Bulk modulus of compressibility

Modulus of Elasticity, Modulus of Rigidity, and Bulk Modulus of Compressibility... 

Most of you have pumped air into a bicycle tire at one time or another. From this and other experiences you know that gases are more easily compressed than liquids. In et jineering, to see how compressible a fluid is, we look up the value of a bulk modulus of compressibility of the fluid. The value of fluid bulk modulus shows how easily the volume of the fluid can be reduced when the pressure acting on it is increased. 

You should undersmnd what is meant by pressure. For stadc fluids, you diould understand Pascal s law, which states that fluid pressure at a point is the same in all direcdons. You should also remember the reladonship between the fluid pressure and the dq>th of the fluicL You should undemand what the fluid properdes such as viscosity and bulk modulus of compressibility mean. You should also have a good idea of how hydraulic systems work. 

Viscosity, vapor pressure, and bulk modulus of compressibility are adffitional fluid properties that engineers consider in design. 

Bulk Modulus of Compressibility A fluid bulk modulus represents how compressible the fluid is. How easily can one reduce the volume of the fluid when the fluid pressure is increased For example, as we discussed in Chapter 10, it would take a pressure of 2.24 X 10 N/m to reduce 1 m volume of vrater by 1% or, said another w, to a final volume of 0.99 m ... 

The increasing of NOjc was shown to be related to a small shift in fuel injection timing caused by the different mechanical properties of biodiesel relative to conventional diesel. Because of the higher bulk modulus of compressibility (or speed of sound) of biodiesel, there is a more rapid transfer of the fuel pump pressure wave to the injector needle, resulting in earlier needle lift and producing a small advance in injection timing (Knothe et ah, 2005). 

Mechanical Properties. Measuremeat of the mechanical properties of diamoad is compHcated, and references should be consulted for the vahous qualifications (7,34). Table 1 compares the theoretical and experimental bulk modulus of diamond to that for cubic BN and for SiC (29) and compares the compressive strength of diamond to that for cemented WC, and the values for the modulus of elasticity E to those for cemented WC and cubic BN. 

In addition to the tensile and shear moduli, a compressive modulus, or modulus of compressibility, K, exists to describe the elastic response to compressive stresses (see Fignre 5.7). The compressive modulus is also sometimes called the bulk modulus. It is the proportionality constant between the compressive stress, CTc, and the bulk strain, represented by the relative change in bulk volume, AV/Vo-... 

Bulk Compressibility and Bulk Modulus is one of the important constants of aa elastic solid Bulk modulus is defined as the tatio of stress to atrsin when the stress is a pressure applied equally on all surfaces of the sample and the strain is the resulting change in volume per suit volume. The reciprocal of bulk modulus Is called bulk compressibility. One apparatus for the direct exnd measurement of the dynamic bulk modulus of a solid was developed at the NOL, White Oak, Md(Ref 1). Some data obtained, on several HE a, using this apparatus are given in Refa 2, Refs l)NAVORD Kept No 1534(1950) 2)NAVORD Rept No 4380(1956) 3)PATR 1740,Rev 1(1958)... 

For description of an apparatus used by Philipoff Brodnyan, see Ref 3, and of that used by McKinney et al, see Ref 4 Refs l)E.Meyer K.Tamm, AkustZeitschr 7, 45 50(March 1942), "An Accustic Method for Determining the Dynamic Compressibility and Loss Factor of Elastic Substances 2)C.S. Sandler, NAVORD Rept 1524(Sept 1950), "An Accoustic Technique for Measuring the Effective Dynamic Bulk Modulus of Elasticity and Associated Loss Factor in Rubber and Plastics 3)W.Philipoff J.Brodnyan, JApplPhys 26, 846-9(1955), "Preliminary Results in Measuring Dynamic Compressibilities 4)J. E. McKinney et al, JApplPhys 27, 425-30(1956), "Apparatus for the Direct Determination of the Dynamic Bulk Modulus 5)W.S.Cramer, NAVORD Rept 4380(Sept 1956), "Bulk Compressibility Data on Several Explosives 6)J.Alster, PicArsn, Dover, NJ private communication(1961)... 

Thus a measurement of the ultrasonic velocity and density can be used to determine the adiabatic compressibility (or bulk modulus) of the material. For homogeneous solids measurements of the compression and shear velocities can be used to determine the bulk and shear moduli (see section 2.4). The Young s modulus of rod-like materials (e.g. spaghetti) can be determined by measuring the velocity of ultrasound. 

Type of Material Apparent Density, kg/m3 Bulk Modulus, MPa Compressive Modulus, MPa... 

The amorphous phase appearing above 20 GPa at room temperature (see above) has also recently been studied by X-ray diffraction [135] and Raman scattering [132,133]. Serebryanaya et al. [135] identify the structure as a three-dimensionally polymerized Immm orthorhombic lattice, but find that compression above 40 GPa gives a truly amorphous structure. In contrast to the orthorhombic three-dimensional polymer structure discussed in the last section, the best fit here is found for (2+2) cycloaddition in two directions, with (3+3) cycloaddition in the third, and thus some relationship to the tetragonal phase. From the in situ X-ray data a bulk modulus of 530 GPa is deduced, about 20% higher than for diamond. Talyzin et al. [132, 133] find that this phase depolymerizes on decompression into linear polymer chains, unless the sample is heated to above 575 K under pressure. A strong interaction with the diamond substrate is also noted, such that only films with a thickness of several hundred nm are able to polymerize fully [ 132]. Hardness tests were also carried out on the polymerized films, which were found to be almost as hard as diamond and to show an extreme superelastic response with a 90% elastic recovery after indentation [133]. 

The compressibility k is the reciprocal of the compression modulus or bulk modulus of the material. This important property will be discussed in Chap. 13 (Mechanical properties of solid polymers). The application of Eq. (7.27) is restricted to polymer melts. For amorphous polymers below the melting point, the internal pressure n may be defined as well ... 

Composite structure of fibres, 33 Composition parameter, 858 Comprehensive tables, 858 Compressibility, 224,385 Compressional waves, 390-1 Compression (bulk) modulus, 514 Compressive failure, 834 Compressive strength, 835 Concept... 

One of the basic mechanical properties of the foam is its compressibility (elasticity). By definition the bulk modulus of elasticity Ev is expressed by... 

Much of the work on the compressibility and bulk modulus of liquids reported in the literature was motivated by problems in mass hydraulic flow, such as raising a hydraulic fluid to a pressure in the range 68.9-137.8 MPa (10,000-20,000 Ib/in ) and circulating it through the hydraulic system. In this type of problem most of the emphasis is on the isothermal compressibility of the fluid. 

The partial occupancy of the Ml site by divalent cations, and a greater Si content in the tetrahedral sheet, should decrease the compressibility. Therefore the presence of a phengitic component probably increases the mica stiffness, as shown by the increased bulk modulus of phengite-SZ in comparison with that of end-member muscovite (Pavese et al. 1999b). The difference found, however, could be partially ascribed to the different mica polytype. A statistical study on the occurrence of metamorphic phengites by Sassi et al. (1994) seems to show that the crystallization of the 3T polytype is mainly favored by high PIT ratio conditions. 

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