Today's lecture is on capillary fluid incompressible flow and hydrodynamic lubrication. This is under module 2 which is fundamentals of fluid flow and properties. In the last classes we have learnt some basic properties of fluid and also basic mathematics on the fluid flow such as momentum energy equations etcetera. In this lecture we shall learn about the mathematical development of the incompressible fluid flow in capillary passage. Now if we look into this figure what we find at the top on a parallel plate another parallel plate is moving and the gap is h and it is maintained throughout the plate or in other words if the bottom one is larger the moving one is smaller then we can consider the field is the area of the upper one and bottom what we see that the h is gradually decreasing from h2 to h1 within this field. Now we assume that plates are flat with good surface finish and the hydraulic fluids have very good adherence to the materials of the plates. Now if we think of the one plate is moving on the other and in between there a fluid is there then we may think of that if perhaps there is slight roughness the lubrication will be better it is not that it is always better that surface should have good finish but the fluid should adhere to the plates. This means that the layer of the fluid is touching the bottom plate that will never separate and which the layer touching the upper plate that will not separate then what may happen if there is it is a viscous fluid the when one plate is moving to the other then the oil will try oil will be dragged and it will try to move not oil it might be any fluid as such. Now this gap you may ask the what is the dimension of this gap this gap are in the order of few microns 20 25 microns or slightly more than that. Now therefore I have written that it should have good adherence property to the plate material the oil inside this capillary passage which develop a velocity gradient of a b. Now this line is you can say this is a straight line this is a straight line what this point is not moving. So what the oil if I take a point on the oil bottom layer it is touching here and if this point is not moving whereas the in upper layer who the point o has moved to a. So there is a velocity gradient however it will remain uniform unless the gap diverges or converges along the flow directions what we have shown here it is converging at the bottom one we are showing that it is a converging gap in that case what is happening if we think of the this point is moving over here. So at the top also this point will move the same distance here also it is the same distance. But if you look into this the gap has reduced here but this is an incompressible fluid and there is no slippage. So amount entered here has to go out through this each one gap therefore definitely this line will take a it will gradually take a concave shape or in other words what it should actually here it will be a concave then straight line and then it is a convex. So that area of these three are same that only on a unit length along the transverse directions will give the same volume. Now if this I consider this is h2 this is h1 and if this velocity is u in both the cases and h2 plus h1 divided by 2 is equal to h say here here you will find this triangle and this triangle will be same. Now this is quite interesting what we find that this oil is taking gradually the velocity of the midpoints are increasing in this case the oil is incompressible. And therefore for continuity in flow area of Oav it remains constant this area will always remain constant which I have already told you now consider an element of fluid as shown in figure 2.52. Now this is the figure what the element we have considered this is let us consider this is like a cube. The axis system is that along the direction of flow or along the direction of motion the capital U is the plate velocity small u is the fluid velocity in that direction capital U direction axis is x and along the h direction axis is y and along the transverse directions there will be z axis. Now inside that fluid film we have considered a cube of fluid in other direction it might be del z other direction is del z that means volume of this fluid is del x into del y into del z. Now look at this if at that point velocity is u then at the top level of this element the velocity will be u plus del u del y into del y this should be del y like this anyway. Now if we think of the force balance what the force is acting mind it we have taken a fluid at the middle not at the bottom or not at the top for our clarity then what we find this side there is a pressure field P and here definitely pressure will be P plus del P by del x into del x similarly what force is acting over there this is moving like this so what force F is acting that will be here F plus D F del y by del y. Now this is we can see this one component may be 0 anyway if we write down the equilibrium equation for this element then clearly tau plus del tau del y by del y tau is the shear stress between the layers into del x into del z that means this x into del z we have considered this area minus tau plus del x del z is the force in this directions and here I think here this will be tau not F here this will be P plus del P by del x consider this is a small P not the capital P del y into del z minus P del P into del y del z. So this will be the equilibrium we are considering this force this minus this force is equal to this minus this force P minus this force this will be tau. So this is for the equilibrium of this element now we can see that all terms will be cancel out except the terms this terms will remain there. So what we find that the change in shear stress this is the shear stress change in shear stress in y direction is equal to the change of pressure in x direction now this is again the theory from the theory of shear stress and fluid the shear stress is given by mu del u del y where mu is known to us which is dynamic viscosity. So if we we can check the dimension this is Newton per meter square Pascal's so mu is given in Pascal seconds and this is meter per second by meter. So this is Pascal's means Newton per meter square. Now differentiating with respect to y what we get del t by del y is equal to del tau by del y is equal to mu del square u by del y square we have differentiated this one and we get this. Now del t by del y is equal to del P by del x. So we can next phase we can write del P by del x is equal to mu del square u del y square. So from the equilibrium of the fluid in a capillary passage we have arrived into an equation that change in pressure in x direction is defined by viscosity into del square u del y square this means that rate of change of u in y clearly if del u by del y is constant in case of flow between two parallel plates then del P by del x will be 0 because second derivatives of del u by del y will become 0. So del P by del x is 0 this means that no pressure will be build up. Therefore wedge is essential for varying del u del y that means plate one plate is to be inclined to the others gaps should gradually should decrease to have positive pressure that means to vary this because there will be change in u then only there will be del u by del y that is to generate pressure gradient and thus the lubrication fluid frame. Now this lubrication fluid frame needs there should have pressure gradient in the field or in the flow in the capillary passage only then this frame will be generated. Now I was talking about that if there is a rough surface then what might be the problem apparently at the top surface some fluid will be more adhered to the plate but due to this roughness there will be breakage in the fluid frame it will be disturbed but if the plates surface are good finish and the fluid film or the fluid is adhered to that then this fluid film will exist there. Now in this figure we have shown this converging field and the plate is moving in this directions then what we see that to keep this area constant initially there was a concave curve from this side it was a concave curve and then the straight lines and then it is a convex curve that means the fluid velocity is gradually increasing when the plate is moving in this directions. Now this means that here del square sorry del square u by del y square is positive in this case it is 0 at the middle where the gap is h you can say and here it becomes negative which is also shown in this form. Now as this at this point and this point the plate there is no existence of plate and definitely pressure will be the atmospheric pressure and 0. So this must be that pressure map the pressure gradient will be such that we can see this maximum pressure at the middle. So now we can consider on this plate this is the pressure distribution. So this pressure this plate will float and we can estimate if this is there then obviously if there is no load the gap will try to be increased. So if we can put a load here and the magnitude of this load will depend on how much pressure is being developed here. Definitely the this gap has a role this magnitude of this gap will have a role depending of this gap the either I mean pressure will be more if the gap is less but sorry if the gap is less then the pressure will be more. However we cannot make this gap very small at least there should have some magnitude that depends on fluid property and other parameters. So in case of converging graph in the direction of motion and upward thrust will develop due to build a pressure thus the load carrying capacity of the plate will increase which is the basic condition of hydrodynamic lubrication we call this hydrodynamic lubrications. Now contrary to that there is also hydrostatic lubrication and in many fluid power components there are hydrostatic lubrications. These are done by creating a hydrostatic pressure from external source. Say for example in that case one plate is moving on the on another plate which is having a gap uniform gap in that case from the stationary plate we can make several holes and we can allow the high pressure oil to go in. Anyway the we will look into the hydrodynamic lubrications and the pressure field in case of capillary passage. The theory is applied for capillary flow as well as to develop hydrodynamic lubrication theory in sliding contact bearing which include the slipper pad and the journal bearing lubrications. Now even if we would like to find out the pressure distribution in a capillary passage between two stationary plate or one is moving and at the entry side and the exit side there is a pressure difference the same equation can be used only in that case you will become 0. Let us see how it can be derived. Now in this figure what I have shown there is one outer member and this is the inner member. Now one is moving over the other not only that it has some not a simple motion not just rotary motion or not sliding motions rather we can consider that one plate is moving with respect to other one is the plate is having rotational motion as well as it is revolving on other plate which on a fixed center. Say this plate is moving with respect to this point one is the rotation about its one axis other is that it is revolving about this axis. Now here we can say that say