So, what we will do is before we go to derivation of the momentum equation which is anyway quite involved is going to take some time, we have not taken up any questions since morning. So, we would like to start with questions some question answer sessions for now. So, we go to YC college, Nagpur. So, any little question about the Prandtl number criteria which is cited in the morning session, actually you cited when the Prandtl number is greater than 1, then there is a very less diffusion of the heat, but as we see in the chart the Prandtl number for the gases is very low, but the Prandtl number for oil is more than 1, first still we are preparing the oil cooled engine or the gas cooled engine, why this is so? The question asked is the Prandtl number of oil is much larger than that of Prandtl number of air. So, why is still oil is preferred over air in oil thermal boundary layer thickness is smaller compared to that of air? So, that itself is answering directly. Number one actually first of all why are we using oil is not from boundary layer thickness because its specific heat is very high. So, its heat carrying capacity is very high that is the reason why we use oil. So, it is not directly related to boundary layer thicknesses. So, it is related to specific heat, its heat carrying capacity if I take for a given mass flow rate MCP delta T is very high in case of oil compared to that of air compared to that of even water. So, CP of air is 1050 and CP of oils will be more than water which is water CP is around 4180, I am sure CP of oil is much more than 4180. Please go ahead. With reference to the previous discussion I will make one comment sir. Please correct me if I am wrong. If there is we have to we have to select certain fluid for the specific application then the criteria of the Prandtl number will not be sufficient. We have to take the specific heat and the other thermo physical properties will account. The question asked is if we have to choose the fluid for any specific application for maximizing the heat transfer actually it is little premature but still I will go ahead and answer this question. See actually if we see irrespective of the Prandtl number we are going to see let us say it is flow over a flat plate. So, Nusselt number is going to be a function of Reynolds number and Prandtl number. Now that we have defined Reynolds and Prandtl I think we can we can appreciate this Reynolds and Prandtl quite easily. But the function the functional form that is the Nusselt being dependent on Reynolds and Prandtl that functional form will be different in case of Prandtl numbers less than 1 and Prandtl numbers greater than 1. So, using those Prandtl numbers we will compute the Nusselt number in turn we will compute the heat transfer coefficient whichever is having the higher heat transfer coefficient is the one which we are going to choose. So, directly we cannot say based on CP I am going to use the oil or based on density I am going to go for air or water or oil it is not so. It is based on Reynolds Prandtl using which I will take the heat transfer compute the heat transfer coefficient and whichever fluid is fetching me higher heat transfer coefficient I am going to choose that fluid. So, but still I think we will understand this in great detail tomorrow when we compute the Nusselt number distributions for flat plate case and pipe flow case we will appreciate this problem in greater detail. For now this much should suffice PSG college Coimbatore. Yes, this is with respect to the problem on the fins some two days back. So, we occurred there for individual fins the Q and un-fins also and we added both in and multiplied by the number of fins which has been given as 200. But number of un-fins will be 201 that we have left. Yeah, actually the question as these for finned problem there is for finned portion and the un-finned portion we have multiplied by 200. Yeah, one of the participants one of the professors is saying that for fins it will be 200 and for un-fin it will be less than 199 it will be less than 200. Yes, professor you are right we have just neglected that because the area of the un-finned portion is very small, but yes you are right I have to un-finned portion I have to take 199 and fins I have to take 200 you are right professor. Thank you. Go for it. Sir, I have a question regarding the fetch. So, how it come possible to have a temperature gradient if y equal to 0 that means no slip condition in which T s equal to T s of the surface is equal to a temperature of the fluid that is at the rest condition and in contact with the surface. Your question is when I say no temperature jump condition the fluid in contact with the surface is at T s same as the surface temperature right then how is the possible for us to have dT by dy at the wall which is greater than 0 is that your question. Yeah, yeah of course. So, actually what we are saying is the heat is going to be transferred from this fluid to the next layer of fluid which is going to be at a lower temperature correct the surface fluid layer will be at T s, but the subsequent layer there is going to be a slight difference in temperature. So, that difference is what is manifested as dT by dy at the wall what we are saying is what you are saying is correct velocity is very easy to understand because one of the quantities is 0 other is a finite velocity ok next layer of fluid is at a finite velocity here also it is the same thing you have one fluid which is at one layer of fluid which is at T s next layer of fluid which is at a temperature if you are heating the fluid next layer of the fluid is at a lower temperature. So, there is going to be a gradient between the first layer and the second layer and that is what is going to cause the heat transfer which is given by minus k dT by dy at the wall we are doing it at the wall because it is we are doing it for that elemental for that element in contact with the wall that is all ok. Sir second question can we say at a lower Prandtl number conductive heat transfer through the liquid is greater than the convective heat transfer. The question is for lower Prandtl number can we say conductive heat transfer is greater than the convective heat transfer the answer is as follows irrespective of the Prandtl number the concept that the heat transfer