 Hello students, myself, Siddhaswad B. Thurjapura, Associate Professor, Department of Mechanical Engineering, Walsh and Institute of Technology, Solapur. So in this session, we are going to see the minor losses in the pipes, the learning outcome. So at the end of this session, students will be able to identify and calculate different types of minor losses in a piping system. The contents, the definition of the minor loss, then it is different types of minor losses in calculation of minor losses and then lastly the references, definition of minor loss. So minor losses are the losses which are occurring due to the change in the velocity. Now as we are knowing the velocity, it can be changed in the form of the magnitude or also in the direction. So as it is a vector quantity, we can have only change in direction also and in some cases we might have the change in the magnitude also. So if the velocity is changing, in case of that one, the minor loss, it is going to occur. There are different reasons why the minor losses, these are occurring. So in this case, the first one is at the entrance of a pipe, this is the first. The second one, so it is due to sudden enlargement of pipe, third one, due to sudden contraction of pipe, the fourth one, due to bend in a pipe, the fifth one, due to obstruction in the pipe, sixth one in various pipe fittings and the last one, it is at the exit or outlet of the pipe. Now let us see one by one the different types of the losses. The first one it is the minor losses at the entrance of a pipe. Now we can see that here we are having this one as a tank and the pipe it is connected to this one. So this section is the section where the pipe is connected to the tank. So this is called as entrance of the pipe or it is the inlet of a pipe. So in case of the entrance or inlet of the pipe, the loss is occurring and that loss is given by the formula, the head loss at the inlet is equal to, it is 0.5 into v square by 2g. So now in this case the velocity v, it is the velocity of the liquid in the pipe. The velocity of the liquid in the tank it is going to be 0. So when it enters into the pipe, the fluid particles they are gaining the velocity and the velocity in the pipe it is required for the calculation purpose. Next to that one the second one is the minor losses due to sudden enlargement of pipe. So in case of the diagram you can observe that we are having initially the diameter of the pipe as lesser. Then suddenly the diameter of the pipe it has increased at this section and the enlarged section it is lying towards the right hand side. So now we can consider the two different sections section 1, 1 and section 2, 2. So the section 1 we are having the cross section area different and lesser than that of the cross section area at the section number 2 it is. So in case of this we are going to have the suppose velocity at the section 1 it is v1 and the velocity at the section 2 it is v2. The head loss here it is dependent upon both the velocities. Now here you can observe that say we are going to have the formation of the eddies here. So the eddies these are formed due to the say increase in the cross section area. So according to the continuity equation when we are going to have the discharge as constant if the cross section area increases we are going to have the decrease in the velocity. So decrease in the velocity will lead to increase in the pressure and due to the increase in the pressure so the reverse flow it is going to start and the formation of the eddies will be there here and say due to that one to some extent the losses will be there. So we are going to have also say the loss due to the sharp edge etc to some extent we might have. Then the head loss due to the sudden enlargement it is given by the formula v1-v2 this is in the bracket and that bracket square divided by it is 2g. Third one it is the minor loss due to sudden contraction of pipe. So exactly opposite to the earlier one we are having here the cross section area it has suddenly decreased at this particular section. So here due to the sharp edge again we are going to have the losses and here again at the section cc we can observe that here the vinyl contractor it has been formed that is the cross section area of that particular flow or jet it is going to be smallest and then again it acquires the entire cross section area of the pipe and then at section 2 again the full flow is there. So here the head loss due to the sudden contraction it is equal to it is given by the formula it is 0.5 into it is v2 square by it is 2g that is the loss is dependent upon the velocity at the section 2 only. So minor losses due to the bend in a pipe. So in case of the bend we can observe that here we are going to have the direction vertically upwards in each area and then we are going to have the direction of the fluid towards the right hand side. So when we are going to have the liquid changing the direction we are going to have the head loss. So it is purely due to the direction change it is and here we are not going to have any cross section area changing and the minor loss due to the bend in a pipe it can be given by the formula here it is hb is equal to it is kb into it is v2 by 2g where kb corresponds to the coefficient of the bend. Now think about the losses in the two parts which we are calling it as one it is bend the second one it is elbow both are capable of changing the direction through the right angle and then we are going to have the losses here also and here also. So what do you think where the losses will be more whether it is in bend or whether it is in elbow see the answer is elbow because in case of the elbow you can observe that the sudden change in the direction it is occurring so from here to here the sharp change is there whereas in case of the bend the curvature it is larger radius and we are going to have the smooth change in the direction in case of the bend whereas in case of the elbow so less radius of curvature is there and sudden change in the direction is occurring hence the losses in the elbow this will be more it is so but the space required by the elbow this will be lesser accordingly we should be able to select it is the minor loss due to the due to an obstruction in the pipe say sometimes an obstruction might come in the say pipes and say it will be to the flow and then in case of this we are going to have the obstruction here which is shown hatched and then section 11 we have taken here where it is going to be largest in the cross section area and then section 22 it is the normal cross section area of the pipe it is say head loss due to the obstruction it is given by v square by 2g into bracket it is a capital A refers to the cross section area of the pipe cc refers to again coefficient of contraction here again the venocontract it is going to form and then we are going to have the again the enlargement in the cross section area of the flow so coefficient of contraction is coming here also and small area refers to the maximum area of obstruction and say it is minus it is 1 is there so with the help of this formula we can determine the head loss due to the obstruction minor loss in various pipe fittings so different types of the pipe fittings we are generally using like say different types of the walls are there so flow control walls are there or shut up walls are there or say we can also go for the different types of the couplings to join the two pipes etc so in case of those head loss in the pipe fittings that is HFI it is it can be calculated or it can be given by the formula KFI referring to the coefficient of fittings and then the formula is KFI into it is v square by it is 2g is there so the last one so in case of the last one we are having the minor loss at the exit or outlet of the pipe so now here we can observe that we are having one pipe which is connected to this tank tank number suppose 1 and the pipe is connected again to the tank number 2 so here also the connection is there here also connection is there now from left to right when the flow is occurring at that time this is going to become inlet and this is going to become the exit or outlet of the pipe so in case of the exit or outlet of the pipe we are going to have the losses as given by the formula it is v square by 2g so H at outlet is given by the formula it is v square by 2g now in all we have observed that the bend or the elbow these are the say only parts which are changing say the direction of the fluid and they are not changing the velocities so similar to this one we can have the other say fittings also so like say the 45 degree elbow we can have instead of the say 90 degree or 60 degree etc we can have so minor losses these are corresponding to both that is the change in the direction and also the change in the magnitude of the velocity if it is occurring then also the minor losses these are going to occur these are the references thank you