this is outer member and this is the inner member if I consider this is fixed then this one is moving like this it is rotating about its own axis as well as it is revolving around this axis. Say one can develop the equation of motion of one plate with respect to the other. Now why we have taken such a case because in case of many fluid power machines and devices a parallel surface moves with respect to another fixed surface where one side of this capillary passage is exposed to high pressure fluid. Say for example side plate of a gear pump I think you may not have the idea of gear pump but in case of gear pump just imagine two external gears are rotating within a enclosed space and there are two side plates and it is pumping oil from one side to other side. So, definitely there is a pressure field inside the cavity inside the space and then there will be leakage through the side plates that can be analyzed with the theory what we are going to study now. Flow in such capillary passages occur both due to hydrostatic and the hydrodynamic pressure gradients. Although in many cases hydrostatic pressure dominates in case of fluid power system this I have explained a little bit but I would always say usually in case of hydrostatic machines in many occasion you will find that between in the capillary passage one side there is a high pressure in other side there is a low pressure. For example the case we have considered in that case also it is like that. So, referring to this earlier figure which I have shown the equation of pressure distribution can be derived as follows. Let us consider the earlier equation which we have derived can be rearranged at the written in two dimensional form as follows. So, del square u by del z square is equal to 1 by mu del p by del r. Now here we have considered the cylindrical coordinate system that means there is a from a center there is a r direction and theta directions and z direction is the opposite I mean the towards the thickness and u is the velocity along r directions and v is the velocity along theta directions. So, this can be derived as del square v del z square 1 by mu r del p by del theta for u we can derive this and for v we can derive this. This the same equation which we developed for x directions now we are applying the same theory for r and theta directions. Where u the fluid velocity in r directions v is the fluid velocity in theta directions and from the bulk continuity in cylindrical coordinate system the bulk continuity is written in this form r is the general radius. So, and h is the gap the limits from 0 to h is the limit. So, del there r by r u del z plus integration over 0 to h del v by del theta into del z is equal to 0. These are the standard equation which we have adopted here. What is this continuity bulk continuity? This means that the in case of incompressible fluid the amount of fluid entering to the capillary passage it will go out at the same amount by the same amount there will be no conservation of mass inside the capillary passage. So, that equation can be written in this form that means accumulation of fluid inside the capillary passage is equal to 0. So, we have developed the pressure versus velocity equations and this bulk continuity equations. Now, to solve these three equations simultaneously we will integrate twice the equation 2.5.6 at first. So, we get we have integrated that del square u by del z and we have got these equations. This integration is not difficult you can carry out and you will arrive into these equations.  So, again I repeat. So, we have got earlier equations in terms of del square u by del z square and del square v by del square del theta square. And from that equation we have carried out this integration twice and we have got these two equations. Now, again coming into this motion of this plate one over the other what will be the boundary condition now at z is equal to 0. In that case we are considering the capillary passage the capillary gap is in the z directions. So, at z is equal to 0 both u is equal to 0 and v is equal to 0 no sorry z is in the direction of the velocity when z is equal to 0 u is equal to 0 and v is equal to 0 one moment. Yeah z actually we here instead of y we have considered the z. So, at the bottom that means the on the stationary plate z is equal to 0 u is equal to 0 v is equal to 0. Now, at z is equal to h you see in the h direction this sliding velocities of an element in radial and tangential directions are derived as in this case if I consider this point velocity of this point this we can have sorry this is I think this figure has come over here this is u this one is u and this is v. So, u is coming omega minus omega 0 into c 0 sin beta here v is equal to omega minus omega 0 to c 0 cos beta minus omega r. Now, what is omega this is rotating at the speed of omega and this one is rotating at the omega 0. Now, this omega and omega 0 that has a definite relations mind it this plate we have we have not described about the motion of this plate, but this equation you have to accept and what is c 0 c 0 is this the distance between these two centre. So, these equations probably say for example if you are asked to find out the pressure distribution of these two plate these equation you will be given because you are not deriving these two equations. So, this is the boundary condition 2 at z is equal to h u is equal to this and v is equal to this one. So, this is the boundary conditions. Now, what we do substituting these boundary conditions in equation 2.5 minus 9 we get directly k 2 is equal to 0. If you look into that equations and if you substitute these boundary conditions the first boundary condition you will get k 2 is equal to 0. And then from the other one you will get k 1 is equal to 1 by h omega omega 0 c 0 sin beta minus h by 2 mu d p by d r. Then you will become 1 by 2 mu del p by del r to z square minus h z plus z by h omega omega 0 c 0 sin beta. Similarly, from the boundary conditions and equation 2.5 10 the same way we will get this equation for the velocity v in theta direction is equal to 1 by 2 mu r del p by del theta to z square minus h z plus z by h omega minus omega 0 c 0 cos beta minus omega into r. This derivation will not be difficult, but the omega minus omega 0 sin beta components that we have accepted for the velocity. Substituting in the continuity equation 2.5 minus 8 we get. Now, what we are doing now we are substituting u and v in the continuity equations. Then we get this big equation del by del r into r del p by del r 1 by 2 mu integration from 0 to h z square minus h z del z plus del by del r c 0 by h into omega minus omega 0 sin beta integration 0 to h z del z plus del del theta del p del theta 1 by 2 mu r integration 0 to h z square minus h z del z plus del by del theta into 1 by h into whole into omega minus omega 0 into c 0 cos beta minus omega r integration 0 to h z del z is equal to 0. This means that for incompressible fluid we find this whole is 0. So, this is equal to 0. Then if we put our limits we integrate and then put our limits we get then this equation del by del r del p by del r 1 by 2 mu z cube by 3 minus h z square by 2 0 to h plus c 0 h omega omega 0 sin beta z square 2 by 0 sin beta z square 2 by 0 to h del square p del theta square 1 by 2 mu r z cube by theta minus h z square by 2 0 to h then 1 by h del theta whole into omega minus omega 0 cos beta minus omega r z square 2 beta 0 h. Now, sorry here one conditions this was not coming over here. If you look into this this angle is this has a direct relations with theta t with this angle this angle has direct relations. That means with respect to this this will be constant the rate of varying this angle with this is same. So, therefore, substituting this condition here we find that ultimately this equation will be reduced to this and this part will be c 0 h by 2 omega omega 0 by sin beta and this will also become a sin beta this part if you put that conditions somehow this is missing here. Anyway we will arrived into this equation what we find directly this and this will be cancel out. So, this part will become 0. So, this means that r del square p by del r square plus del p by del r plus 1 by r del square p del theta square is equal to 0 which also can be written as del by r d p by d r plus 1 by r del square p by del theta square is equal to 0. In many cases you will find the equation is written in this form. However, another form we can directly write from here r we cancel out dividing the whole left hand side by r we get this equations. So, we will find the equation either in this form or in this form. What is there that it is independent of the velocity of the moving plate? We have considered a fixed plate another plate is moving we have considered the fluid velocity of the due to this drag we have considered. But while we have arrived into the pressure distribution equation what we find that it is independent of you. This means that if you take a simple case on a plate another plate is rotating simply the pressure distribution will become the same. Now, the question is that in that case then what is the benefit of developing these equations? These equations we have developed considering the gap is constant there is no converging field. This means that if the gap is capillary gap is maintained constant then irrespective of the motion of the plates velocity distribution will be in this form sorry this pressure distribution will be in this form. And then whether there will be change in pressure or not that will completely depend on the boundary conditions. If there is no pressure difference so pressure will be equal at each and every point within the plate. We shall now consider the gradually varying capillary gap in the direction of motion. So earlier what we have found that is there is no variation in the gap uniform capillary passage. Now we shall consider the capillary gap is varying more specifically the converging passage in the direction of the motion of the body over the other which have constructed the capillary passage is considered. The most common example is the rotating journal in fixed boses which I have shown here. Now here say this outer one is the boses inner one is the journal and the journal is rotating and outer one is fixed it may be otherwise also inner one is fixed outer one is moving. In some cases say for an example planetary gears you will find both are moving but we need only one should have relative rotation with respect to the other. Now look at this in usually this journal bearing there will be gap that means if we measure the inside diameter of the boses and outside diameter of the journal you will find that there is a difference this difference are in the order of micron. So may be 20, 30, 40 microns gap are there for the journal lubrication. Now if we would like to apply the rectangular coordinate system what we do we fix that coordinate system at the point of analysis then x is the tangential directions. Suppose we have considered this point so tangential direction will be x it is rotating like this. So may be the flame is the oil is moving like this. So we will consider the in the direction of motion x is the positive and y is along the radial directions that means in the