within the boundary layer does not change what we are saying within the boundary layer the conductive heat transfer that is minus k del T by del y at y equal to 0 is always going to be equal to by what we got by Newton's law of cooling that is h into T s minus T infinity irrespective of the Prandtl number this concept is not going to change because h into T s minus T infinity has to be equated with the heat transfer by conduction within the boundary layer. So, this statement has no relevance with respect to only a particular Prandtl number or Reynolds number for any fluid for any Reynolds number for any Prandtl number conduction is equal to convection within the boundary layer. In fact, the definition of h does not involve anything like Prandtl number at all it is only the thermal conductivity of the fluid which is coming in by virtue of Fourier's law. Now, I understood your question why you are saying heat transfer coefficient is going to be higher for higher Prandtl number is it because of lower k no you we cannot look at k itself correct we have to look at the temperature gradient for lower Prandtl numbers my temperature gradient would manifest itself in one particular fashion for higher Prandtl numbers my temperature gradient would manifest itself in a different fashion. So, how del T by del y at y equal to 0 is going to pop up none of us can predict that we have to measure or compute it is not easy just by seeing k or C p or mu we cannot tell that. So, from the definition of the Prandtl number the molar diffusion at lower Prandtl number molar diffusion is lower as compared to heat transfer diffusion. Yeah. Molecular diffusion. Momentum. Momentum diffusion. That means the what will be the mode of heat transfer at the lower value of Prandtl number. See that is what I am trying to see see who is causing this heat transfer who is causing this heat transfer actually let us go back to fluid mechanics. The answer can be answered by the question asked is Prandtl number is defined as momentum diffusion to. Heat diffusion. Heat diffusion. So, for lower Prandtl number the expected thing is heat diffusion is less it cannot be answered just directly like that. See who is responsible for the heat diffusion again the velocity gradients again the molecular momentum diffusion and also remember in the morning I said the momentum diffusion is can be characterized by velocity gradients and also the turbulent stresses turbulent stresses. So, how the turbulent stresses are going to be there are again dependent on the Reynolds number. So, that is what we are saying we cannot directly tell for lower Prandtl number lower heat transfer for higher Prandtl number higher heat transfer no it is decided by my stresses that is the turbulent shear stresses and the laminar shear stresses. But how whom whom on they are dependent on they are dependent on the Reynolds number. So, it is all it is all mixed group effect it is not individuals effect just by directly Prandtl number we cannot say yeah V I T Pune. Average convection heat transfer coefficient and local convection heat transfer coefficient is this concepts are applicable for flat plate solar collector also. Ok the question asked is the concept of average heat transfer and concept of local heat transfer coefficient is it applicable for solar collector plate also. I would go ahead and make a very generalized statement it is applicable everywhere. The heat transfer coefficient are not going to be same for any application whether it is flat plate or solar collector plate or flow around a cylinder or flow in an air flow around an aerofoil or a gas turbine blade cooling passage or a circular pipe. Why do I make that statement heat transfer coefficient is dependent on temperature gradient who is deciding this temperature gradient my velocity profile my velocity turbulent stresses and these stresses and these gradients are going to be different in different location. So, naturally my temperature gradients are going to be different at different location. So, naturally I should be having the heat transfer coefficient different at different location. So, given any application heat transfer coefficient will not be uniform, but in most of the papers you might have seen that heat transfer coefficient is constant even in flat plate case. Why because he might have taken the flat plate very thick plate if you take a thick plate and put one thermocouple there actually who is averaging we are not averaging the thick plate is averaging and the thermocouple is measuring that average temperature using that average temperature I am getting the average heat transfer coefficient essentially averaging is not done by computer or calculation, but it is done by the copper plate. But on the other hand instead of copper plate if I take a thin metal foil let us say stainless steel metal foil which is as thin as 0.05 mm then I can if I lay thermocouples all over the place I will get the local heat transfer coefficient. So, the point is local remains local no matter what is the application that is the answer for this question. What about plate area temperature is ok what about area of plate see the question is temperature is ok what about the area of the plate the question is if the temperature is varying everywhere where is the question of area coming into picture. Small area or large area there will be variation there is variation. So, if you take small area over which you have put the thermocouple I said that is what I said if you put a thermocouple putting multiple thermocouples does not mean anything the plates thermal conductivity means a lot if I why did I take the example of stainless steel foil because two things there stainless steel is made of lower thermal conductivity than that of copper and stainless steel I said thin metal foil that means it ensures that averaging is not being done. So, it is not about area professor it is about averaging it is about again temperature gradient. I hope you are convinced. Sir there is one more question ok while we studied different motions of the particle we have seen that particles get stretched. Yes. Is it the particle or small mass of the fluid gets stretched and second question is how and why particles will be stretched. The question asked is how the fluid particle is having a certain fluid mass