Bulk Modulus

The bulk modulus is a constant that describes how compressible a substance is. It is defined as the ratio of an increase in pressure to a reduction in the volume of a substance. The bulk modulus, together with Young’s modulus, shear modulus, and Hooke’s law, characterises a material’s reaction to stress or strain. In equations and tables, bulk modulus is usually denoted by K or B. While it may be applied to any substance, it is most commonly used to explain the behaviour of fluids. It may be used to forecast compression, compute density, and infer the types of chemical bonding inside a substance indirectly. Because a compressed material returns to its original volume once the pressure is removed, the bulk modulus is considered a descriptor of elastic characteristics. Pascals (Pa) or newtons per square metre (N/m2) in the metric system, or pounds per square inch (PSI) in the English system, are the units for the bulk modulus.

Definition of bulk modulus

The bulk modulus is a numerical constant that characterises the elastic characteristics of a solid or fluid when it is subjected to pressure on all sides. When pressure is applied to a material, its volume decreases, but it returns to its normal volume when the pressure is released. The bulk modulus, also known as the incompressibility, is a measure of a substance’s capacity to sustain changes in volume when compressed on all sides. It is calculated as the quotient of applied pressure divided by relative deformation. Steel has a bulk modulus of around 2.310⁷ psi, or 1.6×10¹¹ pascals, which is three times that of glass. As a result, just one-third the pressure is required to decrease a glass sphere to the same extent as a steel sphere of the same beginning size. The proportionate loss in volume of glass under equal pressure is three times that of steel. Glass may also be said to be three times more compressible than steel. Compressibility is, in reality, defined as the reciprocal of the bulk modulus. A difficult-to-compress material has a high bulk modulus but a low compressibility. A compressible material has a high compressibility but a low bulk modulus.

Formula

The bulk modulus formula is B =ΔP/(ΔV/V). Where, Bulk Modulus = B Pressure variation = Δ P Volume Variation = ΔV The unit bulk modulus Pa or KPa units, and MPa is the greater value. We symbolise it with the letter K. It has a force per unit area dimension. In the metric system, we express it in newtons per square metre (N/m2).

What is the importance of bulk modulus?

The bulk modulus of a fluid is a characteristic that reflects its compressibility. With many of today’s hydraulic systems working at pressures of 5000 psi or more, disregarding bulk modulus can jeopardise system reaction time. Rather than compressing the fluid, applied pressure should have a direct effect on the system’s activity.

Effect of temperature and pressure on bulk modulus

Pressure and temperature are common physical factors that influence subsurface porous systems under both ambient geology conditions and engineering operations such as fluid injection and thermal operations. As a result, in order to plan subsurface activities efficiently, trends in elastic parameter fluctuations with temperature and pressure must be studied. Temperature and pressure effects on the bulk modulus of saturated porous systems have been measured in the petroleum literature. Experiment findings have been reported, and they forecast fascinating and clear tendencies. The influence of pressure and temperature on the bulk modulus of the saturated porous system under undrained circumstances, which is largely applicable to low permeability settings, is mathematically explored in this study.

Why does liquid have a bulk modulus?

Fluids have a bulk modulus but no shear modulus (both liquids and gases). It may appear strange that an entire class of materials has nonzero resistance to one type of deformation but no resistance to another. The key distinction between a bulk modulus and a shear modulus is that bulk deformation entails a change in volume, whereas shear deformation does not. Because there is no shear stress, any arbitrary little shear force can cause a fluid to flow. If we neglect any resistance given by the box, any arbitrarily little force can cause the top of a square box to slide to the left, transforming it into a parallelogram.

Conclusion

The bulk modulus is a constant that describes how compressible a substance is. It is defined as the ratio of an increase in pressure to a reduction in the volume of a substance. The bulk modulus, together with Young’s modulus, shear modulus, and Hooke’s law, characterises a material’s reaction to stress or strain. Because a compressed material returns to its original volume once the pressure is removed, the bulk modulus is considered a descriptor of elastic characteristics. The bulk modulus, also known as the incompressibility, is a measure of a substance’s capacity to sustain changes in volume when compressed on all sides. Key distinction between a bulk modulus and a shear modulus is that bulk deformation entails a change in volume, whereas shear deformation does not.