direction of h the flame thickness and sorry this will be again z there is a mistake the z is axial direction along the shaft. So now we are studying hydrodynamic theory mechanism of fluid lubrication in a capillary passage the one dimension flow equation can be written as del square u del y square is equal to 1 by mu del p del x which we have derived earlier 2.5 by 5. Now integrating twice with respect to y we get the after the first integration del u by del y is equal to 1 by mu del p by del x into y plus k 1 and after the second integration we get u is equal to 1 by 2 mu del p del x y square plus k 1 y plus k 2 y where k 1 and k 2 are integrations constant. This is same as we have done earlier in case of two flat parallel plates. Now we apply the boundary condition here the boundary condition is that when y is equal to 0 u is equal to 0 and at y is equal to h u is equal to u u means the velocity of the moving plate capital U. Also considering only one dimensional flow now for deriving this equation we are considering the flow is only in the direction of the capillary passage in the x directions. So we apply the first boundary conditions we get k 2 is equal to 0 and again substituting in equation 2.516 we get k 2 is equal to 0 and again substituting u is equal to 1 by 2 mu dp by dx h square plus k 1 h. Now here if you look into this we have now we have now one word used ordinary differential form rather than the partial differential form. The earlier while we are deriving the equation we used partial differential form to get that variation in pressure might be all directions. So we must use the partial differential equation but here we are as we are considering only in one direction we will write the equation in this form. Now using second boundary condition we get k 1 is equal to u by h minus h by 2 mu dp by dx. So finally we get u is equal to 1 by 2 mu dp by dx y square plus u by h minus h by 2 mu dp by dx into y. We can rearrange this and then we can write this equation in the form 1 by 2 mu dp by dx y square minus h by plus u y by h. The first part now look into this equation this first part of the above equation presents pressure induced flow clearly this is a pressure induced flow. So this only will exist if there is a pressure difference and the second part is the drag flow. Drag means one plate the moving plate is dragging the fluid over the other. Now applying the continuity in flow assuming no breakage in flame. Now here it is important this theory cannot be applicable where the oil flame is breaking. Now how we can understand this oil flame is breaking or not you will find that for continuity in the fluid flow for continuity in the flame or the flame will not break we have to satisfy some conditions. So that automatically will come and we will see that whether it is being satisfied. But there are some external reason also say a flame is breaking satisfying all hydrodynamic conditions. Flame may break suppose there is a particle inside the fluid somehow it has enter or a roughness has developed in a surface that also may cause the breakage. But let us consider that there is no breakage there is no particle inside the flame. So for an unit length in z directions because if you want to match the dimension you will find that in this equations one dimension is missing. So we have considered that we have taken unit length in z direction in this case z means the along the axis of the shaft. You can see this directions. So this is along the axis of the shaft and this is the x directions this is the y direction we have considered. And converging capillary passage it is moving like this. So from here to here where the minimum gap there will be the converging fluid and here the pressure distribution will be there we will see later. But let us see that what we find now in this case Q is equal to U d y. Now why this equation we have written in this form not in the cylindrical form. Because here although this capillary passage is a circular but we have considered as if it is a flat one. We have considered the developed one capillary passage the same equation will holds good. Substituting the expression of U from equation 2.518 we get Q is equal to integration from 0 to h 1 by 2 mu dp by dx y square minus h y plus U y by h d y. Now we integrate and put the limits then we get this equation in this form 1 by 2 mu dp by dx y cube by 3 minus h y square by 2 plus U y square by 2 h. This gives the form like this 1 by 12 mu dp by dx h cube plus U h by 2. So we can rewrite the equation again that Q is equal to U h by 2 minus h cube by 12 mu by dp by dx. Now here if the U is equal to 0 then this part will become 0 and then this will be only the pressure gradient due to the inlet and outlet pressure. But in case of journal bearing U will be always there that is the peripheral velocity and so Q will take this form. Now for an incompressible fluid say mineral oil Q is constant therefore del Q by del x will be 0 and then substitute the equation 2.522 in equation 21 and then differentiating with respect to x we get U by 2 del h by del x is equal to del d by dx into h cube by 12 mu dp by dx. Now consider the flow in z direction. We have considered along the peripheral direction of the hydrodynamic bearing. Now we are also considering the along the axis. Why it is important? Because bearing will have certain length. So we must consider the equation also in the z direction. This means that if there is a pressure gradient in z directions there will be also leakage flow. Now the equation will take the same form. So this is the full equation for journal bearing lubrications d by dx h cube by 12 mu dp by dx plus d by dz h cube by 12 mu dp by dz is equal to U by 2 dh by dx. It is Reynolds differential equation for two dimensional flow with pressure gradient in a converging flame in the direction of motion and considering end leakages. No general solution for p exists. Case to case it is solved applying boundary conditions. So now if we consider the irrigation in journal bearing design. Now Sommerfeldt he proposed that r by c f is equal to function of r by c square mu n by p that is equal to phi into s. This means that this quantity he proposed which is defined by s and called as Sommerfeldt number and it is a dimensionless quantity which can be verified from this. It is a dimensional quantity. Now what are these parameters where s is the Sommerfeldt number or bearing characteristics number r is journal radius c is radial clearance. This is exact diameter of boost minus exact diameter of journal divided by 2 in meter. Then mu is equal to viscosity in Pascal second. N is rotational rotating speed of journal in revolution per second. P is the average pressure on projected bearing area which is clearly that load on bearing divided by length of boost into diameter of boost that is f divided by l into d and phi is a function f is coefficient of friction. Now Sommerfeldt he developed he proposed that it can be written in this form. But again this is not a close form solution. So, Raimondy and Boyd the two engineers they developed some charts out of those using those equations. For solutions Raimondy and Boyd consider practical and particular cases. They consider both full that is 360 degree bearing and partial 180 degree bearings and infinite that is l by d is equal to 4 and above. l is the length of the boost d is the diameter of the boost. If it is more than 4 it is called infinite l by d below 1 4 is called short bearing and mu that he considered is the constant. They considered as a constant. They used computer techniques to translate the results of hydrodynamic equation to various operating characteristics for various l by d ratios against a range of Sommerfeldt numbers. Interpolation techniques are used for the intermediate l by d ratios. They preferred charts which is graphs for various bearing parameters and characteristics. Those are adequate to select design a journal bearing for general purpose applications. Now in a bearing actually what happens if you look into this H0 when this is operating you will find there will be a minimum fling thickness H0 and E is the journal displacement this eccentricity and there will be eccentricity ratio. Now everything will be defined in this form. This means that if we solve a practical case we have to find that what is the minimum H0 how much the eccentricity ratio is coming which will give us a clear idea where this pressure generation will be there or not. So it might be say all gaps everything are same but due to the speed this is not being generated. Now if it is generated again the question is that how much is the H0 where is the maximum pressure and what is the angle up to which this pressure is there. We are applying the load in this directions. So we have to find out all such angles. F is the load acting on single bearing this is actually F not P. P we have considered for pressure so this is F along with the described bearing nomenclature there are other factors also J is the mechanical equivalent of heat and gamma is the density of oil C H is the specific heat of oil delta T is the temperature rise in degree centigrade Q is the total flow in oil flim zone in x directions Q S is the side leakage from flow oil flim from oil flim in z directions that is in the axial directions and you will find that there are chart available for S is the summer field number this is dimensional less R by C into F R is the radius C is the clearance and F. So you will get this chart from here we can calculate F because R and C are known factor S versus H0 by C that H0 is the gap at 0 position that means directly towards the in the direction of load then we will also find S theta H0 that means what is the angle of H0 no sorry H0 is the minimum thickness minimum flim thickness S versus Q by R C n L. So we can have this if we have this L then or directly from there we can find out what should be the L or Q. Now also we find Q S by Q. So Q is the flow in the direction of the periphery whereas Q is the side leakage. So knowing this amount we can calculate this amount also then we can find out the what will be the temperature rise inside the fluid from this chart and S versus P by Pmax what is the pressure? Pressure P is the pressure in the projected area load divided by the projected area of the bearing that is L into D and what is the maximum pressure we can find out from that ratio and then we find out at what angle this Pmax occur. Now also we can find the theta P0 where is the P0 is the pressure at H0. Now once we find this then we can verify whether our design is satisfactory or not also we can think of the how much oil is being dragging in and what may be the temperature rise there and whether we should use any cooling arrangement or we should use more oil there if the length is satisfactory or not. So basically we can select a bearing and whose bearing and then we can verify all these if we find these are satisfactory then we can use that bearing for our design. This is general purpose but for very precision bearing we have to calculate many other parameters also. Now these charts are available in this book however in the next lecture I will show you some charts and as well we will calculate some parameters. Thank you.