or not that is part number one and part number two how is the fluid particle getting stretched. See first question yes when I say fluid particle we have not stated one thing I want to state this very clearly whatever we are studying in this fluid mechanics we are studying actually continuum mechanics that is the we say that whatever effect is there if I take whatever cubes we are drawing all over the place today for conservation of mass or momentum that cube is a small cube we can imagine that as 1 mm by 1 mm by 1 mm. So, if I imagine a 1 mm by 1 mm by 1 mm cube definitely it is containing fluid mass may be of approximately I think my number might be wrong that is it is of the order of 25 into 10 to the power of 6 number of molecules would be there. When I say a pressure within that infinitesimal controlled volume I am actually saying that I am actually saying that it is the net effect of the various molecules which are colliding with each other and that is the net pressure. This is what we have studied even in thermodynamics. So, the answer for your first question is that the small infinitesimal fluid particle fluid particle is a small infinitesimal volume and it is consisting of a mass of a fluid as much as it can get filled based on its density based on its density within that fluid volume number 1, number 2 who is stretching it who is stretching it how does it flow how does it flow it cannot flow on its own it has to be there has to be some pumping power even if there is a head that head has to be generated either by potential head or by a pump. So, when I am pumping when I am pumping the fluid particles that pumping power is pushing because of that pushing nature there is stretching or angular deformation or translation or rotation this is what is happening. So, who is stretching my pump is stretching while it is flowing is that ok professor. Hello sir my question is related to somewhat general query in the conduction that is I want to have the explanation regarding two terms that is equivalent thermal conductivity and the variable thermal conductivity equivalent thermal conductivity. Ok the question asked is I want to have a definition of equivalent thermal conductivity and variable thermal conductivity no problem confusing question what we mean by first I will take variable thermal conductivity what I mean by variable thermal conductivity is there are n number of questions asking thermal conductivity varies with the temperature or we took k equal to k naught plus a t where a can be positive or negative that is variable thermal conductivity that is the thermal conductivity varying with the temperature. Now, let us come to equivalent thermal conductivity equivalent thermal conductivity concept is usually introduced like this in fact we answered for all eyes for example we have material a material b we mixed it and we came up with the plausible explanation I do not say right explanation plausible explanation as k equal to k a k b upon k a plus k b this can be told this can be considered as equivalent thermal conductivity is that ok. Sir there is one experiment in the heat pipe that we have to find the equivalent thermal conductivity of the heat pipe ok this is an average experiment see the question I ok now I understand in heat pipe you have something called equivalent thermal conductivity so without details I will not be able to answer this question I would implore upon you to put up the details of your experimental setup and this equivalent thermal conductivity definitely we will come back to you ok then yeah. Sir there are two ingredients for the acceleration unlike a material flow one is one that one that varies one that varies with the time and other varies with the space that means the relative position of the particle with reference to some data. So, traditionally we define acceleration as something that varies with when the velocity varies with time so I just cannot comprehend how we can call that second component as acceleration is that physically possible to call that second as acceleration ok. So, the question asked is it is very difficult to physically feel this is regarding substantial derivative or the total derivative in which we have acceleration or the change in the velocity with respect to time and also change in the velocity with respect to space. See in traditionally in plus 2 at least I was introduced to acceleration in plus 2 where in which I was told that v equal to u plus a t that is a equal to v minus u by t that is what I learnt. So, for me also acceleration always was getting accelerated that is getting picked up my car is getting accelerated when I put on my accelerator I think even the world accelerator comes from that. So, but however what we mean by acceleration is increase of velocity with respect to time or with respect to space it does not tell. So, that is what we mean. So, acceleration means it is increase of velocity professor took up the example of nozzle even in steady flow there is increase of velocity, but not with respect to time because it is steady flow, but with respect to space. So, all that I think we need to comprehend or we need to appreciate here is that acceleration mean increase of velocity with reference to what we have not told, but in plus 2 we have been taught usually acceleration as velocity increase of velocity with respect to time, but all that I would say is that acceleration can be with velocity increase with respect to space or time. Just let us go back to the whiteboard where we had drawn the nozzle see if you try to draw the stream line let us take there are 5 particles and you are tracking the 5 particles the stream line represents the relative position of each of them. You will see the stream lines are far apart here, but when they come to the exit of the nozzle they come very close to each other.  