved as a whole, as a solid bar, or as an incompressible fluid would be. This is due to the Compressibility of the fluid. For the given force dF (= p ′ A), the volume of fluid next to the piston is locally compressed from V 0 to V 0 + dV over a time interval dt (where V 0 is the volume subject to compression, and dV < 0 for compression) through a reversible and adiabatic 1 process (Figure 8.1). The compressed fluid absorbs the volume compression work done by the piston as elastic potential energy; this corre- sponds to internal energy in the conservation of thermal energy. Furthermore, the compressed fluid attains kinetic energy through the flow work done by the piston in mechanical energy con- servation. Thus, the internal energy and kinetic energy of the compressed fluid in the volume of V 0 + dV are locally increased in time, under the conservation principle of total energy. Once the fluid is locally compressed (or dilated), the compressed (or expanded) region will propagate via interactions of the fluid molecules. 2 8.1.2 Volumetric Dilatation Rate In compressible fluids, the fluctuations of physical quantities such as pressure, density, temper- ature, and velocities from an ambient condition (or a time-averaged value) are related to the volumetric dilatation rate ̇ D: ̇ D = 1 V DV Dt = ∇ ⋅ ⃗ 𝑣 (8.1) where the volumetric dilatation rate represents the total rate of change of the volume per unit volume, i.e.
- Scott S. Bair(Author)
- 2007(Publication Date)
- Elsevier Science(Publisher)
CHAPTER 4 Compressibility and the Equation of State 4.1 Background For most engineering applications, liquids are treated as incompressible. In acoustics and low-pressure hydraulics, where the Compressibility is certainly important, the com- pression, V 0 − V , may be regarded as linear with pressure and very small relative to the ambient pressure volume, V 0 . Elastohydrodynamic lubrication, EHL, is quite dif- ferent from these examples in the magnitude of pressure and the relative compression involved. A liquid lubricant pressurized to 1 GPa at 0 ◦ C may experience a relative com- pression, (V 0 − V )/V 0 , of 20% and at 200 ◦ C of 30%. The compression is nonlinear for EHL pressures. The first half of the compression at 1 GPa comes at a pressure of 1/3 GPa at 0 ◦ C and at only 1/4 GPa at 200 ◦ C. Here and throughout this book, the dis- tinction between p = 0 and p = 1 atmosphere is neglected owing to the relatively high pressures. Now the Compressibility of the lubricant is clearly a second order effect for the generation of a film thickness. Variations in velocity and viscosity can effect orders-of-magnitude changes in the film thickness while the effect of Compressibility is to approximately reduce the central film by the amount of the relative compression [1], h incom c − h compr c h incom c ≈ (V 0 − V ) V 0 = 1 − V V 0 (4.1) An understanding of the Compressibility of a liquid lubricant is required for the estimation of the refractive index, I, of the lubricant at the film pressure so that interferometry may be used to experimentally measure the thickness of the EHL film. The refractive index is related to the density or volume by the Lorenz–Lorentz equation [2] (I 2 − 1) (I 2 + 2) (I 2 R + 2) (I 2 R − 1) = ρ ρ R = V R V (4.2) 54 Compressibility and the Equation of State 55 where subscript R refers to a reference state.
