 Sachin Deshmukh, working as an assistant professor in civil engineering department of Valgenz stock technology. Today, we are going to learn how to find out the discharge through venture meter, particularly we are going to derive the equation to find the discharge through venture meter. You are knowing that venture meter is one of the most important application of Bernoulli's theorem. The Bernoulli's theorem, you know it very well that is energy at section one that is pressure potential and kinetic energy at section one is equal to potential pressure and kinetic energy at second section. But the modified equation says there are some losses, so the losses are added on the right hand side. So, the pressure energy, static energy, kinetic energy is equal to the pressure energy, static energy, kinetic energy plus losses and the second section. The best application, the important applications were venture meter, rotameter, orifice meter, the mouthpieces, etcetera. Here in this topic, we are studying to find out the discharge through venture meter and at the end of this topic, you can able to derive the equation for measurement of discharge through venture meter. And you can calculate the theoretical discharge through venture meter as well the actual discharge. So, in this study that is Giovanni Battista Venturi, he worked a lot on Euler's equation and as well as Bernoulli's theorem. His primary expertise was fluid dynamics and hydraulics engineering. In his study, fluid flow expanding the work performed by the most generous Bernoulli and Euler and he discovered and explained certain very useful behavior of fluid phenomenon in pipes particularly. So, he worked a lot on increasing the velocity and decreasing the pressure. He has developed one instrument that is this meter and this meter is called as by its name that is Venturi meter. It is the most one of the important practical application of Bernoulli's. You can observe in fluid mechanics laboratory this particular instrument is attached. See this instrument, this is a pipe, this is a pipe to this pipe here it is the diameter is reduced, the diameter is reduced here it is the least diameter and then again the diameter is increased. This is a pipe to which a dissection, this section we can say it is a inlet section we can say it is a inlet section, this is a outlet, this is a outlet or we can say it is upstream and this is a downstream. Here in the inlet section you can see observe here, here the manometer is attached, this manometer is attached, this particular central portion is called as a throat section. This portion is called as a throat section and where the diameter is reduced, see here the diameter is reduced, this is called as a convergent cone and here you can observe the diameter is again increasing and it is joined to the pipe on the other section or we can say downstream. The other end of the manometer is attached to the throat. Now here clearly we can observe here the velocity is different, here the velocity is different and you can observe here, here the level of the manometric liquid is going up from this datum level, this is the datum level going up, this is the datum level. The section one is inlet, section two we can say it is a throat section. Here we can observe the similar way that we have already studied in the Bernoulli's that is reducing the diameter of the pipe, velocity increases and pressure decreases. The same principle is here and here one more thing, one more thing you can observe over here this figure, this particular length is more, this particular length of the diversion cone is more. Why? To avoid the cavitation, to avoid the cavitation as the cross section is reduced here the velocity will be more and here you can observe that liquid can pass very fast over here. So here the chances of cavitation that is why the length of the diverging cone is always more than the convergent cone. Now we will start for the derivation of the theoretical dishes how we can find out. This is an instrument which we have seen used to measure the rate of flow or the discharge in the pipe and often fixed permanently wherever we want to find out the rate of flow we are going to fix that particular instrument in that particular point at the different section of the pipe and maybe the eventually meter is horizontal, vertical and inclined as per the requirement of the particular setup of that section. It consists of that we have seen first is converging cone, central is throat and then diverging cone. These are the three important parts and the remaining that is manometer differential manometer is attached to the convergent cone that is inlet section to the throat section to find out the difference of the mercury level that we have written as H m that again we have to convert it into that water with the liquid which is passing through that particular meter. Now pause the video and answer. Venturi meter is based on integral form of Euler's equation you have to say is it true or false and second is venturi meter is used to measure average velocity at a point discharge or pressure at a point these are the answers yes venturi meter is based on integral form of Euler's equation venturi work a lot on Euler's equation and then we found the equation to find out the discharge second venturi meter is used to measure discharge rate of flow not this average velocity velocity at point and pressure no venturi meter is used to measure discharge then we will move forward we will find out the expression for the rate of flow the same figure just go through this these are the D 1 diameter at inlet area at inlet then pressure at section 1 velocity of fluid at section 1 and all these things at section 2 this was section 1 and section 2 these are noted similar whatever the things are there these are at the second section see here we are applying we have selected these two points inlet as well as throat we have selected inlet as well as throat it may be here slightly or here but in the throat section ok here it is a manometer again ok so we are applying the Bernoulli's equation or Bernoulli's theorem to section 1 1 and 2 2 this is the particular equation Bernoulli's equation this is the pressure head plus kinetic head plus static head is equal to the pressure head plus kinetic head plus static head at different section section 1 and section 2 as it is horizontal z 1 and z 2 are same simplify it p 1 upon w minus p 2 upon w here specific weight is not going to change that is why p 1 minus p 2 upon w and v 2 square minus v 1 square upon 2 g we know that p 1 minus p 2 upon w is a difference of pressure heads at section 1 and 2 that is h put this value go through this continuity equation again put the value of v 1 in the above equation substituting this value we get this particular equation discharge q is equal to a 1 a 2 upon square in the square root a 1 square minus a 2 square multiplied by under root 2 g h this equation 4 gives the discharge under ideal conditions and this discharge is the theoretical discharge ok then at the constant of inch perimeter over here the q actual is c d into the same equation a 1 upon a 2 upon under root of a 1 square minus a 2 square into under root 2 g h where c d is called as a coefficient of inch perimeter and this c d value is always less than 1 or 1 actual discharge which is less than the theoretical discharge always and this h value we can find this h value we can find out where we required for under root 2 g h this is the equation for this these are the 2 different conditions cases we are going to study this differential equation differential manometer from this we can find out this height ok the specific gravity of that liquid and specific gravity of what that we can find out these are the reference books for you solve some more problems on this