Hello, welcome to another video in the understanding thermodynamics series. My name is Adrian and today we are continuing our focus on substance properties and we are going to have a look at phase change and the different phase diagrams. In this video, we will look at phase change and the two phase systems. We will discuss the concept of equilibrium, the degrees of freedom of two phase systems. We will look at the phase diagrams of water specifically. And then lastly, we will also look at the three dimensional phase diagram of water. There are three two phase systems possible between the solid, liquid and gas phases of water. Ice and water is a solid liquid two phase system depicted in the first picture, which is a glass containing water and ice. A liquid gas interface results when water is boiling. We usually call the gaseous phase of water in a two phase system a vapor. Then lastly, when a snowflake forms, water vapor is transformed directly to a solid phase in what is called de-sublimation. Next, let's look at equilibrium. When we isolate a system from the environment and its properties does not change with time, we say the system is in equilibrium. Now consider the glass of liquid water and solid water or ice. When we add ice cubes to tap water in a glass, the temperatures of the ice and water are initially not the same and they are not in equilibrium. Some ice will melt and the temperature of water will drop after a while. However, if we prevent heat exchange with the environment, the amount of ice will remain constant and the temperature of the ice and water will be the same and remain constant at zero degrees Celsius. We can now say that they have reached a state of equilibrium. Usually, we consider three types of equilibrium. Thermal equilibrium is when the temperature of the phases are the same. The boiling water of the previous slide may be in thermal equilibrium, but not in mechanical equilibrium, which is the second equilibrium state, as there is no equality of opposing forces. Now, mechanical equilibrium is only reached once all the bubbles has risen to the top and there is no more bulk movement of the liquid and vapor phases. Then lastly, we get chemical equilibrium and that is reached when a chemical potential of the different phases are equal. With pure substances, phases do not undergo chemical reactions and chemical equilibrium always exists. Now, let's have a look at a phase diagram. In this graph, there are three different two phase systems which line the lines separating the different phases. We have the solid liquid interface, we have the liquid vapor interface, and then here at the bottom, we have the solid vapor interface. Now, let's consider an example of heating an ice cube, which is taken out of a freezer initially at subzero temperature. Now, I assume the ambient pressure is 100 kilopascals and the temperature is minus 10 degrees when we take the ice out. Now, on the phase diagram, this state is presented by the little circle. Initially, it's in the single phase, which is ice, which is a solid. And as the temperature rises, when we reach the solid liquid phase boundary at 100 kilopascals, the ice will start to melt and a two phase mixture will form. Now, upon further heating, a single phase liquid will result and as we continue heating it up until 99.63 degrees Celsius, the water will start to evaporate and the state is now indicated by the little square in the phase diagram. This is the equilibrium temperature of water at 100 kilopascals. Sure, it is starting to get hot in here or is it just me? Let me just have a drink of water first. If we increase the rate of heating, the rate of evaporation will increase while the temperatures stay the same. Only once all the water has evaporated, the temperature will start to rise and the state become that of superheated vapor. The little diamond shape is the state of water at 300 degrees Celsius in the superheated region. It is important to note that in two phase systems, temperature and pressure are no longer independent. If we increase the pressure on a liquid vapor system, as in a pressure cooker shown here, the boiling point of water will increase and the food inside the pressure cooker will be done quicker as the higher temperature speeds up the chemical reactions. The point on the graph where the three states meet is called the triple point and it is at 0.61 kilopascals and 0.01 degrees Celsius. At the triple point, free phases are in equilibrium and the degrees of freedom are zero. If we change either the temperature or the pressure, one or two phases will disappear. Lastly, we usually assume that the phase boundary between ice and liquid is vertical. This means that water at pressures higher than 0.61 kilopascal and temperatures lower than 0 degrees Celsius is solid ice. Now this figure represents water's phases on a temperature pressure diagram and we can also represent phase change on a temperature specific volume diagram. As mentioned already, if we heat up liquid water enough, it will start to evaporate. It will undergo a phase change. Now it's always nice to visually see the events that occur as a pure substance undergoes a phase change on a specific volume temperature diagram shown here. Now let's consider water at 101.325 kilopascal in a piston cylinder arrangement. Assume the combined effect of the cylinder and the ambient pressure around the cylinder results in a pressure of 101.325 kilopascal inside the piston cylinder setup and the piston is also frictionless and can therefore move up to accommodate any increasing volume and maintain a constant pressure inside. Now initially, the water inside the piston cylinder setup is at 20 degrees Celsius, a temperature lower than the boiling point at this pressure. Therefore, it is a single phase system. Its specific volume is 0.001 002 cubic meters per kilogram. Next, let's heat up the water while the pressure remains constant at 101.325 kilopascal. The volume increases slightly as the water is heated and the temperature rises. Now when we reach 100 degrees Celsius, the specific volume has increased to 0.001043 cubic meters per kilogram. A few water molecules have enough kinetic energy to break free from the liquid phase and the first small vapor bubble forms, which is shown there. The state is that of saturated liquid. On the pressure temperature phase diagram, which you've seen on the previous slide, the state is now on the phase boundary between the liquid and the vapor phases. As more heat is added, more vapor forms. All the heat that is added to the system is used to change the liquid into vapor and the temperature remains constant. As more heat is added to the system, the state of the water turns into a two-phase equilibrium mixture consisting of what is also known as saturated liquid water and saturated vapor water. And this can be visually shown here where we have vapor, which is light blue, and saturated water, which is dark blue. Now upon further heating, the state reaches the solid line boundary on the right. Only a very, very small liquid droplet remains with the majority of the water being converted to water vapor. We can also look at the same process on a pressure specific volume diagram. And the same holds true when we start again with water at 20 degrees Celsius and 100 kilopascals. The specific volume is 0.001, 002 cubic meters per kilogram and we heat the water and once it reaches the saturated liquid state at 99.61 degrees Celsius, the specific volume has changed to 0.001, 043 cubic meters per kilogram. We now continue heating the water and more vapor forms and the state moves horizontally to the right inside the dome. Inside the dome, the state is a two-phase equilibrium mixture consisting of saturated liquid water and saturated vapor water. Eventually all the water has evaporated and the state is saturated vapor. If we continue heating the state, it will move into the super heated region right to the saturated vapor line shown with this little diamond here. The relationship between the three phases of water forms a three-dimensional surface shown here. When you look from the right, you will see the pressure temperature phase diagram. We can trace the state of water at constant pressure heating at a pressure lower than the critical pressure. If we start off here, the water is in solid state or ice and we start heating it up, it will reach the equilibrium line between the solid and liquid water. After all the ice has melted, it will be subcooled water and as we heat it up more, it will reach the equilibrium line at 99.63 degrees Celsius. As we add more heat, we will enter the two-phase region where we have saturated water and saturated vapor. As we reach a purely saturated vapor line and heat it more, we will go into the super heated vapor region. When we look at it from the front, which is the pressure specific volume graph that we showed previously, we can trace another constant pressure scenario. As ice melts to water, your specific volume will decrease and then it will slowly increase as it's heated up. Once it reaches the saturated water line at 99.63 Celsius, if we heat it up more, the specific volume will increase until all the water is converted to vapor and it will increase further as the water moves to the super heated vapor region. So in summary, there are three possible two-phase systems. You get the solid liquid two-phase system, the liquid vapor two-phase system and the solid vapor two-phase system. Now for two-phase systems, temperature and pressure are no longer independent. At the triple point, all three phases are in equilibrium and there's no degrees of freedom at the triple point. And that's it. The course notes which these videos are based on is available on my website, adreonsblock.com. I'm also on Twitter. My Twitter handle is at ASVN90. If you have any questions, you're more than welcome to ask them and I will gladly answer them. Thank you for watching and I will see you in the next video. Bye.


A little factoid for you, St. Lucia was named after St. Lucie of Syracuse, a name bestowed upon the country and the French rule. In addition to being the only country named for a woman, St. Lucia also is known as Helen of the West Indies, given the multiple battles between the British and French for the island. The nickname was earned after a British historian compared St. Lucia to Helen of Troy's Griff methodological character, because she too mobilized an entire navy. One final note on International Women's Day, the Ministry of Commerce, International Trade, Investment, Enterprise Development and Consumer Affairs, as part of its Love St. Lucia campaign celebrates the success of women who contribute to the growth and development of St. Lucia by wishing them a happy International Women's Day. The primary aim of the Love St. Lucia campaign is to improve consumer awareness and increase domestic market share of local manufacturers and service providers. This month, the Ministry takes this opportunity to highlight women in the construction sector. According to the International Labour Organization, ILO, the COVID-19 pandemic has had a significant impact on the construction sector, which is sensitive to economic cycles, yet on the upside, construction holds much potential to stimulate recovery thanks to its potential to create jobs and, in turn, recovery measures can support the sector's transformation toward sustainability and digitalization. Over the last few years, the local construction sector employed almost 7,000 persons annually and approximately 3% were females. The Ministry serves all women, particularly women, in construction. The Ministry celebrates the success of three women who own businesses in the construction sector for over 10 years. Mrs. Deborah Tobier of True Value Building and Hardware Supplies, Ms. Tracy Carrington of TR Realty, and Ms. Nicole John of NJ House Painting.


