Lecture - 10 ( vapour pressure and cavitation )

Vapour pressure (Pv )

Let us consider a closed container that is partially filled with liquid. Now what happened is evaporation takes place inside the container. The air above the liquid can absorb the water vapour molecules upto a certain limit and this limit is known as saturation limit. As we saw in surface tension of Lecture - 5 that the molecules present inside the water are under balanced Cohesive forces so they are stable and molecules present on the surface of water are under unbalanced Cohesive forces so they are under unstable conditions. Therefore the molecules on surface of liquid are in highly excited state and by taking energy from molecules below it these molecules will evaporate. The air above the liquid will absorb these molecules only upto saturation. A saturation is such a condition in which the number of molecules evaporating from surface will become equal to the number of molecules rejoining the surface on condensation and such a situation is known as equilibrium condition. the pressure exerted by the vapour molecules over the surface of fluid under saturation condition is known as saturated vapour pressure (Pv ) or simply vapour pressure. As we increase the temperature the vapour pressure also increases.

Cavitation 

When the pressure of a flowing fluid becomes less than the vapour pressure, then boiling will start and Bubbles are formed. These Bubbles move to high pressure region and the high pressure fluid will collapse these bubbles and strikes the walls, which may lead to wear and tear and also brusting, this phenomenon is known as Cavitation. To avoid Cavitation the designing must be done in such a manner that the pressure of flowing fluid will always be more than its vapour pressure. Cavitation is also a low pressure phenomenon. 

Highly volatile liquids like petrol have very high vapour pressure. Mercury is having least Vapour pressure and this is the most important property of mercury that it is used as a manometric fluid.

Let us consider a converging-diverging type tube in which water is flowing as shown in below diagram.

Here 'V' represents velocity of water, 'P' represent pressure of water. 'P1' represent pressure at 1 section. 'P2' represent pressure at 2 section.As water is flowing from section 1 to Section 2 its area is decreasing therefore according to steady flow equation the velocity of water will increase. With the increase in velocity the pressure of water as it move from section 1 to Section 2 will decrease. Now if this decrease in pressure at section 2 will become less than vapour pressure then boiling will start so bubble will form. Now when water will move from section 2 to section 3 the area of the tube is increasing therefore velocity of water will decrease and with this pressure will going to increase. Now those bubbles will move to this high pressure region and they will start brusting, due to which material of the tube from inside will wear out and also brusting increase lot of vibrations. Therefore there must be a limit of pressure drop, pressure cannot be less than vapour pressure if you want to avoid Cavitation. This of pressure also put a limit on velocity of fluid flowing inside it. 'Pmin ' represents the minimum drop of pressure inside tube which must be greater than vapour pressure so that the flow will be normal.

Steady flow equation is A1*V1 = A2*V2

As we move from A1 to A2 area is decreasing now to satisfy the equation velocity V2 must increase accordingly as compare to V1. Steady flow equation is basically a conservative equation. To make flow of any fluid possible this equation must be satisfied. We will study steady flow equation in detail in my upcoming lectures. 

Let me explain with example that how pressure is changing with respect to velocity. 



Let's take a look at other example also.

Here as we blow air from the top of the paper the particles of air moves away with high speed and a empty region is created over the top surface of paper which lowers the pressure at top surface of paper as compare to atmospheric pressure. Whereas on the bottom surface of paper atmospheric pressure is there. Due to the difference of pressure an upward force is generated which lift the paper. This is the basic phenomenon that work behind the flying airplane.

Boiling of water at room temperature  

The main phenomenon working behind this concept is of vapour pressure. It is a well known fact that water boils at 100 degree Celsius when atmospheric pressure conditions are there. However few people will know that at different pressure water will boil at different temperature. For example if we increase the pressure in pressure cooker for an instant the boiling point of water increase, hence cooking is more efficient. Few people will know however that at reduced pressure water will boil at lower temperature. The following graph of water on pressure vs temperature diagram will help us to understand this.

If we start giving supply of heat to ice at atmospheric pressure (1atm or 100Kpa) then after zero degree celsius it convert into liquid and after 100 degree Celsius it convert into vapour. As we decrease the pressure the melting point of water will increase from zero degree celsius and boiling point of water will decrease from 100 degree Celsius. At 0.61 kilo Pascal or below it, if we supply heat to Ice then it will directly convert into vapour, liquid stage will not appear.