ðŸ‘‰ **Explain bulk modulus of elasticity.**

The fluids also possess elastic characteristics like elastic Solids, i e the fluids may be compressed by the application of external force, and when the force rs removed the compressed volume of fluids expand to their

original volumes. This property of compressibility of a fluid rs quantitatively expressed as inverse of the bulk modulus of elasticity K of the fluid, which is definded as

**K= Stress/Strain = -dp/[dv/v]
= – Change in pressure / [Change in volume / Original volume]**

Thus, bulk modulus of elasticity K is a measure of the incremental change in pressure dp which takes place when a volume V of the fluid is changed by an incremental amount dV.

in S.I. units, the bulk modulus of elasticity is expressed in N/mz. The bulk modulus of elasticity for water and air at normal temperature and pressure are approximately 2.06 X l09 N/m2 and l.03 X 105 N/m2 respectively.

However, the bulk modulus of elasticity of a fluid is not constant, but it varies with pressure and temperature. It increases with increase in pressure. This is so because when a fluid mass is compressed, its molecules come close together and its resistance to further compression increases. For liquids, K decreases with the increase in temperature. However, in the case of gases, since pressure and temperature are inter-related and as temperature increases,

pressure also increases, an increase in temperature results in an increase in the value of K.

For liquids, the bulk modulus of elasticity is very high, thus, the change of density with increase of pressure is very small. Th 5, theirâ€˜compressibility is very low close to zero and can be neglected und-r ordinary conditions.

ðŸ‘‰ **Explain the terms –
(i) Real fluids (ii) Vapour pressure (iii) Compressibility **

**(i) Real Fluids:**

Real Or practical fluids are those fluids which are actually available in nature. These fluids possess the properties such as viscosity, surface tension and compressibility and therefore a certain amount of resistance is always offered by these fluids when they are set in motion.

**(ii) Vapour Pressure:**

All liquids possess a tendency to vaporise when exposed to air or gaseous atmosphere. The vaporization takes place due to liquid molecules escaping from the free surfaces. The rate at which this Vaporization occurs depends upon the molecular energy of the liquid (which is dependent upon the nature of liquid and its temperature) and the condition of the atmosphere adjoining it.

When the liquid is confined to a closed vessel, the ejected vapour molecules get accumulated in the space between the free liquid surface and the top of the Vessel. Alter a certain time air in free Space will contain enough liquid molecules to exert a partial pressure on these molecules to rejoin the liquid surface, Eventually, an equilibrium condition will reach when number of vapour

molecules ejected wiil become equal to the number of molecules rejoining the liquid surface. At this equilibrium condition pressure exerted by vapour molecules on liquid surface is called vapour pressure.

The boiling of a liquid is closely related to its vapour pressure. When the pressure impressed on liquid surface is brought slightly below the vapour pressure limit, the liquid start boiling. This means that the boiling can be achieved either by raising the temperature of the liquid so its vapour pressure rises or by lowering the pressure of the overlaying air below the vapour pressure of the liquid.

**(iii) Compressibility: **

All fluids may be compressed by application of external pressure to some or more extent. When pressure is removed fluid returns back to its original volume. Thus fluids also possess elastic characteristics like elastic solids. This property of compressibility of a fluid is expressed as the inverse of the bulk modulus of elasticity, K. Hence,

**Compressibility = 1 / K **

Where, K= – dp/dV/V

For liquids, the value of K is very high, hence they have compressibility ve close to zero and can be considered as incompressible under ordinary conditions While gases are easily compressible and with the change in pressure, their dens’ decreases considerably, hence effects of compressibility cannot be neglected.

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