Bulk modulus of a substance provides the information about the resistance of substance to the uniform pressure. Therefore, calculating the formula for the bulk modulus of a concrete structure is important for calculating the seepage and mechanical properties. The bulk modulus letter k is a measure of the resistance of a substance to compression on all sides. Bulk modulus formula definition, equations, examples. Elastic constants youngs modulus, modulus of rigidity. It is defined as the ratio of the infinitesimal pressure increase to the resulting. Note that this is not uniaxial strain due to poisson e ect in this expression, eis youngs modulus. Apr 30, 2018 bulk modulus is the measure of resistibility to the external forces acting on the body. Bulk modulus definition of bulk modulus by medical dictionary. Bulk modulus, numerical constant that describes the elastic properties of a solid or fluid when it is under pressure on all surfaces. Lets dig deep into the topic to understand in a more clear manner. Bulk modulus of elasticity today we will look at of of the interesting topics in physics that is bulk modulus. Compressibility, definition of bulk modulus at high pressures, clearco silicone fluids are much more compressible than comparable organic fluids.
The bulk modulus appears to be less sensitive than the shear modulus to the relaxation that occurs after the application of the homogeneous strain. In english units, shear modulus is given in terms of pounds per square inch psi or kilo thousands pounds per square. What is the physical significance of derivative of bulk. Actually, compressibility is termed as the inverse of the bulk modulus. Bulk modulus definition and meaning collins english dictionary. Bulk modulus is a modulus associated with a volume strain, when a volume is compressed. The static moduli are those directly measured in a deformational experiment. The bulk modulus concept is mostly applied in liquids.
Sometimes referred to as the incompressibility, the bulk modulus is a measure of the ability of a substance to withstand changes in volume. Bulk modulus definition, a coefficient of elasticity of a substance, expressing the ratio between a pressure that acts to change the volume of the substance. Modulus of elasticity is used in solids and k values are differs in gases. The bulk modulus k \displaystyle k k or b \displaystyle b b of a substance is a measure of how resistant to compression that substance is. The inverse of the bulk modulus gives a substances compressibility other moduli describe the materials.
One definition of a fluid is a substance with a shear modulus of zero. In much simpler words, the bulk modulus is nothing but a numerical constant that is used to measure and describe the elastic properties of a solid or a fluid when pressure is applied. The bulk modulus k of a substance measures the substances resistance to uniform compression. The body of a human, especially when large or muscular. The applied pressure reduces the volume of a material, which returns to its original volume when the pressure is removed. Jan 30, 2019 a large shear modulus value indicates a solid is highly rigid. The bulk modulus elasticity or volume modulus is a material property characterizing the compressibility of a fluid how easy a unit volume of a fluid can be changed when changing the pressure working upon it. The fit will yield bulk modulus b 0, derivative of bulk modulus b 0 and volume at zero pressure v 0. The formula for bulk modulus is bulk modulus pressure applied fractional change in volume.
Bulk modulus definition and meaning collins english. Bulk modulus definition of bulk modulus by the free dictionary. The bulk modulus k or b of a substance measures the substances resistance to isostatic compression. Bulk modulus signifies the measure of substance resistance under pressure. In the high pressure xrd, pressure versus volume data is fitted by birchmurnaghan equation of state bmeos. Gases have a bulk modulus that varies with initial pressure, which makes it more of a subject for thermodynamics in particular the gas laws.
The bulk modulus can be formally defined by the equation. A small shear modulus value indicates a solid is soft or flexible. The modulus of elasticity of a liquid varies widely, depending on the specific gravity and temperature of the liquid. An elastic modulus also known as modulus of elasticity is a quantity that measures an object or substances resistance to being deformed elastically i. The bulk modulus k \displaystyle k or b \displaystyle b of a substance is a measure of how resistant to compression that substance is. Bulk modulus definition of bulk modulus by the free. Bulk modulus and fluid elasticity engineering toolbox. A distinct mass or portion of matter, especially a large one. It is nothing but a numerical constant that is used to measure. This document is highly rated by class 11 students and has been viewed 4763 times. Bulk modulus is the measure of the decrease in volume with an increase in pressure. It can be calculated from the elastic modulus by the following formula. Stainless steel with bulk modulus 163 10 9 pa is approximate 80 times harder to compress than water with bulk modulus 2.