So, that is causing an acceleration in a fluid particle n i t 3 chi over to n i t 3 chi. With reference to the transient heat conduction you said the long infinite cylinder could be considered as a short cylinder and flat channel I do not understand what this the short means how do you consider that as a short cylinder and a flat. No the question asked is a long cylinder and a long cylinder can be considered as a short cylinder and a flat plate that is the question that is the question asked, but the answer is actually the question seems incorrect because a short cylinder can be considered as a combination of a long cylinder and a plane wall it is not the other way. A short cylinder is formed by the intersection of a long cylinder and a plane wall which is cutting through the cylinder. So, what we are saying is the two second dimensional effect of this shortness in height comes in when we take into account this whatever you say product solution of this long cylinder and the plane wall which is in the y direction. So, it is not that a long cylinder is not composed of a short cylinder and plane wall that is not correct the correct thing correct question should be short cylinder how is it a combination of long cylinder and plane wall. Any other questions from here? Sir, in journal purpose they are referring in the internal flow when we are inserting some turbulators we are disturbing the we want to disturb the thermal boundary layer why we want to disturb the thermal boundary layer when we are disturbing the thermal boundary layer there is increase in the heat transfer, but when we are inserting that any turbulator there is decrease in increase in pressure drop. The question asked by one of the professors is that when we put the turbulators in the pipe actually we are breaking the thermal boundary layer because of which there is increase in the heat transfer coefficient and this also results in increase in pressure drop it is little premature actually I am going to deal with this in convective heat transfer in great detail. However, let me go ahead and answer because I have introduced already laminar sub layer what we are doing when we put the rib turbulators or any turbulators or any enhancers is that in the morning lecture I had introduced laminar sub layer, buffer layer and turbulent boundary layer. What we are saying is that when we put this rib enhancers or rib turbulator we are going to break this laminar sub layer such that my boundary layer becomes completely turbulent and we all know that turbulent shear stresses are orders of magnitudes higher than the shear stresses because of laminar that is because of the velocity gradient. So, my heat transfer coefficients will go up significantly so that is the reason why we put the rib turbulator so, but at the same time pressure drop is increasing because my shear stress is also increasing that is because of minus rho u prime v prime shear stress is increasing means resistance for the flow is increasing that means pumping power required should be high. So, that is the answer for your question but to get more insight into this as we go along actually we will be dealing this in greater detail in internal flows this much would suffice for now for this question. Jabalpur college any questions please. Yes sir I want to know only three layers in turbulent section not more than three why. So, the question asked is in turbulent boundary layer we have classified three layer structure that is laminar sub layer, buffer layer and turbulent boundary layer why only three why not four why not two why not one ok that is a valid question. In fact, historically if we see historically actually there are only two layers that is one was laminar sub layer and the other one was turbulent boundary layer, but when they did the Karoo fitting with the shear stresses whatever they measured and then they plotted there was continuous there was sudden discontinuity when they ended up in the buffer layer that is in the buffer layer both the laminar shear stresses and the turbulent shear stresses are of equal magnitude. To make the Karoo smooth they introduce this concept of buffer layer. In fact, if I remember correctly this was introduced by professor von Cormann it is called as von Cormann's mixing layer concept buffer layer concept. So, it was professor von Cormann who introduced this intermediate layer that is the buffer layer. So, that answers you why only three layers with these three layers we are able to model the complete boundary layer that is the reason we are sticking to three boundary layer why not more than three because we do not need more than three to model this that is why we are stopping at three, but people make simplifying assumptions and go ahead on three also, but we know that if we take three we can smoothen out our shear stress distribution when we move along the y. Okay, VJTI Mumbai any questions? Yesterday I was asked the question regarding the boundary layer. Within the boundary layer the fluid flow is there as per our today's discussion. I have answered your question. I think it takes less. But repeat your slide. Conduction heat transfer within the boundary layer. The question asked is yesterday also one of the professors had asked the question within the boundary layer whether my fluid is still. So, we had said that we had answered today during the class session know the there is flow in the boundary layer, but now the question posed is a very valid question asked by the professor if the fluid is flowing how can you apply conduction equation Fourier's law of conduction, but what are we doing? We are not applying for the complete boundary layer. We are applying just on the layer above the flat plate and at that flat plate there is no slip condition, no temperature just the first layer of fluid. The first layer which has zero velocity. Yes, that is minus k del T by del y at y equal to zero y equal to zero there is no slip condition it is stationary. So, there is no what to say paradox in this it is straight forward it is straight forward. I hope now you would have understood what we mean by conduction heat transfer. So, conduction happens in the first layer of fluid and that heat from that first layer has to go out by convection. So, if you think of this flat plate or the thin layer of fluid E in is by conduction E out is by convection. That is right. So, much about questions we will move on to Navier-Stokes equations now. So, far we have studied what is called as continuity equation. So, I am just going to look at the same equation in little different way let us see what can we or in which way we can look at it that is what professor taught us is that so we have the equation d rho by d T plus rho of del u by del x plus del v by del y plus del w by del z all that I