 Hello students. Myself Siddhaswabit Urjapura, Associate Professor, Department of Mechanical Engineering, Valchand Institute of Technology, Solapur. So, in this session, we are going to deal with the topic, it is Determination of Hydraulic Coefficients of an Orifice, the learning outcome. At the end of this session, students will be able to derive the equations for calculating various hydraulic coefficients. The contents are introduction to hydraulic coefficients, flow through an orifice, coefficient of velocity, coefficient of contraction, coefficient of discharge, and lastly the references. Let us first have introduction to these hydraulic coefficients. So, in case of fluid systems, these hydraulic coefficients, these are needed to calculate the actual values of the parameters from the theoretical values. So, we are having some relation between the theoretical values and the actual values, and that relation is given by the hydraulic coefficients. Suppose, you are knowing the say actual values and if you want to go for theoretical values also, that is also possible. So, in case of these hydraulic coefficients, these are helping us to find the one parameter if the another is known with reference to the theoretical and actual values. See these hydraulic coefficients are three in number. Say one, it is coefficient of velocity, second it is coefficient of contraction, third one it is coefficient of discharge. Now, let us first see the flow through an orifice. We are having say one tank is there, on one of the faces on the right hand side, we are having one orifice plate fitted here. So, orifice means it is a hole is there, so in that plate. Say we are having the liquid inside this one, the liquid it is going to come outside through the orifice, we are keeping the head of this one as constant one, so that we will see again later. So, the jet it is going to come outside through the hole here or that orifice here. So, due to the sharp edge of this orifice or the hole, say the loss of energy it is going to occur and we are going to have the diameter of the jet getting reduced and further one smallest cross section area of the jet it is going to occur at a zone which is called as Vena contracta. So, this Vena contracta zone which is the smallest cross section area of the jet, so it lies at a distance of half the diameter of the orifice. So, now we will move further. Now, just you have seen that the tank is there and we are now having say the liquid inside that one, say it is water or any other liquid and through the orifice at the bottom side, the liquid it is coming outside. Now, suppose if we are keeping the level there, say it is in that tank we have poured some liquid and now liquid it is coming outside through the orifice and now it is coming with certain velocity. We are thinking of now the level of liquid in the tank and secondly the velocity of the liquid. So, whether the velocity of liquid is going to change if the level of the liquid in the tank is changing that is the question. See the question, we are having some level of liquid in the tank and we are having the liquid coming outside with a certain velocity say coming outside through the orifice and we are interested in knowing whether velocity of liquid which is coming outside the orifice is dependent on the level of the liquid inside the tank. Think of this, see the answer is yes. Velocity of water will be more if level of liquid in the tank is higher and velocity of water it will be lesser or say that liquid it will be lesser if the level of the liquid in the tank is low. So, now let us move to the coefficients this is this is the first coefficient it is say coefficient of velocity we will see firstly the definition the coefficient of velocity we are having. So, it is coefficient of velocity is nothing but it is the ratio of actual velocity of jet at Vena contractor and to the theoretical velocity. So, actual velocity to the theoretical velocity like that you can have and actual velocity it is with reference to the say that Vena contractor zone we are having. Now see this particular diagram earlier that overflow and other things we are not having in the earlier say diagram here now what we have done is we are having one supply of say water it is continuous to this particular tank suppose and we are made one say hole here and we have attached one overflow pipe and the supply it is always larger so that say if the say level this much it is reached so the overflow it is going to occur but the level it is going to remain constant. So, supply of water it is continuous and full so overflow it is occurring continuously you can have and then the level of water it is going to remain this much only so that is what is needed for us and then the jet it is going to come outside so that we are having. Now let us consider one point on the jet and the distance of that one horizontal distance from the Vena contractor it is suppose x and vertical distance of the same from the say axis of this orifice we are having vertically downward distance as it is suppose y the point considered is p. So, now in case of this so it is x is equal to we will have x is the distance covered is there that V velocity into it is time so in case of y which is vertical distance covered so this can be calculated with the help of the basic formula it is s is equal to ut plus half 80 square so there say s is the distance covered here it is y so you initial velocity in the tank it is 0 then instead of acceleration a say we are going to put it as gravitational acceleration g so this one will be y is equal to half gt square so what you can do is so the value of t from the first equation it is x upon v so that you can put in the second equation so it will become y is equal to half g into it will be x square upon this v square then v square is equal to you can have the rearrangement and say it will be g x square upon it is 2 y then v is equal to it is under root g x square upon it is 2 y is here then we will consider again the same but with reference to the application of the Bernoulli's theorem so applying the Bernoulli's theorem at the two points one point it is lying inside the liquid and the second point it is at the Vena contractors so it is at point number 2 or it is in the atmosphere so now here we are having the Bernoulli's theorem application as p1 by rho g plus v1 square by 2g plus z1 is equal to p2 by rho g plus v2 square by 2g plus it is z2 so on the axis of this orifice only second point is there so because of that one z1 and z2 these are going to be same so that those cancellations will be there and corresponding to the pressure at point number 1 so from free surface of liquid it is distance h is there so this p1 by rho g that is the pressure head it will be equal to capital H point number 2 it is lying in the atmosphere so atmospheric pressure it is considered as 0 so p2 by rho g will be equal to 0 then we will put these values so p1 by rho g it is capital H v1 velocity of the liquid in particle at point number 1 inside the tank it will be 0 so then z1 it is already cancelled so p2 by rho g atmospheric pressure it is 0 plus v2 square by 2g we will have and this v2 is equal to it is under root 2g h so in the earlier case if you think say we have considered the distance covered horizontally and vertically etc so it refers to the practical so it is actual one and here for this velocity which we have got is so this one it is with reference to the Bernoulli's theorem which is for the say ideal condition it is theoretical on the right hand side we are not having any parameter corresponding to the loss because of that one this v2 is equal to under root 2g h is nothing but it is the theoretical velocity so now we are having the ratio of ratio as say it is coefficient of velocity is equal to say actual velocity v divided by it is the theoretical velocity so if you are putting the values of these two say we are going to get this one as under root x square upon 4 yh so x square say square root of that one if you are taking it will be x upon it is under root 4 yh we will have then let us go for the second coefficient that is coefficient of contraction so as you are knowing so it is due to the sharp edge of the orifice the jet it is getting contracted in the diameter and the cross section area of the jet it will be smallest at the venocontractor zone so the ratio here for the coefficient of contraction is say it is with reference to the area of jet at venocontractor to the area of orifice it is so these two ratio of these two parameters it is taken so area of jet at venocontractor to the area of the orifice the last one it is say coefficient of discharge so coefficient of discharge is defined as again the ratio of it is actual discharge to the theoretical discharge so just now we came to know regarding the actual velocity theoretical velocity etc and again the diameters at the venocontractor or the cross section area at the venocontractor and say cross section area of the orifice orifice diameter we are having and there the area of flow is there so what we are now having is say in case of the coefficient of discharge it is say actual discharge divided by it is theoretical discharge and actual velocity divided by theoretical velocity multiplied by actual area divided by theoretical area so the first one is nothing but it is say ratios of velocities is there actual and theoretical so it is coefficient of velocity and the second one is ratio of areas is there so it is again actual to theoretical so it is coefficient of contraction so in case of coefficient of discharge it is nothing but it is the multiplication of coefficient of velocity and coefficient of contraction. These are the references used for this particular session. Thank you.