The bulk modulus k characterizes this and is defined as the pressure rise dp per fractional volume decrease dvv. Th or q th are derived from equations that relate k t p to vibrational frequencies v i as a function of pressure for cubic structures or those that have only one nearest neighbor distance, by assuming that the mode gruneisen parameters. When the bulk modulus is constant independent of pressure, this is a specific form of hookes law of elasticity. What is the difference between compressibilty and bulk. It is the ratio of the infinitesimal pressure increase to the resulting relative decrease in the volume. Bulk modulus definition is the ratio of the intensity of stress to the volume strain produced by stress used of an elastic medium subjected to volume compression. The following relation, known as the arco formula, can be used to calculate the bulk modulus for crude oil. Bulk modulus is the proportion of volumetric stress related to a volumetric strain of some material. Pdf a comparative analysis of different techniques for calculating the bulk. The bulk modulus itself, which, by definition, is the pressure divided by the strain, may be expressed mathematically as. Simple relations between the first or second pressure derivative of the bulk modulus and first or second thermal gruneisen parameter. Mechanical deformation puts energy into a material. What is the the bulk modulus formula for anisotropic.
The above results show that the only possibility for. Youngs modulus, bulk modulus and elastic moduli class 11. It is defined as the ratio between pressure increase and the resulting decrease in a materials volume. Table 1 bulk modulus of power steering fluid for various pressures pressure bars bulk modulus at 65 c bars bulk modulus at 50 c 2 12977.
Bulk modulus when a body is subjected to three mutually perpendicular stresses, of equal intensity, then the ratio of the direct stress to the corresponding volumetric strain is known as bulk modulus. Here, dp is the change in pressure, dv is the change in volume, and v is the initial volume. Bulk modulus of elasticity definition, formula, examples. Bulk modulus definition of bulk modulus by merriamwebster. With many of todays hydraulic systems operating at pressures 5000 psi and higher, ignoring bulk modulus can compromise response time of a system. Gases are easily compressed, while solids and liquid are only compressed with difficulty. What is the physical significance of derivative of bulk modulus.
It is measured by a measuring instrument when another object is placed under pressure. The reciprocal of bulk modulus is called compressibility. The bulk modulus or of a substance is a measure of how resistant to compression that substance is. Together with youngs modulus, the shear modulus, and hookes law, the bulk modulus describes a materials response to stress or strain. Typical values are less than 30,000 psi to greater than 300,000 psi, depending upon the liquid. Material properties material properties for gases, fluids and solids densities, specific heats, viscosities and more. Bulk modulus is the measure of resistibility to the external forces acting on the body. Shear modulus definition is the ratio of the shearing stress in a body to the corresponding shearing strain. The bulk modulus of a substance measures the substances resistance to uniform compression. Jun, 2014 the pdf suggests the use of effective bulk modulus. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. If a fluid were compressed under some pressure, its volume would drop, however slightly. A flat slope signifies a fairly compressible fluid one with a low bulk modulus.
It is defined as the ratio of shear stress to corresponding shear strain within elastic limit. Bulk modulus definition of bulk modulus by medical. The term bulk modulus usually means the reciprocal of compressibility and defines the slope of the curve when plotted against specific volume, figure 1. Metals and alloys bulk modulus engineering toolbox. The bulk modulus k0 can be formally defined by the equation where p is pressure, v is volume, and dpdv denotes the derivative of pressure with respect to volume. Bulk modulus formula definition, equations, examples toppr. The term bulk modulus usually means the reciprocal of compressibility and defines the slope of the curve in figure 1. Bulk modulus of elasticity of a substance is basically defined as the ratio of compressive stress or hydro static stress to volumetric strain and it will be displayed by the symbol k. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Among silicone fluids, the low viscosity grades exhibit the greatest compressibility. Bulk modulus is defined as the proportion of volumetric stress related to the volumetric strain for any material. Stressstrain curve for a linear elastic material subject to uniaxial stress. To put in more simple words, bulk modulus is nothing but a numerical constant that is used to measure and describe the elastic properties of a solid or fluid when pressure is applied on all the surfaces. The bulk modulus of a solid or a fluid indicates its resistance to a change in volume.
