 Hello students, myself, Siddhasher B. Tulsapure, Associate Professor, Department of Mechanical Engineering, Valshan Institute of Technology, Solapur. So in this session, we are going to cover the topic, it is hydraulic gradient line and total energy line, the learning outcome. At the end of this session, students will be able to make use of HGL and TL, which are hydraulic gradient line and total energy line for solving problems related to flow through pipes. Let us see the contents, the contents are the definition of the hydraulic gradient line and total energy line, then how to draw the hydraulic gradient line and then the drawing of total energy line and then the references. Now firstly, we will see the how what is the meaning of HGL or hydraulic gradient line. So hydraulic gradient line we are saying, so it is going to be a line, so which is drawn say for drawing of this line, say it is requiring some reference and next to that one this line is drawn by say considering the pressure energy and next to that one the datum energy that is P by rho G and Z, the pressure head and the datum head and next to that one. So this is with reference to some reference line we are having, it is reference line. So hydraulic gradient line is consisting of only two parts, one it is the pressure head and the second one it is the datum head and these are the lines which are drawn for the flow fluid flow through the pipe it is and next to that one, one more is there that is the total gradient line or it is TGL, so total energy line, so it is TEL. So in case of this one, so we are going to have the consideration of the velocity head also, so here it consists of, so total energy line is a line which is drawn which is indicating the pressure head plus it is velocity head and also the datum head and so this is also with reference to some reference line and this is also in case of the fluid flow through the pipes. So now let us see how to draw the HGL and the TEL it is. Now let this be a tank and now in case of this one we are going to have the pipe of uniform diameter and this one is connected to the tank phase. Now this tank it is having the liquid and now we are going to draw one reference line which is passing through the center of the pipe it is, so this one it is reference line. So this reference line will be utilized to draw the HGL or the hydraulic gradient line. Now in case of this let the free surface of the liquid, so it is free surface of liquid B at a distance is equal to it is H. Now in case of this one we are going to have the HGL we are going to draw and now for this purpose we are going to consider the different points suppose point A is there, suppose point B is there and at the end of the pipe suppose point C is there. So now in case of this one say total energy at A is equal to we can consider, so total energy at A suppose we are writing it as PA by rho G plus it is VA square by it is 2G and then plus it is say ZA. So we are interested in both that is total energy line and HGL and in case of that one we have considered first the total energy line. Now so what is the pressure at A, see the pressure at A is atmospheric and this is considered as equal to 0 and the velocity of the fluid particles in the tank will be equal to 0 and only thing is the datum we are going to have, so this one is H, so the height from this particular reference we are going to have the total height of the free surface as H, so total energy at H in the A will be equal to H, so total energy at B. So at B what is happening is we are having the minor loss with reference to the entry of the water at the inlet of the pipe, so in case of this one so it is going to be total energy at A which is just before the entrance of the pipe minus the H at the inlet of the pipe it is, so head loss at inlet of pipe. So this one it is going to be the loss which we are having and this loss it is minor loss. So next to that one in case of the point number C, so total energy at point C is equal to total energy at point B minus we are having from here to here when the fluid it is flowing the head loss it is going to occur which is going to be major loss, so it is minus H F. So when we are going for the drawing of the total energy line in case of that one, so we will have firstly say it is, we will start with this one where the total energy at A it was equal to H, then the vertically downward we have to come, so this much it is corresponding to the head loss, so it is H at inlet, so head loss at inlet next to that one from there we have to come towards the right hand side and the head loss how much it is occurring it is occurring equal to it is H F, so in case of that one. So let us say that this much is equal to the H F that is the frictional head loss, so up to here we have to draw the total energy line, so this one this line it is to be drawn. So this line corresponding to the length of the pipe that is from here to here, so this one is nothing but it is, so it is total energy line. So now we are interested in the value of in the say determination of the HGL also, in case of the HGL and TL we can observe that the difference is of only that V square by 2G, so what we can do is, so we can draw one line which is going to be parallel to this total energy line and having the difference between these two as equal to V square by 2G rather if you are considering the pressure head and the datum head at the point number C, so in case of this one, so what we are going to come across is say it is in case of the point number C we are having the pressure as equal to atmospheric which is 0 and Z datum is also 0 as it is passing through say it is the reference line. So we can draw one line which is say parallel to the this TL and it is passing through the center of the pipe it is, so this line it is nothing but it is HGL and this vertical distance it is nothing but remember this one it is going to be vertical distance and it is the head loss which is occurring it is the corresponding to the velocity this is V square by 2G, so one is total energy line which is shown by the red color and next to that one the difference between these two that is these two lines these are parallel to each other and difference is equal to it is V square by 2G. Now let us consider one more say case where we are going to have the tank and again the pipe it is connected but this is pipe it is having the expansion and we are having the thing somewhat like this, so here also we are going to have the similar to this earlier one. So let us say that this is going to be the reference one say free surface of the liquid and this is standard reference standard line or the reference line from here say this much is corresponding to H at inlet and next to that one from here to here say it is say vertically we have to measure, so this one corresponds to Hf1 and here due to the sudden expansion again we have to come vertically downward and then we are going to have again say this much due to sudden expansion it is, so it is Hex you can write and from here so up to the end of the pipe you have to go and the vertical downward distance that is the line you have to draw which is going to be parallel, so this much distance it corresponds to Hf2, so here up to this particular end you have to come and so see let us take this point here, so this red colored line now it is showing you the total energy line, so this one it is total energy line. Now let us come to the say one more that is the Hgl, so in case of the Hgl again we can observe that at this particular point pressure head and the datamode these are 0, so we can draw the line which is going to be parallel to this one, so let us draw one line which is parallel to this and next to that one, so here we can come vertically downward by a distance which is equal to say it is v1 square by it is 2g and we can draw one more line, but here we can observe that these two lines are not meeting, so let us go vertically upward and complete the Hgl, so this one it is corresponding to the Hgl, so see what happens is in case of the total energy line we are going to have the continuous fall that is from here to here here again continuously, so total energy line continuously falls, but in case of the Hgl, so there may be rise in the rise and again fall etcetera, so these things the combination of these two it is existing, so we are going to make use of the total energy line and the hydraulic gradient line to study the different types of the fluid mechanics problems consisting of the flow through the pipes it is. These are the references, thank you.