am saying is I am just going to connect this equation with my stretching that is all that is with the fluid dynamics basics what we studied that is what am I trying to say here is that yeah. So, what we are saying is that see we said that volumetric dilation rate that is del u by del x plus del v by del y plus del w by del z is equal to 0 that means net change in the volume is 0. So, when can this occur physically when the density is constant when the density is varying the change there will be change in the volume so that is what it has been restated here in this equation. If the density is constant if the density is constant my del dot v would be equal to 0 this is what we will be using for continuity equation. Moreover we should keep telling our student we always write one dimensional conduction equation rho 1 a 1 v 1 equal to rho 2 a 2 v 2 in fact this is also coming from this equation the only thing is that this is one dimensional conduction equation sorry continuity equation. So, another thing is that I just want to give another way of looking at this total derivative I have one standard example which I always quote I just want to touch that and then go if I write a total derivative of temperature that is d t by d t that is I will have to write that as del t by del t plus u del t by del x because total derivative does not only tell about acceleration I just want to say that this total derivative concept can be used even for temperature that is the reason why I am writing this although this is little early, but it is ok because this is the point where we have to understand the total derivative concept of the substantial derivative concept plus v del t by del y plus w del t by del z. What does this mean del t by del t means temperature variation of temperature with time and this variation of temperature with space by virtue of moving by virtue of moving because of velocity u v and w. Professor Anderson in his fluid aerodynamics textbook he states this example this is what he gives I am just copying his example and telling you restating it same, but I like this example that is why I am restating it see let us say I am entering a room I am entering a room let us say this is the room where in which it is fully ac I am entering from outside to inside when I am entering means what I am having a velocity that is let us say u let us not worry about v and let us not worry about v and w only u is there. So, if I am moving with velocity u, but I am going to undergo a temperature gradient why because I am entering from a hot air environment to cooler environment that is this u del t by del x that is why we call this as convective term convective term, but what is this while entering let us say all of a sudden I have entered, but all of a sudden someone has hit me with an ice cube or a hot ball. So, I am undergoing going to undergo temperature change with because of hitting instantaneously I just before I realized someone has hit me with the ice ball. So, that is del t del t. So, it is not always the total derivative is about acceleration total derivative can be temperature or total derivative can be with the density also. So, it is a it is a concept all that it says that any parameter is going to change not only with time, but also with space that is all it is telling. In case of fluid flow this is very important because with see the derivative concept itself you have u v w if there is no flow then I have I am coming back to only transient that is del by del t. So, with this I think I will move on to what is called as navier stokes equation that is the conservation of momentum. So, this is again same thing I will reuse the same thing that is m dot in what did we use conservation of energy e dot in minus e dot out plus e dot g is equal to e dot st. Instead of that here what we are saying is force is equal to mass into acceleration that is there is a net rate of increase of momentum and there is some momentum entering and there is some momentum getting out. So, the conservation of momentum what does it say force equal to mass into acceleration that is what we apply it to system, but if I have to apply it to control volume I have to apply Reynolds transport theorem. So, this is the change in control volume and this is the change in the control surface that is rate of increase of x momentum I am writing it only for momentum in the x direction x momentum and rate at which momentum is entering in the x direction and the rate at which the x momentum is leaving in the x direction this has to be balanced by whom rate of change of momentum has to be balanced by whom it has to be balanced by the forces applied which forces the forces applied in the x direction that is the sum of the x component forces applied in the control volume, but now the question is what are the types of the forces which are applied. So, there are two types of forces one is surface forces another one is body forces who is creating these surface forces these surface forces are created by normal stresses shear stresses and pressure. So, what is shear stress just now in the morning we have found that shear stress is the one which is caused because of angular deformation angular deformation there is delta alpha and delta beta that is the angular deformation. Now what is normal stress normal stress is because of stretching it is because of stretching or compressing. So, that is normal stress that is because it is acting normal to the surface when can it act normal to the surface when it is either stretching or compressing. So, that is normal stress and pressure we all understand, but always there is a confusion there is a normal stress and there is a pressure also what is this pressure business that is the question always we use we always myself and professor Arun after the class we always come back with two three students who ask us this question the answer is or the way we understand this is like this what is pressure what is pressure when does when to understand pressure I always ask the question back to the student when is pressure zero when do you say pressure is zero when it is perfect vacuum when it is perfect vacuum pressure is zero. What is perfect vacuum how do you define perfect vacuum or how do you realize perfect vacuum when there is no molecule when there is no molecule then