The bulk modulus (K) of a substance essentially measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to effect a given relative decrease in volume. The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ... The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ...

As an example, suppose an iron cannon ball with bulk modulus 160 GPa (gigapascal) is to be reduced in volume by 0.5%. This requires a pressure increase of 0.005×160GPa = 0.8 GPa. If the cannon ball is subjected to a pressure increase of only 100 MPa, it will decrease in volume by a factor of 100MPa/160GPa = 0.000625, or 0.0625%. Look up giga- in Wiktionary, the free dictionary. ... The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Youngs modulus and tensile strength). ... mega- (symbol M) is an SI prefix in the SI system of units denoting a factor of 106, i. ...

The bulk modulus K can be formally defined by the equation:

where p is pressure, V is volume, and ∂p/∂V denotes the partial derivative of pressure with respect to volume. The inverse of the bulk modulus gives a substance's compressibility. In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). ... Fluid Dynamics Compressibility (physics) is a measure of the relative volume change of fluid or solid as a response to a pressure (or mean stress) change: . For a gas the magnitude of the compressibility depends strongly on whether the process is adiabatic or isothermal, while this difference is small in...

Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear strain. For a fluid, only the bulk modulus is meaningful. For an anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law. Look up strain in Wiktionary, the free dictionary. ... Stress is the internal distribution of force per unit area that balances and reacts to external loads applied to a body. ... In materials science, shear modulus S, sometimes referred to as the modulus of rigidity, is defined as the ratio of shear stress to the shear strain: S = shear stress/shear strain = (F/A)/Φ. Another commonly accepted symbol is G. Shear modulus is usually measured in ksi (kips per square... This article does not adequately cite its references or sources. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ... Trunks A tree trunk as found at the Veluwe, The Netherlands Wood is a solid material derived from woody plants, notably trees but also shrubs. ... A blank sheet of paper Paper is a commodity of thin material produced by the amalgamation of fibers, typically vegetable fibers composed of cellulose, which are subsequently held together by hydrogen bonding. ... Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...

Strictly speaking, the bulk modulus is a thermodynamic quantity, and it is necessary to specify how the temperature varies in order to specify a bulk modulus: constant-temperature (K_T), constant-enthalpy (adiabatic K_S), and other variations are possible. In practice, such distinctions are usually only relevant for gases. Thermodynamics (Greek: thermos = heat and dynamic = change) is the physics of energy, heat, work, entropy and the spontaneity of processes. ... Fig. ... In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... In thermodynamics, an adiabatic process is a process in which no heat is transferred to or from working fluid. ... A gas is one of the four major phases of matter (after solid and liquid, and followed by plasma, that subsequently appear as a solid material is subjected to increasingly higher temperatures. ...

For a gas, the adiabatic bulk modulus K_S is approximately given by

where

κ is the adiabatic index, sometimes called γ.

p is the pressure.

The adiabatic bulk modulus K and the density ρ of a substance determine the speed of sound c (for pressure waves) in a material, according to the formula The adiabatic index of a gas, is the ratio of its specific heat capacity at constant pressure (CP) to its specific heat capacity at constant volume (CV). ... The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ... In physics, density is defined as mass m per unit volume V. Mathematically, it is expressed as where, in SI units: ρ (rho) is the density of the substance, measured in kg·m-3 m is the mass of the substance, measured in kg V is the volume of the substance... The speed of sound is a term used to describe the speed of sound waves passing through an elastic medium. ...

Solids can also sustain transverse waves; for these the shear modulus is the key determining factor. A light wave is an example of a transverse wave. ... In materials science, shear modulus S, sometimes referred to as the modulus of rigidity, is defined as the ratio of shear stress to the shear strain: S = shear stress/shear strain = (F/A)/Φ. Another commonly accepted symbol is G. Shear modulus is usually measured in ksi (kips per square...

Bulk modulus values for some example substances

• Water: 2.2×10⁹ Pa (value increases at higher pressures)
• Air: 1.42×10⁵ Pa
• Steel: 1.6×10¹¹ Pa
• Solid helium (approximate): 5×10⁷ Pa

Impact of a drop of water. ... The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Youngs modulus and tensile strength). ... The steel cable of a colliery winding tower. ... General Name, Symbol, Number helium, He, 2 Chemical series noble gases Group, Period, Block 18, 1, s Appearance colorless Atomic mass 4. ...

References

• Bulk Elastic Properties on hyperphysics at Georgia State University