Hi everybody, Joe for Jasper's casewrakes.com happy Tuesday. We got Tuesday night football happening here Washington at Philadelphia Seattle at Rams And we got this here 2021 and Panini impeccable football three box pick your team at number seven Big thanks to this group right here for making it happen Appreciate it. You're on Tuesday the 21st 2021 Matthew ended up with the Packers as last spot mojo before we pulled teams For the those two number blocks random number blocks And I think I did I upload both of those randomizers? No, I think I forgot to upload the Chicago randomizer But I'll do that in just a moment But there are the results right here Over there and here's the other one right here the rooftop means you one spots in the fillers Filler for the filler. Let me post because otherwise, I'm totally gonna forget. So we post the video For the other number block Also while I'm doing this go to Jasper's casewrakes.com check out all the football we have there for those of you watching live We did post another impeccable football So if you're looking for that Looking to get into another one if you miss out on your teams the first time around Don't miss out this time around All right now I'm set with that Steve My fancy football teams humble brag did not have to worry about all the craziness here in week 15 with games being moved around and people on On in COVID protocols and whatnot because both my fancy teams Playoff week one by although not to worry about next week, but For now that didn't have to worry about this week's craziness. I've got a good chance at Winning both my leagues extra blank cards for me Love these Unfortunately for Adam the way things are going. There's a decent chance at him. We'll have to worry about next week. It's actually use one of those blank cards To slow play the hits. We got Josh Jacobs 41 out of 75 For the Raiders That'll be for Aaron and there's Cortland Sutton 32 out of 50 Broncos. I'm actually Gonna be in Vegas to watch To watch these two players My first first Raiders game There's Tana Hill 21 out 35 for Peter and the Titans the Cortland Sutton goes to Derek and Snag two first one is Is Andre Cisco 13 out of 99? 100 That's for Jacksonville Sean Maddock. There's a Kalman rookie landscape autograph 34 out of 99 for Minnesota Steve Locke With The purple people eaters Skull Next up is Charles Haley Indelible ink I think a little happy face inside there Nice that'll be for the Niners. That's gonna be for Sean Maddock We got Devonta Smith rookie landscape autographed well about a 75 Eagles are a number block team part of that Chicago number block group So Eagles 2 is gonna be for Sean Maddock And I think Washington, Philadelphia just about to come out of half-time tied at 10 And down here is Trevor Lawrence there he is T-Law 9 out of 15 two-color patch and autograph Sean Maddock with the Jacksonville Jaguars maybe in a In a post-urban Meyer world we'll start seeing him Evolve a little more quickly. All right nice RPA their next box So the case hit must be in that final box there got a redemption hiding down there We got Andre Johnson 15 out of 75 for Eric in the Texans Six out of ten DK Metcalf We got Seattle and the Rams Seattle and Los Angeles tied at three and the Seattle's in the red zone already. They're inside the Rams five Handoff not to DK Metcalf and touchdown. This will go to Seattle. That's part of the number block team number block group Seattle six is Is for Peter 32 out of 50 Joe Mixon for Cincinnati David B Christian Barmore 57 out of 99 Looks like a good swim move right there right for Christian Barmore. Yeah, he has a defensive tackle Yeah, it's a good swim move look right there Patriots are a number block team Patriots seven New England seven is for Josh who won that spot in that number block We got Chad Johnson 47 out of 49 Ocho Cinco Nice That's David B and the bangles nice one bangles and the redemption here. Let's hold on the redemption. Here's Najee Harris rookie landscape 31 out of 99 Oh, thank you. Oh, yeah break room. Thank you, sir Najee Harris Pittsburgh David B Maybe has a shot at offensive rookie of the year and back here is Javante Williams fire starter Autograph that looks sharp 40 out of 50 That is for my rivals the Denver Broncos Derek Denver Steve Locke started off strong with Kelsey, but then it fell apart.  Oh, I almost thought it was gonna be completely blank for a second Impeccable impressions autograph T R a Travis Travis Kelsey Nice one for Kansas City. That's a number block team Part of the New England group. So Kansas City zero Nicholas There you go, man. Happy Christmas Travis Kelsey's pretty good. Have that walk-off touchdown Yeah, I think that's the first I don't know how many Jason pulled when he was on you release it But that's the first one. I've seen the fire starter article. It looks really nice And isn't that crazy? Travis Kelsey Himself can Might be full rosters this week with all the weirdness that's been going on all the protocol stuff You know, Adam, I wasn't really paying attention to the scores around my league Because I have a first round by a humble brag but um, but then after we taught you were talking about all the low scoring yesterday Actually looked at scores around my league and they're yeah, they're they're like definitely Across the board definitely lower than they've been in any other week. All right final box Cam Newton 45 out of 75 Patriots 5 That'll be for Danny Well, that's a one-of-one that's kind of weird You can turn any damage back there, but Here's a one-of-one. Oh, I see what happened You know, that's the that's the pack crimping machine Must have caught that clad ever d layer one-of-one, you know what we're gonna do This is for chiefs one gale. I'm gonna send you because that Damage is usually something that's pretty That meeting will usually take care of we'll send you the UPC code as Well as they usually sometimes they ask for that number right there So we'll send you this maybe even a wrapper You should be able to talk to Panini and be able to get a replacement for that. That is a bummer though I mean, yeah, it's not really on Panini. It's that they actually it's actually the factory there in a They're usually printed in Dallas, but Yeah, it's that factory there So this is not necessarily a panini issue per se rather than it's a little sloppiness on the factory level But gale still a train whistle all aboard the big hit express King saying panini is the worst with replacing damage cards But it can be done though. I think that too Steve Locke 45 out of 99 three-color patch and autograph Terrace Marshall, Jr. That'll be for Carolina Nathan Rossi Really are those are those redemptions that you've seen live already Ryan? Because you if you haven't seen them live then it's usually on the player not on not on Panini Player hasn't been signing card. There's Heinz Ward nice Super Bowl XL autograph and that'll be David B with the Steelers Ronde Barber 18 16 out of 25 indelible ink Bucking ears That's gonna go to Sean Maddock, and we've got a Curtis Martin for the Jets. Ooh, that's a nice-looking autograph 18 out of 25 master strokes on card auto for the Jets Jets are a number block team So that goes to Jets 8 that's on the New England list right here Mike Joseph with a spot that he won gets the Curtis Martin No dolphins are we B King says no dolphins just my luck. He says are we done with the break? I didn't know we were done with the break nice Curtis Martin for Mike last two Play of the whistle King Look at that spoke too soon just your luck For Arthur King is a Jalen waddle two color Dual relic on card autograph 43 out of 75. He's been having a great season. Actually, that's a piece of his helmet I think game not over Play to the whistle ladies gentlemen always always All right now everyone's gonna try that everyone's gonna try the The hey no hits for me All right. We got a silver piece silver piece for The Jets 16 out of 20 Zack Wilson USA flag. That's nice some fine fine silver Who's got the Jets Jets six? That's for Russell With Jets six nice stars and stripes Nice fine silver USA flag Pretty nice ladies and gentlemen. There you go. That was a nice clean break. I don't have to do any randomizers That was impeccable football pick your team at number seven from Jasper's case breaks calm If you're watching live, I did load up pick your teammate So if you want to run that back, let's go Jasper's case rates calm I'm Joe. I'll see you next time for the next football break. Bye. Bye


This is a big week for Nintendo Switch ports. Bioshock, the collection, Borderlands the collection, and XCOM 2 Collection are all being released for the hybrid console, bringing new meaning to the word portable. Publisher 2K Games has released plenty of games on the Switch up to this point, but these three new collections are among the most beloved games of the past decade and a half. While some games in these collections, such as the original Bioshock and Borderlands, are pushing 15 years old, others, such as Bioshock Infinite and XCOM 2, are so technically complex that it's impressive anyone managed to squeeze them onto a handheld device. This incredible achievement is all thanks to the unsung heroes of Nintendo Switch ports, the incredible team at Virtuous Games. Founded in 2004, Virtuous focuses primarily on game ports, and thus is often overlooked by the gaming media as a whole. This is a shame as the team has been responsible for some of the best ports in recent years. According to Virtuous CEO Gilles Longroyu, work on the PS3 port of Final Fantasy 10 and 10.2 led the studio to discover a passion for creating impressive, challenging ports. He said, We realised there was a lot of value in bringing AAA titles to new platforms, if done well. Meanwhile, our partners also began to understand that our ability to line up a larger number of artists and engineers than traditional developers allowed us to be more thorough in our adaptations. Indeed, the company's size is one of its greatest strengths. Virtuous has over 1,600 employees across the globe, with its largest studio space located in Shanghai, China. Any company that chooses to work with Virtuous knows that they're getting top quality work from an expansive team of talented developers. This large studio is necessary for some of the company's trickier projects. It's not easy getting an expansive HD game to run effectively on the Switch. What's more, according to Elijah Freeman, Vice President of Games at Virtuous, older games can often be more difficult than newer ones. But with enough effort and resources, anything is possible. Says Elijah, We often have this conversation with partners who develop their original game for PC or HD consoles and think that it won't run on the Switch. Give enough time to a specialised team and they will find enough technical and content optimisations to make it play seamlessly. It's simply a matter of priority. How do you balance the distribution of tasks for the GPU and CPU to achieve the expected results? This can be especially challenging if it were a classic game with an antiquated codebase, but it's totally feasible. This requires creative thinking when it comes to frame rate and memory optimisation, especially for the larger maps with complex environments. We have a strong team of technical artists who are rearranging and streamlining workflow and we've set up a VIP, a very important place in the room, which is basically a table with TV sets where we constantly cross-compare the Switch version with other SKUs. We're excited about our progress because we feel that we are pushing the limits of what is possible on the Switch. In 2018, Virtuos created Switch ports for Dark Souls, Remastered and Starlink Battle for Atlas. The quality of these ports may developers sit up and take notice. It turned out that more could be achieved on the Switch than many had realised. Enter 2K Games, who had released several games on the Switch up to this point, but were looking for something more ambitious. Fans were desperate to see some of the publisher's iconic back catalogue make its way onto the handheld. And so, the company decided to dump a bunch of ports onto the system at the same time. According to the 2K Chief Creative, Sammy Thesman, well, we've had a huge demand for these games on Switch for some time now, so it was actually because we felt bad that we've kept everyone waiting this long. In announcing and releasing all these games at the same time, we were able to pull this necessary partnership together even more effectively and really establish it. We didn't necessarily have some kind of marketing goal or something like that in mind, but I'm sure it wasn't just a happy coincidence either. Virtuos worked their magic on these games, trying to crunch down art assets without compromising quality. Ultimately, if there was one thing even this talented studio couldn't do, it was make three chunky Bioshock games fit on a single Nintendo Switch cartridge. So, while the games are releasing physically, this is mostly for show, as the games require a large update in order to run. Regardless, the work that Virtuos is doing is incredibly impressive. The moral of the story is that even if something seems impossible, if you're willing to get creative and rely on other people where necessary, you can still make it happen.


