 Mr. Deshmukh Sachin, I am working as an assistant professor in Valgenstof Technology in civil department. Today we are going to learn the concept of surface tension and capillarity. Already we are knowing that many of the fluid properties, but particularly the surface tension and capillarity are very important for civil engineering point of view. Almost every property is important, but the surface tension and capillarity are much more near to the civil engineering and at the end of this topic you will come to know or you can understand what is the concept of surface tension and how the capillarity behaves because capillarity that you know that is in upward direction also and in the downward direction also. Now regarding surface tension to start before that I will just recall your memory. In your school days you might be knowing or your teacher has shown you that a small coin is going to float on a water or a small pin is going to float on a water. Do you recall that? So similar to that on what is a theoretical approach or you can say technical approach behind that that you are going to see today. See here, see the figure on the right hand side a pin is there a pin is there you can see you can observe this pin is floating on water and insect is also there. So first just see these figures and then come to this. This is a pot in which water is stored or collected. Now these are the molecules of water. See here at the top surface at the top surface see there are a lot of particles are there here a lot of particles but at the top at the top you can see here this particular particle is going to be in stable condition because all these particles they are supporting to this top level particles which we can see water surface open water surface. So this is giving the force below that then you can see here the direction and it is to be in equilibrium when remaining all you can say particle they are supporting to it. So these are the best example but what is the definition that we will see in detail. It is defined as the property of the surface of the liquid that allows it to resist an external force which we have seen just now. Due to the cohesive nature of the water molecules cohesive forces among the liquid molecules are responsible for the phenomenon of surface tension. The molecules well inside the liquid are attracted equally in all direction which just now we have seen by the other molecules. They are one above the other near to one other they are going to balance each other. The molecules on the surface experience an inward pull that we can see. Now we are going to see the surface tension for three different cases that is surface tension on a liquid droplet then surface tension on a hollow bubble and surface tension on a liquid jet. So this is a small derivation for that for a surface tension you can consider a small spherical droplet of liquid of a radius r on the entire surface of the droplet. The tensile force due to the surface tension is acting as sigma is surface tension p is the pressure intensity d is the diameter. Let the droplet is cut into two halves that is it is cut into two halves okay like this. So you can find out the tensile force is nothing but the sigma into circumference that is surface tension into circumference. Circumference is pi d. Now the pressure force is p into area that is pi d square by 4. Now these two are equal then and then only there will be equilibrium. So you can equate it p into pi d square by 4 is equal to sigma into pi d you will get p is equal to 4 sigma d that is the first derivation. Now the second part that is for a hollow bubble for a hollow bubble a hollow bubble is like a soap bubble in air has two surfaces you might have seen might have seen when the bubbles are formed by the soap they are having just two you can say two layers okay. So they are one above the other the two surfaces are subjected to surface tension. So here that is sigma pi d that is surface tension into circumference and two layers. So you will get p is equal to 8 sigma d similarly for the liquid jet. Now consider a liquid jet of diameter d and the length you can say l that is p is equal to that l into d that force due to surface tension is sigma into twice it is l that is 2 then equating these two you will we will get p is equal to sigma into 2l upon l into d okay. So these are the questions that you can answer for this what is the surface tension or define surface tension and question number two is what is the unit of or how you can measure the surface tension surface pressure is defined as tensile force acting on the surface of the liquid in contact with the gas or the surface between two immiscible liquids such that the contact surface behaves like a membrane that is why the insect the pin is going to float and it is measured it is measured in Newton meter it is measured in Newton meter okay. Now second we will see what is the capillarity capillarity is also one of the important property it is the ability of a liquid to flow in a narrow space without the assistance of and in opposition to external forces like gravity capillary action is sometimes called a capillarity or capillary motion or capillary viking following are some of the examples drawing of liquids between the hairs of paint brush we just dip that hair that brush and then we paint okay so it due to the capillary action the liquid comes up that draws second is drawing in tips of the fountain pens okay then moving groundwater from wet areas we often see in the rainy season in the rainy season the water comes from the downside we can see the walls get wetted walls get wetted okay so that is also capillarity and rise of a sap in a tree we put the water at the bottom of the tree and that water is going to transfer that sap is going to transfer up to the top of the tree up to the top of the tree okay these are the four basic example you can add some examples like oil that is lamp oil in the lamp okay that oil is coming from the cotton in the lamp so there are many many many problems many you can say examples are there you can see for the capillarity see first we will see what are the types there are two types rise capillary rise and capillary fall now here when the capillary tube is dipped in water it is dipped in water water level rises water level rises okay and you can say this is the angle of contact this is the angle of contact this is the head okay there are two conditions that is just now two you can say types that is rise and fall it is very interesting to see fall actually rise it is common thing when we can dip that piezometric tube in the water there is you can see the rise okay there you can see the rise how we can find out now expression for the rise similarly that is with what we have done in the surface tension similar consider a glass tube of diameter d which is open at both the ends because other end where the atmosphere is going to add the liquid will rise in the tube above the level of the liquid okay then these are the parameters that is h is height of the liquid under state of equilibrium weight of the liquid is equal to force at the surface of the liquid in the tube okay then and then only the equilibrium condition comes now weight of the liquid in the tube that is area into height it is you can get it is a volume into mass density into gravitational acceleration and the vertical component of the surface tensile force is sigma pi d that we know and cos theta that is angle of contact if you can equate this if you can equate this we get h is equal to 4 sigma upon rho gd sigma is surface tension rho is mass density g is gravitational acceleration d is diameter similarly we can find out for capillary fall just see how it behaves the same tube it is dipped in mercury you can see here fall the liquid is fall which is not going to rise it is fall because mercury is having maximum you can say specific gravity that is 13.6 it is a tendency of liquid to be depressed in the tubes of small diameter in opposition to external forces like gravity it is due to cohesion now the what is the expression the similar way that we can find out and equating this okay surface tension and the vertical component surface tensile force and vertical component we will get h is equal to 4 sigma cos theta upon rho gd where theta is taken as 128 degree that of the theta for water is taken as 0 okay this is 0 not we are not going to take any see here we are not going to take any though it is we can see here but it is you can say very nearer to this surface so it is taken as 0 okay so 4 sigma upon rho gd it is for capillary rise and 4 sigma cos theta 4 sigma cos theta upon rho gd that is for mercury okay mercury we are taking we are using for many of the experiments in fluid mechanics so here it is very interesting to see the behavior of the mercury when the glass tube is dipped instead of you can say the diameter is very less very small diameter is there so small diameter tube is when inserted in mercury that is going to be the you can say depression in mercury level so these are some questions what is a capillary rise or defined capillary rise and where you can observe the capillary fall so it is a tendency of liquid to rise in tubes of small diameter in opposition to external forces like gravity and we can observe the capillary fall in mercury only okay so these are the reference books just refer these books if you find any difficulty you can contact me thank you