only we call that as perfect vacuum that means when there is no molecule then there is no question of collision taking place when there are plenty of molecules they hit each other then there is a collision because of this intermolecular collision there is pressure. So, that is pressure, but then what is normal stress normal stress is because of stretching or compressing either del u by del x del v by del y or del w by del z. So, that is because of the velocity gradients remember pressure is because of the intermolecular collisions. So, this is a very important concept very important concept which we need to differentiate between normal stresses and pressure. So, I think this is this is very important I hope you have understood. So, professor Arun wants to pitch in and clarify little bit more. See in fluid mechanics pressure concept was introduced in statics itself. So, non-moving fluid also can have pressure, but hydro static pressure that is why the word static is there hydro static non-moving pressure. So, we have to keep that in mind irrespective of whether the fluid is stationary or in motion there is a pressure associated with it only when there is a velocity component associated which causes this kind of a normal which causes a stretching or elongation in a particular direction there is a normal stress both of these are force per unit area only both of these act normal perpendicular to the surface, but the cause is different all stresses will go to 0 in a stationary fluid except pressure force. So, keep this in mind and I think all students will have these doubts. Yes, you will be you will be asked by your student these doubts these are normal questions. So, next is this is as already professor has told this is force per unit area these surface forces are force per unit area. Now body forces are the forces per unit volume what are the body forces gravity force centrifugal force and Coriolis force these are called body force because they are acting all over the volume that is. So, gravity force I think all of us can understand easily and centrifugal force also we can understand whenever there is rotation or whenever there is we are going across a band there is going to be centrifugal forces even when there is a flow in a band 90 degree band it is going to experience centrifugal force. Then what is this Coriolis force the Coriolis force is that force let us say we have a pipe and in a pipe there is a flow taking place at the same time this flow is rotating that is orthogonally rotating that is this pipe is there this my hand which is there towards you is from inward to outward there is a flow from inward to outward there is a flow that is from myself to yourself there is a flow and this is my pipe and this pipe is rotating orthogonally it is rotating like this continuously it is rotating. So, in that case the fluid particle which is moving which is having linear velocity and also rotational velocity is going to experience an additional force called Coriolis force. So, this is the thumb rule what we use right hand thumb rule that is this is the rotational direction this is the fluid direction this is the Coriolis acceleration. So, the Coriolis force would be opposite to that. So, that is what is Coriolis force and this is acting all over the place that is complete volume. So, that is why we are we are using this as a body force this is the Coriolis force. So, you have gravity force Coriolis force centrifugal forces you can have electromagnetic force also that is also a body force one of the participants was asking on the other day how does thermal conductivity vary with a body force which is electromagnetic force electromagnetic force is also a body force with each body force my nature of my conservation of momentum equations or the Navier-Stokes equations are going to change each body force taking it affect effect will be one phd. So, that is how we can look at the body force what we study in the class is we do not consider these Coriolis forces and centrifugal forces we just put it as body force, but we neglect them that is how we handle for getting the closed form solutions in the class, but if you have to account any of these body forces that we that will be involved exercise even if it is laminar flow.  So, what is the momentum in the x direction on this surface delta z delta y what is that mass into velocity that is the momentum which is entry what is the mass what is mass mass flow rate rho a v so rho is rho area velocity is velocity in the x direction we have stated that u and area is delta y delta z delta y delta z. So, this is the mass flow rate and momentum to get the momentum I should be taking mass flow rate into velocity that is u. So, this gives the momentum which is entering into the control volume in the x direction this is what I we had stated in the when we made the statement that is the rate at which the momentum enters, but here we are worried about x direction this is the x momentum direction. Now, what is the momentum getting out the momentum getting out is the momentum getting out is again Taylor series expansion. So, the same thing f of x I will get f of x plus del f x by del x.  Here please read this as delta z I am not able to complete that delta z. Similarly, this is straight forward there is no problem in this, but in the y direction there is little confusion always. So, we have to be little careful. So, you might be wondering we are talking about x momentum, but I am writing in y direction, but what we are saying is there is mass flow rate let me put what is the mass flow rate in the y direction is rho v into area that is delta x into delta z. This mass flow rate can have momentum in the x direction by virtue of x velocity that is u this is the x momentum carried by the mass flow rate in the y direction because of the velocity in the x direction. So, now it is straight forward having understood this it is like a jet being deflected because of velocity in the x direction. So, I will have the getting out mass flow momentum in the y direction is rho v delta x delta z into u plus del by del y of rho u v delta y delta x delta z. I think two long equations you are all getting tired it is fine. So, we will continue with this derivation as we at 2 o clock again. So, professor Arun wants to pitch in and tell something.  This fluid mass coming in the y direction having a momentum in the x direction is analogous to you wanting to cross a road and there are bunch of people walking along the road. So, when you are trying to cross the road you are not going to get a free path to cross you will be pushed along with the people and then only you will be able to cross. So, that is the carrying you are carried physically by the people who are pushing you and in the process you end up crossing the road. So, you are displaced from that particular x coordinate because of this motion of the people. So, I think we will end this session. Thank you.