Hello everyone, welcome to this session. I am Dr. Asha Thalange and today we are going to learn turn off methods of SCR. At the end of this session you will be able to differentiate natural commutation and force commutation method and also explain class A and class B type commutation method. These are the contents we will be covering in this session. In the previous session we studied turn on and turn off mechanism of SCR. Turn off process of an SCR means bringing back the SCR from forward conducting state to forward blocking state. This turn on process of an SCR is called as commutation of SCR. Commutation is nothing but transferring the currents from one part to another. We know that in order to turn off the SCR following conditions must be satisfied. The anode or forward current of SCR must be reduced to zero or below the holding current and a sufficient reverse voltage must be applied across the SCR to turn in off. This is done so because even after the SCR is turned off by reducing forward current to zero, still there exist some charge carriers in different layers which keeps SCR turned on. To avoid this, these excess carriers must be recombined and this is done by applying a reverse voltage across the SCR. This reverse voltage which commutates the SCR is called commutation voltage. Based on the source of this commutation voltage, commutation methods also known as turn off methods are classified into two major types natural commutation and forced commutation. Let us see natural commutation. Figure shows the circuit and waveform for natural commutation. In natural commutation, the supply voltage itself is the source of commutation voltage. Natural commutation is used in AC applications. During the positive half cycle of the supply, before the gate pulse is applied, SCR is in forward blocking state and acts as a open switch. Thus, all the input voltage appears across the SCR and load voltage is zero. As soon as the gate pulse is applied to the SCR, SCR turns on and all the supply voltage now appears across the load. The moment supply voltage becomes negative during the negative half cycle, this negative voltage reverse biases the SCR and turns it off. Thus, all the supply voltage now appears across the SCR and load voltage becomes zero. As here, SCR turns off automatically due to the negative supply voltage and without using any additional circuit it is known as natural commutation. This method is also known as line commutation or source commutation. This type of commutation takes place in phase controlled rectifiers, AC voltage controllers and cyclo converters. Let us now see forced commutation. In DC applications, natural commutation is not possible. Thus, to turn off the SCR in such circuits, additional circuitry is used known as commutating circuit. This circuit forces the reverse voltage across the SCR and brings the anode current to zero. The commutating circuit consists of inductor and capacitor called as commutating components. Based on how the commutating components are connected in the circuit and anode current is made zero, forced commutations are classified into different types such as class A, B, C, D and E. Force commutation is generally used in chopper and inverter circuits. With this discussion, pause the video and think what is the major difference between natural commutation and forced commutation. Well, the major difference is that natural commutation occurs in AC circuits with no additional circuitry requirement for commutation, whereas forced commutation is used in DC circuits along with additional circuitry needed for commutation. Let us see class A commutation. It is also known as self commutation or resonant commutation or load commutation. In this commutation, the source of commutation voltage is in the load. The commutating components L and C are connected either parallel or in series with the load resistance R. Load resistance and commutating components form an under damped resonant circuit to produce natural zero. Figure shows the circuit and waveform for class A commutation. When the SCR is triggered, the forward current starts flowing through it and the capacitor charges in the direction as shown. Once the capacitor is fully charged, more than the supply voltage, the SCR becomes reverse biased. And after the turn of time, SCR turns off and acts as an open switch and all the supply voltage now appears across the SCR. The capacitor now discharges through the load resistance and makes the circuit ready for the next operation. The switchoff time of the SCR depends on the resonant frequency which in turn depends on L and C components. This method is simple and reliable. Let us now see class B commutation which is a self commutation by LC circuit. Figure shows the circuit and waveform for class B commutation. In this L and C LC resonant circuit is connected across the SCR and the L and C components do not carry load current. When the DC supply is applied to the circuit before the SCR is triggered, the capacitor charges to the supply voltage EDC with the upper plate positive and lower plate negative as shown. When the gate pulse is applied, SCR triggers and the current flows in two directions. One is through plus EDC, through SCR, through RL, two minus EDC and another is through L and C. Once the SCR turns on, capacitor starts discharging through C plus, L, SCR and C minus. When the capacitor is fully discharged, it charges in the opposite polarity as shown. This voltage across the capacitor makes the SCR reverse biased and causes the commutation current IC to flow through the SCR in opposite direction of the load current IL. When the commutating current IC becomes greater than the load current IL, reverse current flows through the SCR making the anode current to flow below zero and after the turnoff time, T of SCR turns off. The moment SCR turns off, capacitor again starts charging with the original polarity as shown.  If a periodic gate pulse is applied, then this process is continuous and on-off frequency depends on the values of L and C. Thus, in this session, we discussed natural commutation class A and class B type force commutation methods. These are the references you can refer. Thank you.


commander on the fifth day of the war in Lebanon. India Lone Company served religious soldiers from various yeshivas all over the country. The commanders were secular. The request was unusual. A prayer in the network? This is madness. Later on told the deputy commander, Captain Kravitz. However, I realized what this prayer can do for my men, what the meaning is for them. And so for a long minute on the network there was the ancient Jewish prayer and in the background heavy artillery. At the end of it, the combatant who prayed said, well, say amen. And all of a sudden the voice was heard. Here is the headquarters, amen. And then one tank after the other they all responded, amen. It was as if it was an approval of an order and moreover it was an approval of a common fate, an approval to the understanding that everybody was together, part of that whole of that same narrative called Israel. A short time after that the company Alon was caught in an ambush near Beirut and seven of the combatants were killed. The story of these tankers from the Alon Company is an Israeli story, a story about connections, about friendship, about tankers who are tight together, responsible for one another. One human texture that combines faiths and opinions and various perceptions. It's also a story about a heavy price of war. Hundreds of combatants have been lost in the First Lebanon War and later on they left a gap that will never be filled. Captain Dobkin from the Moshev Tkuma in the Negev, the son of Zehava and Nathan, was killed in the first weeks of the war by a Syrian sniper. Before he fell, Haimke wrote, do not mourn for me too many days, not for that did I sacrifice my life. I gave my life so that you will rejoice, so that you will be able to live a life that I so loved and continue to live as usual and fulfill my dreams. The things I loved, the green fields, the open spaces, the state, the country, the homeland, and then you will know that I did not die, I am alive and I accompany you forever because you fulfill everything that I was hoping to fulfill in my life. So wrote Haimke, he left us a life legacy. No decreed us, all those fallen. At the time I was a young officer in permanent service in that horrible war 40 years ago, a war that wanted to put an end to long lives where the inhabitants of the Galilee lived under terror. In the streets, in the kindergartens, in the schools, in the shelters, we did not rejoice to go to work and we are not rejoicing today either. And in the same breath we can say at the time we didn't allow and we will never allow to violate the peace of the settlements in the north. We are determined and strong. We shall continue to protect ourselves with ourselves at any time and we'll take decisive steps against anybody who tries to harm us. I hope this stops, he says, with a close or far 40 years. After the First Lebanon War broke out, the threat from the north still exists. Iran is threatening, it creates chaos and hostility behind our northern border through its long arm, the Hezbollah, and I reiterate there is no unsolved controversy between the State of Israel and the State of Lebanon. Between the people of Israel and the Lebanese people there is no unsolved controversy. Our struggle is against the Iranian influence which is imposed on Lebanon and the Iranian regime that continues to disseminate hate, terror, pain, and suffering, destroys Lebanon and tries to undermine the stability in the entire Middle East. Dear families, the long Lebanon War and the long stay on it left an open wound in the heart of the nation. You, all of you, the sons of the bereaved families, the MIAs and the injured in body and soul are coping day in, day out with the results of the war. Today and every day we are convening in order to embrace you and to say to you to what extents we pain and feel your sorrow, which is our sorrow, and we thank you. During the first Lebanon War the poet Ehud Manor wrote the words to the song, I do not have another country, a song that has become almost an anthem, 40 years have gone by, we do not have another country, and we will never have another country, ever. May the soul of the sons and daughters who gave their lives in the heavy battle be blessed forever. And that was the Israeli president there, Isaac Houtsog, addressing a special ceremony to mark 40 years since the first Lebanese War, that was the president, we'll also hear from Prime Minister Naftali Bennett, and the Defense Minister Benny Gantzal giving speeches at the Mount Houtsal Memorial Center in Jerusalem, a bit of history then, 1217 Israeli soldiers lost their lives in what is considered the country's most controversial war, well with me in the studio Dan Perry is an international affairs analyst and a former Middle East editor of Associated Press, great to have you with us, Dan, and I'm sure you can give us a