 Hello students. Myself, Siddeshwar B. Tulsapure, Associate Professor, Department of Mechanical Engineering, Valshan Institute of Technology, Solapur. So today, we are going to see the topic, it is flow through the pipes in series. The learning outcome of this session. At the end of this session, students will be able to write an equation to calculate head loss in compound pipes that is the pipes in series. The contents are the definition of pipes in series. The pipes in series connecting two tanks we will see. Then we will go for the calculation of head loss in pipes in series considering minor losses. Then we will see the calculation of head loss in pipes in series neglecting minor losses and lastly the references. Now let us see firstly the pipes in series. So these are also named as compound pipes. So pipes in series or compound pipes are defined as the pipes of different lengths and different diameters. So connected end to end in series that is to form a pipeline. Means what we are having is we are having the pipes of different lengths and different diameters connected end to end. So end to end it is going to form a series to form a pipeline. So complete pipeline we are going to form. Means the pipes of different diameters and lengths we are having. So these are joined end to end. So that is going to become compound pipe as these are joined end to end. So that is named as pipes in series. Now let us see the compound pipe it is connected to the two tanks. We are having one tank on the left hand side. We are having one tank on the right hand side. So in these two tanks these are connected to each other with the help of a compound pipe or pipes in series. Now in case of these you might observe that we are having the firstly the diameter as larger then the diameter it is reduced. And still again the diameter it is reduced for the third section. But not necessarily always we will have the reduction in the diameter when we are going from the first tank to the second tank it is. We may have any diameter for any of the sections and say only thing is the diameters these are different and the connections these are end to end because of that one. So this will be called as pipes in series or it will be called as compound pipe. Now see again what we have done is we have taken the two tanks which are at different elevations. So the tank it is say on the left hand side it is at higher elevation. The tank on the right hand side it is say at lower elevation. So we are having now the connection between these two. So here now compound pipe we can observe. So the first section it is of larger diameter. Then the second section it is of smaller diameter and we are having again the larger diameter for the third section. So as I said earlier so the diameter should be different. So that is what the condition is for the compound pipes and end to end connection should be there. So that is there. So now in case of this one we are having the pipe diameter of the middle one as lesser. So first one to some extent larger and third one also it is to some extent larger. Now the notations which we are going to use is it is L will be used for the length of the pipe. D it is the diameter of the pipe. So small f it is coefficient of friction of pipe. Then V is the velocity of the flow of liquid. Then suffix 1, 2, 3 these are going to represent the pipe sections in the compound pipe. And capital H we are going to have the difference in level of liquid in the two tanks it is. Now think of whether the difference in levels of liquids in the two tanks is due to the difference in elevations of the tanks. So now the question you can observe. So the question is we are having the difference in level of the liquid in the two tanks. So already the tanks are different elevations. So whether the difference in the level is due to the difference in the elevations of the tanks. So I will show you again the diagram. See this diagram. We are now having here the level of the liquid in the say left hand side tank it is say here. And in the right hand side tank the level is somewhere here. So this difference we are having the level difference as it is H. And what the question is? The question is whether this difference in level of the liquids in the two tanks is due to the difference in the elevations of the tanks. Think of the same. See the answer. The answer is no. The difference in levels of the liquid is due to the losses in the pipes connecting the two tanks it is. Say we are having the liquid level as always say horizontal it is. Say in case of these two tanks the say it is not like this the two tanks are there and these are connected with the help of the pipes. And the further things are somewhat like this the liquid it is going to come from somewhere else in the tank number one. Then it will pass through the pipes. Then it will go to the second tank and from second tank it is going somewhere else. So it is not like that it is stored. So in case of the stored one the liquid levels these are going to be same. So in case when the flow is occurring at that time we are going to have the difference in the say level of the liquids in the two tanks. Now the head loss we are going to consider. The head loss now it is going to be of two types. One it is corresponding to the major loss that is called as frictional loss. The second one we are having it as a minor loss. So minor losses these are say at connections between the tank and pipes. So the tank is it is say pipes these are connected to the tanks. There we are having the minor losses. And one at one more place that is when the two pipes of different diameters these are connected to each other. So there also we are going to have the say minor losses. So major loss minor loss like that two types of the losses are there. So major loss it is say considerable minor loss it is having lesser value and of less significance. Say these two types of the losses these are there so that you remember. Now again the same diagram I have done here say I have taken. And we will now go for the equation corresponding to the head loss in pipes say considering minor losses it is. Now if you look towards the diagram and again the say if you remember this minor loss definition and the things we talked about it. So minor losses these are due to the change in the direction change in the cross section etc. we are having. So observe that the pipe it is connected to the tank. So here one minor loss it is going to occur. Then so through the first pipe section we are going to have the liquid flow. So major loss will be there. Again sudden contraction we are having of the pipe. So here minor loss it is going to occur. So again frictional loss in the section 2 we are going to have. Then sudden expansion it is going to occur. So we are going to have again minor loss. The frictional loss in the section 3 and lastly again the section 3 pipe it is connected to the tank. So at that joint again we are going to have the say minor loss. Corresponding to the formally of the minor losses say minor losses due to the say sudden expansion minor losses due to the sudden contraction etc. And say minor losses at the connection between the tank and the pipe etc. So you can write the equation. The first one it is h is equal to head loss h is equal to say it is 0.5 v1 square by 2g. So it is the first minor loss. The first pipe it is connected to the left hand side tank there. Then it is major loss 4f1 l1 v1 square by it is 2g d1. Then it is 0.5 v2 square by 2g. So it is corresponding to the sudden contraction. Then major loss corresponding to section it is 4f2 l2 v2 square by 2g d2. Then sudden expansion it is occurring. So loss corresponding to that one it is v2 minus v3 bracket square we are having and divided by 2g. And plus it is 4f3 l3 v3 square by 2g d3. So it is major loss in the section 3. And lastly again section 3 is connected to the second tank. So there it is v3 square by 2g going to be the loss which is minor loss. Then if you neglect the minor loss because minor losses these are of lesser significant less value these are having. So if you remove these minor losses we are going to come across only the major losses. In case of major loss only corresponding to these 3 different sections we are going to write. So it will be h is equal to it is 4f1 l1 v1 square by 2g d1. 4f2 l2 v2 square by 2g d2. Plus 4f3 l3 v3 square by 2g d3. These are the references which are used for this particular session. Thank you.