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The bulk modulus (or or ) of a substance is a measure of the resistance of a substance to bulk compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume .
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility [1] or, if the temperature is held constant, the isothermal compressibility [2]) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.
Other names are sometimes employed for one or both parameters, depending on context. For example, the parameter μ is referred to in fluid dynamics as the dynamic viscosity of a fluid (not expressed in the same units); whereas in the context of elasticity, μ is called the shear modulus, [2]: p.333 and is sometimes denoted by G instead of μ.
In fluid mechanics, ... , is the specific volume at pressure , is the bulk modulus at , and is a material parameter. Pressure formula. This equation, in pressure form ...
The Cauchy number (Ca) is a dimensionless number in continuum mechanics used in the study of compressible flows. It is named after the French mathematician Augustin Louis Cauchy . When the compressibility is important the elastic forces must be considered along with inertial forces for dynamic similarity.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The third-order Birch–Murnaghan isothermal equation of state is given by = [() / /] {+ (′) [() /]}. where P is the pressure, V 0 is the reference volume, V is the deformed volume, B 0 is the bulk modulus, and B 0 ' is the derivative of the bulk modulus with respect to pressure. The bulk modulus and its derivative are usually obtained from ...
where () and () are the rock bulk moduli saturated with fluid 1 and fluid 2, () and () are the bulk moduli of the fluids themselves, and is the rock's porosity. Step 3: Leave the shear modulus unchanged (rigidity is independent of fluid type):