 Hello students, myself Mr. Siddeshwar B. Tulsapure, Associate Professor, Department of Mechanical Engineering, Walchand Institute of Technology, Sulapur. So, in this session, we are going to deal with the topic from the section, it is fluid dynamics. The name of the topic is application of the Bernoulli's theorem and that application which we are taken for this session, it is pitot tube. The learning outcome of this session, at the end of this session, students will be able to explain the construction and working of pitot tube. Now, the contents of the session are, the first one it is assumptions of Bernoulli's theorem, then statement of Bernoulli's theorem. As it is application of Bernoulli's theorem, we are going for assumptions and then the statement of Bernoulli's theorem, then we will go for the construction of the pitot tube, then working of pitot tube and the effect of the connective coefficient we are going to observe and lastly the references. Let us see the assumptions of the Bernoulli's theorem. Now, the assumptions these are divided into two that is one with reference to the fluid and the second with reference to the flow and in case of the fluid, the fluid should be ideal, so which is not possible in the real-world situation as ideal conditions are not existing and all fluids are having the viscosity, so real-world fluids are there. Secondly, the flow should be steady that is the parameters should not change at a point with reference to time that is the parameters are remaining constant at a particular point in the fluid flow and then with reference to time. We are going for the incompressible flow, incompressible flow generally in case of the liquids will come across and the flow should be irrotational that is the fluid particles should not rotate about their own mass centers or axis when they are flowing from one section to another section. Now, if these previous assumptions these are satisfied, so we are having the total energy at any point as remaining constant, so total energy at any point in a fluid flow remains constant and as we are having the different types of our forms of energies we are going to come across it is the pressure energy is there, then it is kinetic energy and the third one it is the datum energy and the Bernoulli's equation it can be written as it is p by rho g plus v square by 2g plus z is equal to constant and this energies now are represented in the form of the head cities all are having the unit size meter cities and we are going to have the summation of the three heads that is pressure head, kinetic head and datum head as constant one. Now, let us see the pitot tube which is working on the principle of the Bernoulli's theorem. What pitot tube is? Pitot tube is a device which is used to measure the velocity of the fluid in a fluid flow. Now, the conception of that one if we observe we are going to have one glass tube is there which is bent through the 90 degree and one end it is shorter and one end it is larger both the ends of the pipes these are open, so this end is also open and this end it is also open. So, basically a glass tube with 90 degree bent and then we are going to have the two sides which are open of that particular pipe and then next to that one we are going to have this one as a larger one as compared to the horizontal one. Now, let us see the use of this pitot tube for the measurement of the velocity of the fluid flow. Now in case suppose this is a pipe through which the fluid flow it is taking place in case of this one we are going to have the use of the piezometer along with the pitot tube. So piezometer so somewhere here at the center line we can have one hole and one right angle tube similar to the pitot tube can be attached but this tube it is at right angles to the direction of the flow and this one it is piezometer piezometers we have already seen piezometers are used for the measurement of the pressure it is. Next to that one the pitot tube we can observe the pitot tube as seen earlier now it is now placed in the fluid flow so here the pipe it is having some hole through which the pitot tube it is inserted and you can observe that the horizontal side we are having the fluid it is entering directly into the horizontal pipe and then it is going to rise in the vertical pipe and then again the fluid flow it is around this tube pitot tube also and it is moving towards the right hand side. Now let us think what will be the velocity of the fluid when it enters the pitot tube see this one it is pitot tube and we are having the fluid flow from left hand side to the right hand side this one it is piezometer the question presently is associated with the pitot tube we are concerned with the velocity of the fluid when it enters the pitot tube see the answer of this one. Now when the fluid particles they are going to enter the pitot tube that is the horizontal side of the pitot tube when they are entering we are they are having to some extent the velocity velocity of that particular fluid flow and when they enter here there is no further horizontal path for these fluid particles now they are once they are rising in the vertical side of the pitot tube now the further the fluid particles they are not having any velocity so the obstruction is provided to the fluid flow with the help of the vertical side of the pitot tube and the velocity of the fluid particles it is getting reduced to zero. Now in case when we are concerned with the Bernoulli's theorem and we are saying that we are going to have the pitot tube as one of the applications of the Bernoulli's theorem now in case of the Bernoulli's theorem the total energy it is going to remain constant so in case of the present situation when we are going to have the velocity of the fluid particles it is becoming equal to zero when the obstruction is provided with the help of the pitot tube and then the velocity zero leads to the kinetic energy zero so as the kinetic energy becomes zero the pressure energy it is going to be there so conversion of kinetic energy into pressure energy it takes place according to the Bernoulli's theorem and then the total energy it is going to remain constant so now we can observe the difference in the levels of the fluids in the two tubes it is when it is the pitot tube is there so this one and the second one it is the piezometer so piezometer here it is showing the pressure to some extent here the height it is shown as H1 and next to that one when the fluid particles they are entering the pitot tube and the velocity of that one it is becoming equal to zero the conversion of the pressure energy into kinetic energy it is taking place and as the pressure it is more so we are going to have a more rise of the fluid in the pitot tube and the height here it is equal to it is H2 now we are going for the calculation of the velocity with the help of the use of the pitot tube we are now making use of the pitot tube but the later on the formula it should be developed for the measurement of the velocity and that will be done through the small derivation which is of only three four lines now here the Bernoulli's theorem is applied at the different sections and one section it is say the section which is passing through the piezometer that is section number one here and one more section is there that is it is the section is passing through the pitot tube so we are going to have so it is the Bernoulli's theorem we are going to now apply the section one it is p1 by rho g plus v1 square by 2g plus it is z1 and at the section 2 so it is p2 by rho g plus v2 square by 2g plus z2 so let us take the difference it is p2 by rho g minus p1 by rho g this one will be equal to so here we are having the difference of the pressure heads as difference of the heads shown here is H2 and H1 so H2 minus H1 is equal to H say and that atom it is constant here and here so z1 is equal to z2 so these will get cancelled and velocity at the section 2 that is velocity of the fluid particles in the pitot tube it will be equal to 0 so v2 is equal to 0 if we are putting these values that is p2 by rho g minus p1 by rho g is equal to H and then z1 z2 these will be cancelled and v2 is equal to 0 we will get the value of the v1 as equal to it is under root 2gh v1 is nothing but the velocity of the fluid flow through the pipe now we will say the effect of the connective coefficient say v1 actual is equal to can be written as C that is a connective coefficient which takes into account the effect of the stem and the bent leg of that pitot tube and then it is under root 2gh the most commonly used form of the pitot tube is so designed that the effect of the stem and the bent leg cancel each other and the value of the C is equal to 1 that is in case of this we are going to get the v actual as equal to it is under root 2gh only when we are going to have the value as C equal to 1 so these are the references thank