- Scott S. Bair(Author)
- 2019(Publication Date)
- Elsevier(Publisher)
Chapter FourCompressibility and the Equation of State
Abstract
For most engineering applications, liquids are treated as incompressible. Elastohydrodynamics is not a typical engineering application as the pressures are sufficiently large to result in significant increases in density of the liquids. In fact, the pressure dependences of the thermophysical properties of these liquids can often best be correlated with the temperature and density. The simple dilatometer, in which a piston is driven into a cylinder containing liquid, is sufficient for detecting phase changes; however, this approach cannot accurately produce the equation of state which the most precise viscosity correlations require. Relative volume data are provided for some lubricants and well-defined pure liquids and an equation of state is offered for simulations to replace the less accurate universal form in use today.Keywords
Pressure–volume–temperature; refractive index; Compressibility; bulk modulus; dilatometer; thermal expansivity; bellows piezometer; refractometer; longitudinal sound velocity; equation of state4.1 Background
For most engineering applications, liquids are treated as incompressible. In acoustics and low-pressure hydraulics, where the Compressibility is certainly important, the compression,, may be regarded as linear with pressure and very small relative to the ambient pressure volume,V 0− VV 0. Elastohydrodynamic lubrication (EHL) is quite different from these examples in the magnitude of pressure and the relative compression involved. A liquid lubricant pressurized to 1 GPa at 0°C may experience a relative compression,(, of 20% and at 200°C of 30%. The compression is very nonlinear for EHL pressures. The first half of the compression at 1 GPa comes at a pressure of 1/3 GPa at 0°C and at only 1/4 GPa at 200°C. Here and throughout this book, the distinction betweenV 0− V ) /V 0p = 0 and p = 1 atmosphere
eBook - PDF- John Ward-Smith(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
Where conditions are such that an amount of gas undergoes a negligible change of volume, its behaviour is similar to that of a liquid and it may then be regarded as incompressible. If, however, the change in volume is not negli-gible, the Compressibility of the gas must be taken into account in examining its behaviour. A second important difference between liquids and gases is that liquids have much greater densities than gases. As a consequence, when considering forces and pressures that occur in fluid mechanics, the weight of a liquid has an important role to play. Conversely, effects due to weight can usually be ignored when gases are considered. The characteristics of fluids 3 1.1.1 Molecular structure The different characteristics of solids, liquids and gases result from differ-ences in their molecular structure. All substances consist of vast numbers of molecules separated by empty space. The molecules have an attraction for one another, but when the distance between them becomes very small (of the order of the diameter of a molecule) there is a force of repulsion between them that prevents them all gathering together as a solid lump. The molecules are in continual movement, and when two molecules come very close to one another the force of repulsion pushes them vigorously apart, just as though they had collided like two billiard balls. In solids and liquids the molecules are much closer together than in a gas. A given volume of a solid or a liquid therefore contains a much larger number of molecules than an equal volume of a gas, so solids and liquids have a greater density (i.e. mass divided by volume). In a solid, the movement of individual molecules is slight – just a vibration of small amplitude – and they do not readily move relative to one another. In a liquid the movement of the molecules is greater, but they continually attract and repel one another so that they move in curved, wavy paths rather than in straight lines.
- Hugh L. Dryden, Theodore Von Karman, Kalinske Anton Adam(Authors)
- 2016(Publication Date)
UNIVERSITY OF PENNSYLVANIA BICENTENNIAL CONFERENCE Problems of Flow in Compressible Fluids By T H E O D O R E V O N K A R M Ä N , PH.D., DR. ING., SC.D.* IN MANY applications of fluid mechanics the assumption of incom-pressibility or constant density of the fluid yields results of sufficient accuracy for practical purposes. In general it is assumed that this approximation is justified if the velocity, density, and pressure changes are relatively small, as, for example, in most problems of practical hydraulics and aeronautics. Often it is stated that the dynamics of incompressible fluids will give satisfactory results if the velocities involved in the problem are small in comparison with the velocity of sound. However, if we look over the entire field of fluid mechanics somewhat more carefully, we find that besides the high-speed phenomena there are other cases in which density variation or elasticity of the fluid cannot be neglected. In all, the problems in which Compressibility enters as a governing factor can be classified in the following groups: a) Pressure propagation. In an incompressible fluid the pressure changes propagate with infinite velocity. Hence, if we are con-cerned with pressure oscillations in fluids, we have to consider the elasticity of the fluid as the factor governing the phenomena, irre-spectively of the magnitude of the velocities or the pressure changes involved. Problems of acoustics, water hammer in pipes, oscilla-tions in gas conduits, engine manifolds, etc., belong in this class of problems. b) Density currents. In the problems belonging in this group we are concerned with a stratified fluid medium, as the atmosphere or water carrying silt. In such problems the velocities and pressure changes caused by the motion may be small, but the phenomena are governed by the gravity field produced by density differences. c) Slow motion of fluids with large density changes.
