We were discussing the basic definition and significance ofÂ Fluid mechanics, Kinematic viscosity, Dynamic viscosity, various properties of fluid, type of fluids and Newtonâ€™s law of viscosityÂ in our
previous post.Â

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.

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.

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**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.Â

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

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

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.Â

Let us see here the bulk modulus of some common materials

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

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

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.Â

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.Â

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.Â

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

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

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.Â

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

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 + Î”P. As we are increasing the pressure of gas,
volume of gas will be reduced from V to V â€“ Î”V.Â

Increase in pressure = Î”PÂ

Change in volume = - Î”VÂ

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

Volumetric strain = Change in volume / Original VolumeÂ

Volumetric strain = - Î”V / VÂ

Bulk Modulus = Increase of pressure / Volumetric strainÂ

Bulk Modulus = Î”P / (-Î”V / V)Â

Bulk Modulus = - V Î”P /Î”V

Increase in pressure = Î”PÂ

Change in volume = - Î”VÂ

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

Volumetric strain = Change in volume / Original VolumeÂ

Volumetric strain = - Î”V / VÂ

Bulk Modulus = Increase of pressure / Volumetric strainÂ

Bulk Modulus = Î”P / (-Î”V / V)Â

Bulk Modulus = - V Î”P /Î”V

**Compressibility**

The reciprocal of bulk modulus of elasticity will be
termed as the compressibility of that substance.Â

Mathematically we can say that

Mathematically we can say that

Compressibility = 1 / Bulk Modulus

Compressibility = 1/K

We will now discuss the surface tensionÂ andÂ thick cylinder lame's equationÂ in the
category of fluid mechanics in our next post.

Do you have suggestions? Please write in comment box.

**Â**Do you have suggestions? Please write in comment box.

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**Reference:**

Fluid mechanics by Y. Nakayama and R F Boucher

Image Courtesy: Google

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