One of the last remaining independent hospitals in the garden state is set to merge with one of the largest healthcare systems in New Jersey. For 130 years, Anglewood Health, the Anglewood Hospital has served Bergen County as an independent facility. Now, however, it will merge with Hackensack Meridian Health. The merger agreement includes a $400 million commitment by Hackensack Meridian to invest in new operating rooms at the hospital, expanded cardiac facilities and outpatient sites for physicians. Hackensack Meridian has also agreed to take on Anglewood's outstanding debt of 182 million dollars. Anglewood Health's CEO says the deal is all about serving the community. We're going to push access to care out into the communities that we serve. Our friends, our neighbors, our families are going to receive the highest level of care close to home. The hospital's merger with Meridian Health was unanimously approved by Anglewood's Board of Trustees. The agreement must now be reviewed by the State Attorney General's Office as well as the Federal Trade Commission. The process is expected to take about a year.


Good afternoon everybody. Welcome to the next brief. Rear Admiral Brian Luther is the Director of the Department of the Navy's Fiscal Management Branch.  Good afternoon. As you mentioned, I'm Rear Admiral Brian Luther, and I'd like to thank you for the opportunity to brief the Department of Navy's Fiscal Year 2018 President's Budget submission, in which I'll address our portion of the second step of the Department of Defense's multi-year effort to restore readiness. The brief will be broken into four parts. The first will briefly review the current and evolving strategic guidance. The second provides the operational context in which the naval forces operate in today's world. And the third I'll review historical challenges that underlie the requirement for the current readiness reset. And finally, I will provide a summary by appropriation group. The national level guidance that provided us the mission sets which drove the operations of the last decade are under review. Earlier this month, the Department of Defense began a defense strategic review. This brief will not provide fit up or out your procurement quantities due to the ongoing review and a possible change to mission sets in four sizing constructs. The cooperative strategy for 21st century sea power informs naval force employment across the listed naval missions to balance readiness against current fiscal challenges in a global security environment that is volatile, unstable, and increasingly competitive. Senior leaders from the Secretary of Defense, service secretaries, and chiefs to service resource sponsors and program managers have briefed and testified to the growing challenges and sense of urgency to respond to the advanced capabilities and increasing pace of development demonstrated by potential adversaries. Despite fiscal challenges, the global employment of naval forces remains extensive. Over 100,000 sailors and Marines are forward based or deployed around the world. They've operated across the Baltic, black, Mediterranean, red, and Arabian seas, the Atlantic, Indian, and Pacific Oceans, and on the ground in 37 countries. A few examples are participation and inherent resolve to include the Dwight D. Eisenhower and George A. W. Bush strike groups, as well as electronic warfare support for Marine Corps squadrons based in Inserley. The USS Ross and Barry are responding to Syria's use of chemical weapons. Make an island in Baton amphibious ready groups with the 11th and 24th Marine Expeditionary Units, or MUSE, deploying a shore to provide support in northern Syria. Marines from the 2nd Marine Expeditionary Force, or MEF, assisting Afghan partners in Helmand province. The USS Zephyrin-Schmal, which would embark Coast Guard law enforcement detachments, seizing over 5,000 kilograms of contrabanded Operation Martillo. The U.S. NS spearhead conducting civil military operations in Guatemala, Honduras, and Colombia. A hundred Marines from the Special Purpose Marine Air Ground Task Force, or MAGTAF, Southern Command, U.S. SC, Regina, Mesa, and Verda, and elements of the 24th new, again, provided humanitarian assistance and disaster relief to the people of Haiti after Hurricane Matthew. Sailors and Marines participated in Baltops, a high-end joint exercise in the Baltic Sea region, and later Marines tested their war-fighting skills in a cold-weather environment during the Norwegian-hosted exercise Cold Response. On the other side of the world, the largest international maritime exercise, the Rim of the Pacific, RimPak, brought together 26 maritime nations, including China, along with 40 ships and submarines, over 200 aircraft, and 25,000 personnel. A U.S.