eBook - PDFIntroduction to the Numerical Modeling of Groundwater and Geothermal Systems
Fundamentals of Mass, Energy and Solute Transport in Poroelastic Rocks
- Jochen Bundschuh, Mario César Suárez A.(Authors)
- 2010(Publication Date)
- CRC Press(Publisher)
2.2.4.4 Compressibility of the pore volume The unjacketed Compressibility of the pore volume C , is defined as the change of pore volume with respect to the pore pressure change per unit volume when p d remains constant: C = − 1 V ∂ V ∂ p f p d = − 1 ϕ ∂ϕ ∂ p k p d (2.40a) The isothermal Compressibility of the fluid C f , when temperature T and fluid mass M f are constants, is defined as the change of fluid volume with respect to the effective pressure change per unit volume: C f = − 1 V f ∂ V f ∂ p f T = − ρ f M f − M f ρ 2 f ∂ρ f ∂ p f T = 1 ρ f ∂ρ f ∂ p f T (2.40b) Equations (2.39a) to (2.40b) define two different forms of unjacketed compressibilities C s and C . The Compressibility of the pore volume varies with the effective compression, the temperature and the porosity. If the pressure in the pores decreases during the reservoir’s fall off, then important Rock and fluid properties 39 reductions in the pore volume can occur, even with partial or total collapse of pores and fractures (S. Arriaga and Verduzco 1998). The bulk isothermal Compressibility is: C T = − 1 V B ∂ V B ∂ p k T (2.40c) Reported effects of pressure in the pore volume (Ramey et al . 1974) show that its compressibil-ity decreases when pressure increases within a range of 0.1 to 55 MPa, for temperatures between 24 and 205 ◦ C. For higher pressure values the variation is lower. The effect of temperature on the Compressibility of the pore volume is appreciated in experiments with different rocks. Several results show that at 205 ◦ C the Compressibility can be between 12 and 55% higher than at 24 ◦ C. The average of all the samples analyzed by Passmore and Archer (1985) shows a Compressibility increment of 21% when the temperature increases inside this range. Other experimental results from the same authors, using sandstone cores, show that Compressibility increases with porosity in the range between 19 to 28%.
eBook - PDF- William Graebel(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
447 chapter 9 Compressible Flows Chapter Overview and Goals Compressibility of the fluid in the high-speed flow of gases and liquids introduces a new class of flow effects differing from those we so far have seen. We first introduce the speed of sound and the Mach number. The Mach number is the dimensionless parameter that appears repeatedly throughout this chapter. Compressibility effects in liquids are next studied, including the effect of dissolved gases on the sonic speed and Compressibility effects in pipe flow. The thermodynamics of ideal gases is briefly reviewed, and the isentropic flows of these gases is then considered. The possibility of nonisentropic flow regions such as shock waves is introduced, and compressible flow in a nozzle is studied. Nozzle flow offers the possibilities of subsonic, sonic, and supersonic flow existing in the same device, along with the possibility of isolated shock waves. Compressible gas flow in a pipe, where wall friction and/or external heating can be important, is also presented as an illustration of how mechanisms other than area changes can affect the direction in which the Mach number changes. The previous chapters have dealt almost exclusively with constant density flows. Compressibility effects in high-speed flows can cause a dramatically different range of phenomena to appear. These phenomena are important in many physical processes, both in gases and in liquids. In the case of gases we will restrict our attention largely to the flow of ideal gases, for besides being of engineering importance, these flows illustrate with a minimum of mathematics most of the important physics involved with compressible flows. Another feature of compressible flow prompts a note of caution to the student. In incompressible flows we usually deal with pressure differences, and gage pressures can be used.
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