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Today we will see the interesting topic of physics, that is bulk modulus. Bulk modulus is defined as the ratio of volumetric stress to the volumetric strain of any material. In simple terms, bulk modulus is nothing more than a numerical constant which is used to determine and describe the elastic properties of a solid or fluid under pressure.
Bulk’s Modulus
The bulk modulus property of the material depends on its elastic behaviour. It is one of the measures of the mechanical properties of solids. Other similar moduli of elasticity are Young’s modulus and shear modulus. In all cases, the bulk elastic properties of a material are used to determine how much it can be compressed under a given external pressure. Finding the relationship between pressure change and partial volume compression is very important.
The bulk’s modulus is the relative change of the volume of a body generated by a unit compression unit or a tensile stress which acts uniformly along the surface.
The bulk’s modulus explains how a substance behaves when it is uniformly compressed. It is a fact that external forces normal to the surface are distributed uniformly or evenly over the object’s surface. This can also occur if an object is immersed in a fluid and undergoes a change in volume without any change in the shape.
Bulk Modulus Formula
The Bulk Modulus formula is given as
K= V x ΔP/ΔV
Here,
K = Bulk’s modulus
V = original volume
ΔP= pressure change
ΔV= volume change
Bulk’s modulus K is also given as
K=pressure/strain
The bulk’s modulus of liquid is the determination of compressibility of the liquid.
Units of bulk’s modulus are Pa or K.Pa and M.Pa as bigger units.
The bulk’s modulus is symbolically represented as K. And the dimension of Bulk modulus is the force per unit area. It is also expressed as N/m2 in the metric system.
Bulk’s Modulus Formula in Fluid Mechanics
Fluids are generally viewed as objects which flow and adjust to fill their environment. In physics, the definition of fluid is more precise.
Liquid and gas are the types of fluid. The bulk modulus of gas and liquid are given here.
Bulk’s Modulus of Gas
All gases have an equation relating density, pressure and temperature, that is, an equation of state. This helps us derive an explicit relation between density and pressure. These relations are based on the process under consideration, that is, isentropic with constant entropy or isothermally with constant temperature.
The bulk modulus formula for gas is given from
p/h0 = isothermal process constant ————— (1)
p/h0k= isentropic process constant ————— (2)
Here, k = ratio of specific heat at constant pressure cp to the heat at constant volume cv
cp – cv = R
At normal conditions
k=1.4(air)
When we substitute the equations (1) and (2) in bulk modulus formula then we get
Ev= p (Isothermal process)
Ev=kp (Isentropic process)
Hence, the bulk modulus of a gas depends or based on pressure
Bulk modulus of Liquid
Liquids are normally compressing more than solids, although they are less compressible than gases.
But the liquid we deal with most often is water (and the things water has in it). Water is not much compressible, and indeed, during the fluid motion, water is considered as incompressible.
Bulk modulus of a liquid is the ratio of pressure change to the relative volume change.
Bulk modulus for liquid is denoted by B and is given as
B = Δp x V/ΔV
Here,
Δp = pressure change
ΔV = volume change
V = original volume
This quantity helps us to understand how fluids react to pressure changes, and it is also important because it explains the ease with which a pressure wave, like a sound, is moved through a liquid.
The more the value of bulk modulus of liquid, the more pressure required to generate fractional change of volume.
Bulk Modulus of water is 1.96×109 Pa. This is very small as compared to many solids, like stainless steel has 160×109 Pa.
Bulk Modulus of bone is just 15×109 Pa.
Fluid
Fluids are generally viewed as objects which flow and adjust to fill their environment. In physics, the definition of fluid is more precise. Fluids here refer to any material which cannot withstand a tangential shear force and constantly changes shape in response to that shear force.
A liquid is a fluid which has a specific volume but not specific shape. A liquid is not expanded indefinitely (as gas) and also is not compressed infinitely due to the forces between the molecules in the liquid.
Conclusion
The bulk modulus is the relative change of the volume of a body generated by a unit compression unit or a tensile stress which acts uniformly along the surface.
The Bulk Modulus formula is given as
K=VxΔP/ΔV
Bulk modulus K is also given as
K=pressure/strain
Bulk modulus for liquid is denoted by B and is given as
B = Δp x V/ΔV
The bulk modulus formula for gas is given from
p/h0= isothermal process constant
p/h0k= isentropic process constant
