 Hello students, myself Mr. Siddeshwar B. Tulsapure, Associate Professor, Department of Mechanical Engineering, Balchan Institute of Technology, Sulaapur. So in this session, we are going to cover the topic from the section Fluid Dynamics and the name of the topic is Application of Bernoulli's Theorem and the application which we are going to cover is Venturimeter in this session. Now the learning outcome of this session is students will be able to explain the construction and working of Venturimeter. Now let us go for the construction of the Venturimeter. So in case of the Venturimeter, so it consists of three different sections. So now the blue colored lines, these are indicating the pipe. Then we are having this yellow color zone as a Venturimeter. So in case of this one, we are having the three different sections of the Venturimeter. One the first section is called as a converging part. So here we can observe that the diameter of the left hand side of the Venturimeter is equal to the diameter of the main pipe in which we are going to insert the Venturimeter. Then the second zone is there which is of constant cross section area. So this zone it is named as throat and one more zone that is the last zone of the Venturimeter is the diverging part and in case of this one we are going to have the smaller cross section here and the cross section here it is equal to the main cross section of the main pipe. Now here in case of the convergent section and the divergent section, we can observe the difference in the angles of the convergence and the divergence. In case of the convergence we are going to have the angle it is nearly equal to 21 degree plus or minus 1 degree. Then the throat it is of constant cross section area. Then the divergent zone is there in case of the divergent zone the angle of divergence it is say 5 degree plus or minus 1 degree. So now the difference in the angle of convergence and the divergence is due to say in case when we are going for the divergent zone the cross section area it is going to increase and as the cross section area increases the velocity it is going to decrease according to the continuity equation and then we are going for the say in case of this one the as the velocity it is going to decrease we are going to have the increase in the pressure value. So as the pressure it is increasing the reverse flow might start the say flow might separate from the boundary. So to avoid that one we are going for the say 5 degree angle of divergence instead of 21 degree. Apart from this one we are going to have the piezometers here and here. So here it is piezometer for the first section where the diameter of the pipe is equal to the where it is original pipe diameter is there and next to that one the convergent zone it is starting and in the throat we will have one more piezometer it is and now we can observe the difference in the levels here. So here normally it is this level is there and then next to that one when the cross section area it is smaller we are going to have the say increase in the velocity will be there decrease in the pressure will be there. So due to the decrease in the pressure the level here at the throat section it is lesser. Let the section 1 and section 2 are having the values of the pressure as p1 and p2 and velocity is v1, v2 then it is diameter d1 and d2 and then the cross section area it is a1 and a2. Now we will see the derivation of the equation corresponding to the discharge through the venture meter or the formula with help of which we will be able to calculate the discharge. Now we are saying that we are having the venture meter as the application of the Bernoulli's theorem. The two sections we have seen section number 1 and section number 2 and now we are going to apply the Bernoulli's theorem at these two sections. Say the first section we will have applying now the Bernoulli's theorem, applying Bernoulli's theorem at section 1 and section 2 in case of Bernoulli's theorem we are having the summation of the energies as concerned. So it will be p1 by rho g plus v1 square by 2g plus z1 is equal to p2 by rho g plus v2 square by 2g plus z2. So here z1 is equal to z2 hence it will be p1 by rho g we will take p2 by rho g to the left hand side so it is p2 by rho g is equal to say it is v2 square by 2g minus v1 square by 2g. Now p1 by rho g and p2 by rho g these are the pressure heads at the section 1 and section 2. So p1 by rho g minus p2 by rho g is shown in the diagram with the help of the letter h it is. So this one is h is equal to the difference in the pressure head and then this one can be written as v2 square minus v1 square divided by this 2g. Now we can go for v2 square minus v1 square is equal to 2g h now we will go for the continuity equation. The continuity equation is a1 v1 is equal to a2 v2 a1 and a2 these are the cross section areas at section 1 and section 2 v1 and v2 these are the velocities at section 1 and 2. Now v1 is equal to say it is a2 divided by a1 and into this v2. So we will put this value in this equation and say it is v2 square minus it is v1 square so it is a2 square divided by it is a1 square then it is v2 square is equal to 2g h. Now we can observe that v2 square is there v2 square is there we can take it common so it will be v2 square into bracket 1 minus it is a2 square divided by it is a1 square bracket complete is equal to 2g h. Now we can have the simplification of the bracket it is v2 square into bracket it is a1 square minus a2 square then divided by it is a1 square is equal to 2g h. So we can go for v2 square is equal to say a1 square we will have on the right hand side then multiplied by it is 2g h divided by it is a1 square minus it is a2 square. So this v2 now can be written as so taking the square root of both the sides we will have this one as a1 then square root of it is 2g h divided by the square root of it is a1 square minus it is a2 square. Now the equation of discharge we are knowing discharge q is equal to a2 into it is v2. So this q now can be written as it is a2 we are writing say v2 is here only it is a1 multiplied by it is under root 2g h then divided by it is under root a1 square minus it is a2 square. Now we can think of the discharge which is given by this equation q is equal to it is a1 a2 under root 2g h divided by it is under root a1 square minus a2 square whether it is a theoretical discharge or actual discharge. Now in this case you can observe that we have taken the Bernoulli's theorem which is not modified. So it is the say first Bernoulli's theorem say without any modification taking into consideration the say fulfillment of the assumptions etc. So this is not there. So p1 upon rho g plus v1 square by 2g plus z1 is equal to p2 by rho g plus v2 square by 2g plus z2. So this one is not containing on the right hand side the losses etc. So in case of this one this q refers to the theoretical value. So this q theoretical is equal to so it is a1 a2 it is under root 2g h divided by it is under root it is a1 square minus it is a2 square. Now in case when we are interested in the actual discharge say it is q actual divided by q theoretical is equal to we are knowing it is coefficient of discharge. So it is coefficient of discharge is equal to it is cd. So now we will write the formula for the actual discharge so it is q actual is equal to coefficient of discharge into it is a1 a2 it is under root 2g h divided by it is under root a1 square minus a2 square. So we can observe that we are having this formula in terms of the say it is a1 square a2 square referring to the cross section areas at section 1 and section 2 which can be determined from the diameters at these two sections that is at the diameter of the main pipe and then next to that one the diameter of the throat it is and then throat section and then we should be able to determine the difference in the pressure here at the section 1 and section 2. So in case of this one if we are knowing these three that is a1 a2 and h and then the value of the coefficient of discharge which is constant with reference to that venturi meter so if this is also known we will be able to determine the actual discharge. So what we can do is we can have the constants as a1 a2 with reference to the pipe and the venturi meter then only thing is the h it is going to vary so h if we are able to measure by making use of the coefficient of discharge which is constant for that venturi meter we can go for the actual discharge measurement. These are the references which are used. Thank you.