bit more context on this. It started out as an operation to bring peace to the Galilee, we just heard Houtsog allude there to what life was like in the Galilee with these constant attacks from across the border in Lebanon, it turned into a quagmire pretty much, didn't it? It certainly did, because when you think about the Lebanon War, the first Lebanon War, the issue was not just a 1982 invasion, but the fact that beginning with 84 when they pulled out from most of the territory, they stayed in a security zone that became a genuine quagmire, and that lasted for 18 years, achieved nothing. If it has any legacy at all, it was the creation of Hezbollah that accompanied it, the involvement of Iran in dominating Lebanon and a problem that persists to this day, whereby Hezbollah is now the enemy from the north, and Hezbollah exceeds the PLO and magnitudes of damage it can cause Israel and rocket arsenal and so forth by a tremendous gap. And some analysts say that Israel really overestimated the capacities of the Lebanese population there who were friendly towards Israel and really underestimated the Shia population. Israel thought that they could create Christian hegemony in Lebanon, and Christians were once the majority, and indeed when France left Lebanon, they had a chance to have a smaller country where they would be a permanent majority. They unwisely did not choose that route. By the time Israel got involved, they were already a minority, and Israel tried to make sure they ran Lebanon, that backfired rather spectacularly. Would you say this was Israel's one and only failed attempt at regime change? I can't think of another regime change as such, although the word is a little bit fluid. You could argue that various Israel's misadventures with the Palestinians might also be defined as such, but no, not really. It was, and it taught Israel lesson. It's very difficult to interfere in other countries affairs unless they're willing to pay a bigger price than Israel ultimately proved willing to pay. And Israel did pay a big price, of course. Hundreds of soldiers lost their lives in that conflict. And Israel at the time was, of course, the dominant military power. It probably strengthened Iran in the region. Remember when Israel invaded Lebanon, the Islamic Republic was only a few years old. It wasn't clear that they were going to become the master that they are today. It probably encouraged them to do that by trying to play God in Lebanon. The goal, there were three goals. One was to end the rockets. The other was to kick out the PLO that becomes a slightly less defensible, especially when considering the 10 years, hence they invited them into the West Bank and Gaza. And a third was to change the nature of politics in Lebanon. That proved completely unattainable and backfired, as I say, spectacular. So take us back then, prior to the conflict. What was life like in the Galilee region of Israel then, in northern Israel? Well, what people forget is that the First Lebanon War was in a way kind of the Second Lebanon War because there was also a smaller invasion called the Litani operation, smaller scale run by Defense Minister Azar Reitzman at the time, three or four years before, which also didn't achieve the aims. Fundamentally, every few months there were salvos of rockets fired by the PLO from what was called Fatah Lein because the PLO controlled what eventually became the Israeli security zone, the area just across the border from Israel. And Begin used that, some would say as a pretext to invade Lebanon because he was feeling some pressure from having been two-pieceable and giving up the entire Sinai Peninsula to Egypt just a few years before. Right, of course, all wars are kind of informed by what happened previously, aren't they? Yeah, now the official narrative, and I don't discount it entirely, was that they were aiming to put an end to the rockets. But honestly, I remember at the time there was a very strong feeling they were looking for a pretext. And by the way, the ultimate pretext was the attempted assassination of Ambassador Argov in London. Right, and that was cited as a kind of a case of spell for going to war. Like the next day or the day after they immediately rolled into Lebanon, they were obviously looking for an excuse. But the rockets from Lebanon were not a trivial thing. Of course, very sadly, for the past four decades or so, Israel has been facing rockets from different directions as well, it's a problem that seems to dog Israel over the ages. And right now, the biggest threat comes from Lebanon and Hezbollah, backed by Iran. That's an enemy of an entirely different magnitude, and I'm afraid Israel poked the bear here and may live to regret it. Do you think it was a mistake then? Do you think things could have been different today if that war wouldn't have happened? Yeah, I think the current disaster in Lebanon didn't need to be quite this bad. I think the Iranian involvement in Lebanon didn't need to be. And I know that some are controversial positions. There are some academics that say Iran was planning to do so anyway. I don't really buy it. But primarily, the security zone in Lebanon, the occupation that lasted after the war and only ended in 2000, was an unmitigated catastrophe. Many, many hundreds of Israelis lost their lives. Much of southern Lebanon was rendered dysfunctional, Hezbollah only strengthened from it. And Israel lost tremendous political capital. As I look at the past 40 years, it's hard to see- Can I spell capital in terms of- Well, I mean, it looked very, very bad around the world, especially for example, when it killed about 100 people, Kharkhna, and I believe it was 1996, during one of the- Every now and then, they ratcheted up the situation, and there were little mini wars in Lebanon to preserve the security zone. I just see no benefit deriving from that other than- And this attaches to Israeli politics, saving face for the Likud. Likud simply refused to support a full Poland in order to maintain a narrative that the occupation was necessary of Lebanon. Okay, I think we can- Thank you, Dan, do stay with us. I think we can take you back to Mount Haatzel now, where that ceremony is still underway, and you can hear this soldier is singing a famous song in honor of the soldiers. And you were just listening to a little snippet there of it, forgive my Hebrew, end the eret acheret. Is that right, Dan? Yes. Thanks. Well done. I tried my best. We're waiting for the prime minister, Naftali Bennett, who will be taking the podium shortly. There he is. Let's take a listen. Since we do not have another country, the role of all of us is to see that the earth does not burn, to extinguish the fire. The president, Herzog, and Mrs. Herzog, the deputy speaker of the Knesset, Ginzburg, the chief justice Solberg, the minister of defense, Benny Gantz, chairman of the WZO, the head of transportation division, Benatar, the deputy director and head of the division of the bereaved families in the Ministry of Defense, Mu'alem, the chairman of the organization, Yad Labanim, Eli Ben-Shem, the deputy mayor of Jerusalem, bereaved families, distinguished audience. Even after 40 years, since the First Lebanon War broke out, it's important that we remember that not out of joy did we go to this war, but out of a commitment, a deep commitment of the State of Israel to protect its citizens, out of which to bring an end to years of catechias that were launched at Kiryat Shmonai and the other settlements in the north, which has made the life of the inhabitants there into a nightmare. The war was a heavy price. Hundreds of our dear sons, the brothers, the sons, the spouses, the fathers, they are the ones we miss so much, even today, maybe especially today, 40 years on. They never went abroad for a trip, they never fell in love, they never got married, they never had children, life that was lost. The longer there were so the controversies grew in the Israeli society, these were not easy days to the society, to the state, because when the war advanced, not everybody in the society were convinced of its justification, but it's important to know that apart from a few refusals, most of the combatants in the army in the reserves did recruit themselves to war, even if there were controversies, even in such a great crisis it was obvious to everybody that we are fighting for the state and that the state is above all, and the wholeness of the state depends on compliance to its establishment, even if there's a large privacy, politically. Our best sons in the army, in reserves, came, mobilized, and some of them unfortunately fell in battle. They all went out with their face through those yellow lights of Lebanon and in their back the white lights of the settlements in the north. The fallen dead of the war is exactly the image of this mobilization. They fought shoulder to shoulder and fell together. People from the Kibbutz, from the Moshev, people who were born in Israel, or new immigrants, Jews and Druze, religious and secular, people who are rightists and those who are leftists, people who came from all over the world. And therefore in any challenge that we will still have to cope, internally or external, whether it's health or economic, the best perception has to be that the state together the completion of the people of the state at any cost. The battle on the before was one of the harshest that we ever knew, although their forces had the fire and opposition. They continued to storm and they purified the tunnels and through grenades, the Golan brigade where the leaders of this terrible fierce battle that has become a symbol both in the war and also in the long years of the stay of all of us in south of Lebanon. There wasn't a soldier that didn't see the before fortress when he entered and when he left Lebanon. Unfortunately, six out of those combatants did not come back from the battle, including the commander of the Golan brigade. Captain Tamir Masad was born in a Kibbutz third generation. He was here in one of the pictures. Tamir was a commander in the Golan brigade and he led his men to the before to the fierce battle, but he came out alive. Twenty years later, in October 2002, when he was an officer in reserve, Tamir had some position in the army when a suicide bomber came to the station and they had to fight with him and then the terrorists exploded and Tamir was killed on the spot with two other combatants. From Lebanon to Samaria, from the before to the city of Ariel, our mission has not changed. It hasn't changed because in the 74 years of the state still not all our neighbors agree to our existence. That's exactly the reason, even today, that we in Lebanon, in Samaria, in any place in the country, no matter close or far, we are acting covertly or overtly. There's no alternative to standing fiercely to protect ourselves. These days we are witnessing attempts to harm Israelis in other places in the world. The armed forces in Israel are doing everything in order to thwart such attacks and in order to neutralize a priori