Compressibility and bulk modulus

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)... 

Bulk compressibility and bulk modulus 2 DC see Bulk modulus and bulk compressibility 2 B323-B324... 

These are the 2D analogs of the bulk isothermal compressibility and bulk modulus, respectively. The scaling concepts introduced above clearly make sense in terms of the compressibility/elasticity as well. For polymers where the interface is a good solvent, the lateral modulus, sometimes called static di-lational elasticity, is small whereas it becomes larger as the interface becomes poorer. 

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. 

Boyer, R.F. and Miller, R.L. (1984) Correlation of liquid-state compressibility and bulk modulus with cross-sectional area per polymer chain. Macromolecules, 17 (3), 365-369. 

Other authors have studied other correlations. Two are Povarennykh (1964), and Goble and Scott (1985). The latter emphasized compressibility (inverse bulk modulus) as did Beckmann (1971). The bulk modulus is not a reliable measure for the same reason as the cohesive energy. It is volume dependent rather than shear dependent. Still another attempt to correlate hardness and compressibility was that of Yang et al. (1987). This was followed by a proposal by Liu and Cohen (1990) that hardness and bulk moduli are related. This proposal was refuted by Teter (1998) who showed that hardness values correlate better with shear moduli than with bulk moduli. 

R. J. Goble and S. D. Scott, The Relationship between Mineral Hadness and Compressibility (Or Bulk Modulus), Canadian Mineralogist, 23,273 (1985). 

Bulk Compressibility. See Bulk Modulus and Bulk Compressibility... 

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. 

The room temperature elastic moduli, such as the compression or bulk modulus K , Young s modulus E , and shear modulus G of the Ti5Si3 and TiSi2 compounds are presented in table II. The bulk and shear moduli are relatively low in comparison to the Young s moduli. This implies that Poisson s ratio is about V = 0,24 or less indicating that the elastic transverse... 

The modulus of elasticity, E, and the modulus of rigidity, G, as defined above, apply under longitudinal and shear forces, respectively. When a hydrostatic force is applied, a third elastic modulus, the modulus of compressibility or bulk modulus, K, is used. It is the reciprocal of compressibility, /J, and is defined as the ratio of the hydrostatic pressure, cri,> to the volumetric strain, AV/Vo ... 

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

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. 

Most time-independent fluid flow depends upon pressure difference, AP [ML T ] gravitational acceleration, g [LT ] fluid density, p [ML ] viscosity, p [L MT ] surface tension, a [MT ] compressibility as bulk modulus, /3 [ML T ] linear size, L [L] and fluid velocity, V [LT ]. We will use dimensional analysis to determine the most common engineering descriptions for fluid flow. 

The Young s modulus, bulk compressibility and shear modulus can be related through the addition of a fourth constant, Poisson s ratio v. 

Therefore, the macroscopically measurable B and Aco connect directly to the bond length and energy of the specimen and their response to the intrinsic coordination imperfection and the applied stimuli through the BOLS correlation and the LBA approach. Exercises lead to derived information of the cohesive energy and Debye temperature, energy density, compressibility, the bulk modulus and their first-order derivatives, and the analytical correlation between the B and Aco. 

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