What is the Bulk Modulus?

Kirsten C. Tynan

Materials generally can be compressed when subjected to external pressures applied over their surfaces. The reduction in the volume of a material under a given pressure varies widely from material to material. Gases are generally most easily compressed under pressure whereas solids can be compressed relatively little and with great difficulty. The bulk modulus is a material property indicating the degree of resistance of a material to compression. It may also be referred to by a number of other terms such as the bulk modulus of elasticity, the modulus of compression, and others.

Scientist with beakers
Scientist with beakers

One way to think of it is as the reciprocal of compressibility. High bulk modulus for a material indicates a relatively high resistance to compression, meaning it is hard to compress. A low value indicates relatively little resistance to compression, meaning the material is relatively easily compressed. For example, the bulk modulus of steel is several orders of magnitude larger than that of air, which can be compressed relatively easily with an air compressor.

Values of the bulk modulus of a material vary depending on factors such as the temperature of that material or the amount of air that is mixed into it. As a material heats up, its volume will generally expand thereby resulting in a more open physical structure that is easier to compress. Air trapped in a material also affects the physical structure of a material thereby affecting its bulk modulus.

Some fluids, such as water or hydraulic fluid, are sometimes casually referred to as incompressible fluids. This is not strictly accurate, but because their compressibilities are relatively low, the bulk modulus can be ignored in some engineering calculations. Under certain circumstances, however, such as in some high pressure situations, it must be taken into account to ensure proper system design and function.

For example, performance of hydraulic equipment under very high pressure can be degraded if the bulk modulus of the hydraulic fluid is not taken into account in system design. This is because some energy is expended in compressing the hydraulic fluid rather than going directly toward the work the equipment performs. The fluid in the system must be compressed to the point it resists further compression before the equipment and load will be acted upon. Diversion of energy from the primary task may affect the position of the equipment, the power it has available for its intended function, response time, and so on.

The bulk modulus is less often a characteristic of interest with respect to solids since they typically are extremely hard to compress, but it is relevant in some circumstances. The speed at which sound travels through a solid depends in part on the bulk modulus of the material. The amount of energy that can be stored in a solid is also related to this property so it is relevant to the study of earthquakes and seismic waves.

As a mathematical function, this material property is expressed as the ratio of the applied pressure to the change in volume of the substance per unit of volume. This yields a value expressed in the same units used to express pressure because the units of volume cancel out. In graphical form, it is the slope of the curve formed by plotting the pressures applied to a material versus the material's corresponding specific volumes at those pressures.

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