Bulk modulus: Definition, factors, formula

Introduction

It is one of the elemental properties of the solids. The bulk modulus or bulk modulus of elasticity is defined as the ratio of the volumetric stress associated with the volumetric elongation of a particular material when the deformation of the material is within the elastic range. To define bulk modulus it may be called a numerical constant used to measure and describe the elastic properties of a solid or liquid when pressure is applied to any surface. 

The bulk modulus factor is an indicator that measures the mechanical properties of a solid. Other moduli of elasticity include modulus of elasticity and modulus of shear. In both cases, the volumetric elastic properties of the material are used to determine the compression ratio at a specific external pressure. The key here is to find and pay attention to the relationship between the pressure change and the partially compressed volume.

Bulk modulus definition

The Bulk modulus (K or B) of a substance is a quantified measure of its pressure resistance. It can be defined as the ratio of a minor increase in pressure to the resulting relative decrease in volume. Alternatively, it can be defined as a relative change in the volume of an object created by compressive or tensile stress applied uniformly to the surface.

Mathematical representation of bulk modulus of elasticity

This is the result of the relationship between the applied pressure and the resulting decrease in material volume. Mathematically, it is:

K = ΔP / (ΔV / V)

where:

K: bulk modulus

ΔP: Variation in pressure or force acting on a material per unit area.

ΔV: change in material volume due to compression

V: Initial volume of material (in English units) and N/m2(in meters).

Bulk Modulus Factors

The main factors affecting the mass modulus of a liquid are-

• the temperature and 
• the fluid being entrained.

The volume coefficient decreases with increasing temperature. In other words, the lower the temperature of the liquid, the harder it is to compress it. The entrained gas (mainly air) has a significant influence on the mass modulus of the liquid. The more gas there is in the liquid, the lower the volume ratio. The exception is that the volumetric modulus of elasticity of the liquid is lower than the volumetric modulus of compression of air and vice versa.

 Application

Bulk modulus is an important factor that must be considered in hydraulic systems. 

The mass modulus of materials can be measured experimentally using a variety of methods (e.g. powder diffraction). In this procedure, X-rays or electrons directly irradiate dust or microcrystalline samples. However, simulated values are more common today. These patterns must be entered as other tested or known attribute values to get the mass modulus value.

Here is an example of an empirical test configuration for the volume module:

• Vibration tester
• Acoustic connection
• Holographic interferometer
• Electronic point interferometer
• Doppler interferometer

 Bulk modulus of water

Liquids are usually more compressible than solids, but much less compressible than gases.

However, the most common liquid that biology deals with is water. Water is no less compressible. When describing the movement of a liquid, water is considered incompressible. Let’s dive deeper into the bulk modulus of water

The bulk modulus of water is 1.96 109Pa. It’s much smaller than a lot of solids. For example, the bulk modulus of stainless steel is 160 109Pa. However, since the volume elasticity module of the bone is 15 × 109Pa, the compressibility of water is less than a tenth of the compressibility of biological solids.

Trends observed in the compressibility of water as a liquid

Since pressure and volume change with depth, we will use the volume modulus to determine how the density of water changes with depth, which is important. 

• The weight of the liquid pushing it from above increases the pressure as the depth of the liquid increases as per the Archimedes principle. 
• With water, the pressure increases by 101.3 kPa per 10 m depth) at a depth of 100 m, the pressure increase (Δp) is 1013 kPa (10 times more than at the surface). 
• The amount of water (ΔV / V) decreases with increasing pressure. 
• Using this formula, a small change in this volume can be calculated as

ΔP / B = 5.2 10-4. This is 5 parts out of 10,000, or about 0.05%. 100 meters or 300 feet deep!(Where is B bulk modulus of water is 1.96 109Pa ).

• With decreasing volume, the density of water increases from 1000 kg m-3 to 1000.52 kg m-3. As a result, the density of the water increases slowly with the increasing depth of lakes and seas. 

In most cases, water can be considered incompressible.

How do animals survive under this pressure?

This enables the animal to survive as well as possible at different heights, especially at different depths. Some animals retain moderate amounts of gas and change size with pressure, while others avoid this problem by using incompressible liquids or low-density solids. A more unusual way of holding air in the body by a squid. Its name comes from the cartridge, an incompressible foam-like structure that can hold gas at different pressures. Other creatures change their body chemistry to control their density and avoid using compressible amounts of air to balance buoyancy. These significant changes take time to accumulate, but they are more stable and do not depend on great changes in pressure.

Conclusion:

Bulk modulus is the volumetric measure of elasticity of a solid. Unlike Young’s modulus of elasticity it extends to fluids as well. The absolute value of the bulk modulus has a significant influence on the system performance in terms of position, power level, response time and stability. Two factors that play an important role in quality control are the fluid temperature and the fluid content. With today’s demand for higher performance and response time, paying attention to quality factors is more important than ever. It is one of the prime fundamental properties that engineers look at during the selection of material for various purposes.