What is the the bulk modulus formula for anisotropic material. Compressibility, definition of bulk modulus clearco products. A steep slope signifies a stiff, only slightly compressible fluid one with a high bulk modulus. Bulk modulus simple english wikipedia, the free encyclopedia. Information and translations of bulk modulus in the most comprehensive dictionary definitions resource on the web. To begin with, bulk modulus is defined as the proportion of volumetric stress related to the volumetric strain of a specified material, while the material deformation is within elastic limit. An increase in the pressure will decrease the volume 1. Bulk modulus and fluid elasticity introduction to and definition of bulk modulus elasticity commonly used to characterize compressibility of fluids. Bulk modulus definition, a coefficient of elasticity of a substance, expressing the ratio between a pressure that acts to change the volume of the substance and the fractional change in volume produced. The shear modulus is defined as the ratio of shear stress to shear strain.
A simple theoretical model for the bulk modulus of elastomers based. Grain size dependence of elastic moduli in nanocrystalline tungsten. But as far as bulk modulus is concerned, it is the ratio between mean normal stress and volumetric strain, subjected to hydrostatic stress which is the mean normal stress. This longitudinal modulus of elasticity is called youngs modulus. In other words, a large force is required to produce deformation. Pressure derivatives of the bulk modulus hofmeister 1991. The pressure on the cube is defined as the normal fore per unit area. The fit will yield bulk modulus b 0, derivative of bulk modulus b 0 and. The static and dynamic moduli of the same rock may significantly differ from each other. Because specific volume is dimensionless, units of bulk modulus are the same as pressure psig bar, pa, nm 2.
Sep 18, 2015 you need to appreciate the concept of modulus of elasticity of a material the fact that we are talking of elasticity naturally implies our acceptance of the material as being necessarily deformable under application of external pressure the. Bulk modulus is usually obtained from experimental or theoretical or semi theoretical theory with experimental work to fit energyvolume data. Pressure derivatives of the bulk modulus hofmeister. Modulus meaning in the cambridge english dictionary. Jan 28, 2018 if a fluid were compressed under some pressure, its volume would drop, however slightly. The objective of this study was to examine prospective tests for determining the bulk modulus of elastomers used in the construction of elastomeric bearings. Bulk modulus article about bulk modulus by the free dictionary. The pdf suggests the use of effective bulk modulus. A decrease in the volume will increase the density 2. Bulk modulus of elasticity definition, examples, diagrams. Shear modulus definition of shear modulus by merriamwebster. Strain energy density for a given value of the strain, the strain energy density per unit volume. The aim of this study was to characterize the bulk modulus properties of the upper arm under relaxed and controlled contraction which is defined as 25% of the maximum voluntary contraction. The elastic modulus of an object is defined as the slope of its stressstrain curve in the elastic deformation region.
The bulk modulus is a constant the describes how resistant a substance is to compression. Pdf technique for calculating the bulk modulus researchgate. Bulk modulus article about bulk modulus by the free. At high pressures, clearco silicone fluids are much more compressible than comparable organic fluids. Jan 27, 2019 the bulk modulus is a constant the describes how resistant a substance is to compression. Bulk modulus is related to modulus of elasticity and poissons ratio as. The great bulk of necessary work can never be anything but painful. The bulk modulus is a property of materials in any phase but it is more common to discuss the bulk modulus for solids than other materials. Volumetric strain and bulk modulus engineers gallery. Solution for the effective bulk modulus of a medium with square pores. A stiffer material will have a higher elastic modulus. The bulk modulus, also known as the volume modulus of elasticity, is the ratio of normal stress.
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