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Saturday, 9 December 2017

COMPRESSIBILITY AND BULK MODULUS IN FLUID MECHANICS

We were discussing the basic definition and significance of Fluid mechanics, Kinematic viscosity, Dynamic viscosity, various properties of fluid, type of fluids and Newton’s law of viscosity in our previous post. 

Now we will understand here the basic concept of compressibility and bulk modulus, in the subject of fluid mechanics, with the help of this post.

Compressibility and bulk modulus

So, let us discuss first basic concept and importance of bulk modulus and later we will see here the concept of compressibility.

Bulk Modulus

Bulk modulus of elasticity of a substance is basically defined as the ratio of compressive stress or hydro static stress to volumetric strain and it will be displayed by the symbol K. 

Bulk modulus of a substance provides the information about the resistance of substance to the uniform pressure. 

In simple, we can also say that Bulk modulus of a substance provides the information about the compressibility of that substance. 

Let us say that if a substance is highly compressible, it indicates that substance will have low bulk modulus. Similarly, if a substance is less compressible, it indicates that substance will have high bulk modulus. 

Let us see here the bulk modulus of some common materials

As we can see from above figure that value of bulk modulus for solids is quite larger than that for liquid and therefore solid substance will be less compressible as compared to the liquid. 

Similarly, value of bulk modulus for liquid is quite larger as compared to the value of bulk modulus of gases and therefore gases will be much more compressible as compared with liquid. 

In simple, we can say that solid substances will be least compressible and gases will be most compressible. 

Let us consider a cylinder contained with gas and fitted with piston and piston rod as displayed in following figure.

Let us consider that initial volume of gas inside the cylinder is V and pressure is P. Let us think that we are increasing the pressure of gas from P to P + ΔP. As we are increasing the pressure of gas, volume of gas will be reduced from V to V – ΔV. 

Increase in pressure = ΔP 
Change in volume = - ΔV 

Negative sign indicates that volume of gas enclosed in cylinder will be reduced once pressure will be increased. 

Volumetric strain = Change in volume / Original Volume 
Volumetric strain = - ΔV / V 
Bulk Modulus = Increase of pressure / Volumetric strain 
Bulk Modulus = ΔP / (-ΔV / V) 
Bulk Modulus = - V ΔP /ΔV
Compressibility
The reciprocal of bulk modulus of elasticity will be termed as the compressibility of that substance. 

Mathematically we can say that
Compressibility = 1 / Bulk Modulus
Compressibility = 1/K

We will now discuss the surface tension in the category of fluid mechanics in our next post. 

Do you have suggestions? Please write in comment box.

Reference:

Fluid mechanics by Y. Nakayama and R F Boucher
Image Courtesy: Google

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