the proxies of the terrorists and themselves. We are not going to hesitate to do anything in the world in order to maintain and keep our citizens. My dear, bereaved families, when the First Lebanon War broke out, I was a child of 10 in the fourth grade. I remember that Saturday in my youth movement, I spoke to Noam Solberg just a while ago. He was a neighbor of mine on the eve of Sabat. I remember that all of a sudden, very strangely, a car came to pick me up. I know it wasn't so important, but the one who was in the car was my father and a friend of his who took my father, so we, the three brothers, were in the back. My father was near the driver, and I remember the anxiety, how afraid I was. I was so anxious for my father because I started imagining he may not come back. I remember my mother when we came home, and she tried to hide their concern. I remember how glad I was when my father came back alive from the war. But unfortunately, you, the families, you were not privileged. I remember that day, just a few days in the middle of the day in the school, where I was all of a sudden a knock on the door of the classroom, and one of the kids was called Elie Becher. He was sitting next to me. They took him out, and they told him that his brother, I think his older brother, Israel Becher, we all knew him, has fallen. You were not privileged to have your family members come back alive. They did not come back from the battle. Their anxiety that you had and the great concern have become, all of a sudden, to reality, a painful, awful reality with an emptiness. Even after 40 years, there are no words that can console you, and nothing can heal the pain. However, we continue. In any case, you have to know that we remember the fallen, and we evaluate their courage and their dedication. We are committed to continue to guard the security of the state of Israel, and the togetherness, togetherness of the people of Israel. May the memory of the fallen be blessed forever. And that was the second speaker at this memorial event over at Mount Halsal in Jerusalem. The Prime Minister, Naftali Bennett there, speaking to the families who lost soldiers in that war 40 years ago, the first Lebanese war. I'm joined in the studio by Dan Perry, former Middle East editor at Associated Press. Dan, we were just talking there, weren't we? We were listening to Naftali Bennett talk about his own experience of Lebanon, and indeed remembering as a child what it was like to have his father fighting as well. And we were talking about the difference between the first and the second Lebanese war. How would you characterize those differences? Well, both have weirdly differently mixed legacies. The first Lebanon war succeeded in ending the rockets for a while and kicking out the PLO. It had the unintended consequence of helping Hezbollah come to a rise, which became, I think, a far more dangerous enemy, creating generations of genuine enemies in Lebanon who remember being bombed by Israel, and Israel has no real desire to make an enemy of Lebanon. And of course, the 18-year quagmire being stuck in the buffer zone, which I characterized as pretty useless and highly ill-advised. The second Lebanon war was post-Israel's withdrawal from the buffer zone in 2000. It happened in 2006. Again, Hezbollah was proving to be pesky and a threat and so forth. And that war is extremely unpopular in Israel for reasons which I at least find slightly mystifying. However, it was mishandled in a variety of ways and also exposed some weaknesses in the IDF in terms of training and weaponry and other things. But the fact is... There was a high level of casualties on the other side. A lot of Lebanese civilians lost their lives in that war. Sadly, I don't think that's why it's so unpopular in Israel. I wish I could say it is. But the main thing in Israel is that it's perceived as a failure, whereas the reality is that for 16 years there's been silence on the border of Lebanon and no rockets fired across the border at all. And Nasrallah, the head of Hezbollah, has been largely in a bunker. So if the goal of that operation was to bring peace to the Galilee, as the first one was named, it manifestly has succeeded despite the image of having been a failure. I think largely it attaches to Edward Olmert, who was unpopular and of course was drummed out of office and ended up in jail. Right. And I wonder what people think victory in Lebanon would look like, indeed. Would people prefer Hezbollah to be wiped out altogether? Yeah, victory in Lebanon would be that Lebanon agrees to be a friendly country, as Israel would like to be towards Lebanon as well. And Lebanon ceases to be a territory that is essentially lawless and from which an armed gang supported by Iran is able to establish a arsenal of thousands of rockets aimed at Tel Aviv. Lebanon should cease to be a danger. That is what Israel would like to have happen in Lebanon. Yeah, and it's hard not to see the contrast between Israel and Lebanon. Here is Israel, you know, with a thriving economy, a high-tech sector making new friends in the region, of course, by the Abraham Accords, Lebanon currently in the grips of the worst economic crisis in history. It's a genuine tragedy. Lebanon is a dysfunctional state. It's a failed state. It has tremendous potential, obviously, but it has done the opposite of realizing that potential. It could be argued that if it acquiesced to Israel and stopped being an enemy of Israel, Israel and its delight would be so generous and would extend such a helping hand that it would benefit them. But I'm not so sure that the 60 to 70% of Lebanon that is Shiites and Sunnis and Druze would play along. Do you ever see that happening then? Can you see any situation where there might be peace between Israel and Lebanon and what might bring that about? How long do you have? I mean, peace maybe not in our time, but eventually, yes, because at the end of the day, Israel and Lebanon have no territorial dispute. Lebanon is, for an Arab country, relatively westernized. It has a very large sector of the population that is mercantile and practical-oriented and highly westernized and even French-speaking. It's conceivable. Yeah, and of course, we've seen the French President Emmanuel Macron visiting several times, trying to kind of see the situation there as well. We're going to head back to Jerusalem now. We are waiting to hear on the Defense Minister, Benny Gantz, who will also be addressing at the audience there. So let's take a listen. President Herzog, Prime Minister Bennett, distinguished audience, bereaved families. When the First Lebanon War broke out, I was in the United States in a special course. When I came back to Israel, I rejoined my unit and I went into the place that actually shaped my service in the IDF, namely Lebanon. That war that was designated to protect the inhabitants of the Galilee helped us to push the fire deep into Lebanon to hit the terror places and also took a heavy place which you have paid, the people of the bereaved families who are sitting here. So each of us, personally, together with the combatants and the comrades at war, also lost my best friend whose family is here with us today, Captain Goldberg, who went together with me to office's course. He also went to the war and he fell when he was leading his men to rescue other people. And that incident accompanies me to today. When I heard of his falling, I was deeply bereaved morning that was mixed with the continuation of the war. My heart refused to believe that we lost somebody with such a brilliant future. He finished school when he was 17. He was an admired commander. But you, people who are here with us today, you know very well that each and every one of the fallen dead had ambitions, a family, friends, and comrades in arms. And all of them we are embracing.  As one who was one of the first to enter Lebanon in the Littani operation and fought in the First World War and was the last one to lock the gate after a long, long stay, I know very well to what extent the lessons of this war are indebted in us. And I also can say that the state of Israel of today knows and has to define qualitatively its goals in wars and in operations if and when they happen. Forty years after that war, Israel is the strongest force in the region. And I look today at Lebanon and the capabilities of the IDF. I have no doubt in my mind that if we are required to act again, our action will resonate and will end with a definite victory. We can act anywhere in Lebanon in any range and any dimension in the air, at sea, cyber, and obviously on land as well. I know it because the capability, the faith and the moral and operational force are getting stronger. Recently, we completed a maneuver of chariots of fire where we checked our capabilities and we will continue to exercise all the scenario and at the same time to also extend to our bitterest enemy our hand for peace. And when peace arrives, it will arrive out of force. In the song that we just heard, Alon Avidar wrote about the war and the loss. A witness forever. You will always know what is the point of being on the ground. And there together, there is no terror, there is no fear, and the taste of tears also tells us about the future. Avner Gadassi, who just sung it, now he said, men are crying at night. Her sound is not heard, there's nothing to hide, as we just heard in a fantastic performance just now. Many of those who served in the Lebanon War or in other wars as well came back scarred. They lost friends, they were injured, they have traumas because of the images and the memories from the battlefield. In their past, this was a shame to talk about it or to share it and it's impossible that this will be the situation today. And from here, I call upon the men and the women, there is no shame in pain, there's no shame in difficulty. It's a great pride to fight for this country and it's a great importance for the country to support those who paid the price. Our moral duty is to support you, to recognize the pain and to help you cope. And therefore, just as we promote our force vis-à-vis our enemies, we are promoting, with the same determination, the reform of the soul for our soldiers. It's a long and complicated process. It's painful and necessary and people from the rehabilitation center are leading it together with the disabled of the IDF and we shall not rest until we finish it. Dear bereaved families, we are standing here, painting together with you and saluting your dear ones and all the other combatants and the heroes. Let us hope that all the members of the families who are here will have moments of happiness and good that we will not know pain and that we will know as a state and as individual to win over every challenge. May the memory of the fallen be blessed. The Defence Minister, Benny Gantz, they're wrapping up that ceremony for the fallen soldiers of the war with Lebanon 40 years ago. I'd like to thank Dan Perry for being with us, giving us a history.


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