-led naval training maneuver near the Gulf of Guinea was transformed into a counter-piracy mission, where navies from five African countries tracked the hijacked tanker through their waters and successfully freed the vessel and rescued the hostages. In support of Combined Joint Task Force Horn of Africa, U.S. Naval Forces Command operates Camp Lemonnier, the United States' sole forward operating base on that continent. Earlier this year, the Marine Corps relocated their first operational squadron of F-35Bs to Iwakuni and increased the capability of its rotational aviation combat element in Darwin, Australia, with four MV-22 Ospreys. Overall, the Navy Marine Corps today remains deeply engaged, operating at a high tempo in harm's way, providing options for national leadership, assuring allies and deterring adversaries. There is no expectation that demands will slow down based on the last 15 years as shown on this slide. It shows that deployment lengths have been increasing as the fleet has been decreasing 40%. The chart shows fleet size and gray starting in 1993. Annual deployments in blue and deployment lengths are shown by the green line. It shows over time the Department of the Navy has deployed a growing percentage of the fleet by increasing the average length of deployments. The optic is clear. A smaller force, more heavily used, will burn out faster. The recent oversubscription of naval forces that has accelerated the aging of our ships and aircraft, increased maintenance requirements, and compressed training and maintenance schedules is shown in more detail here. This shows the last four years of sea-based deployments. The red line depicts the maximum number of deployable ships the Department of the Navy can provide using its sustainable force generation model, known as the Optimized Fleet Response Plan. Services, as force providers, must balance the needs of generating both the current and future force requirements with available funding. The blue area represents the actual number of deployed ships by month. The box in the upper right is the oversubscription for that year. It is worth noting that the average use of the last four years is 5% more than the funding provided could generate. The oversubscription of deployed forces, combined with BCA reductions, exacerbates the impact of shore establishments, non-deploying forces, and readiness-enabling accounts. An illustrative example of a readiness-enabling account is aviation spares. This slide represents funding and associated full-mission capable rates for the last 17 years. There are multiple takeaways from this slide. First, high sustained operating tempos require sustained levels of higher funding. Second, readiness trends lag fundings both ways. Third, it's difficult to maintain FMC on multi-emission aircraft. It's harder when the force is heavily used and harder still when the force is aging. In modernization, all too often a bill payer is key to maintaining capabilities. The funding profiles on this slide are familiar. The black line is the 2012 budget. The last time, strategy and budget were aligned. The red is the funding by BCA, and the maroon is the enacted budgets, every one of which was delayed by a continuing resolution. It is worth noting that the final enacted budgets for the first two years of BCA were below BCA. And that the FY17 budget, when submitted last year, was 3.9% below the President's budget of 2016. This forced the department to make hard choices to balance, during which only three areas were exempted. Deployed and next to deployed forces. Personnel and shipbuilding. Shipbuilding being the least reversible of our mitigations. The takeaway, however, is not the dollars, although important. The takeaways are what the profiles represent. A strategy funding mismatch. Budget instability, combined with consistent and lengthy CRs. And most importantly, the squandering of a precious resource of time. Time that should be spent maintaining our tactical advantages. Every year we operate under the mismatch. In a CR, we pay a price in time. Decrease productivity and reduce purchasing power. Beyond showing a reduction in funding, the area between the Black and Maroon lines by year represents the decline in training of non-deployed sailors and Marines, a decline in material conditions of ships, of aircraft, of ground equipment and shore facilities. And the total area between the lines represents the urgency with which we should address this shortfall. Reversing this trend and rebuilding the readiness of the current force was the guidance from Secretary of Defense Mattis. His budget direction was clear. Improve war-fighting readiness, which was addressed and enacted in the FY17 bill. Restore program balance by continuing to rebuild readiness and filling holes in this summit. And finally, after the defense strategic review is complete and during the next President's budget submission, build capacity and improve lethality. Additional guidance from the Secretary was to gain full value from every taxpayer dollar spent on defense thereby earning the trust of Congress and the American people. Accordingly, this budget supports auditability goals set by Congress and the Department of Defense, which is to undergo an audit in FY18. The Marine Corps will be under full financial audit this year. The 2018 President's base increased $12.3 billion from $159 to $171.5 billion in this summit. Operations and maintenance increased to $54.6. Military personnel increased $2 billion to $47.6 billion. Procurement accounts increased $800 million to $49.5 billion. Research and development $500 million to $17.6 billion. And infrastructure increased $370 million to $2.2 billion total. The next section of slides will provide a detailed overview of how the Department addressed, by appropriation, requirements to enhance readiness to include modest personnel increases, how the ship's aircraft and ground vehicles will be sustained, the proper training of our personnel in preparation for their deployments, and how we maintained our ship procurement profiles, made difficult tradeoffs and aviations, enhanced weapons procurement, and made investments in key technologies to better posture us. It is important to note, however, the effects of multiple years of insufficient resources cannot be corrected by the increases of one budget year. The Department will require stable, predictable funding over multiple years to achieve sustained positive results. The ship depot maintenance fund to 100% using base and OCO funds it funds 10 additional ship availabilities for a total of 71. It complies with the current 246 law by the end of FY17 will have six cruisers inducted in modernization. This submit will also fund an additional subset for an additional induction. It funds LSD midlife modernization. It increases planning engineering and maintenance support manpower to align the workforce to the projected workload. And it modernizes major shipyard equipment and IT infrastructure at a rate above benchmarks to improve workforce performance. We continue to leverage the skill sets and capacity of private industry to augment our efforts. And for the future we work to continue a backlog of deferred maintenance which currently stands at $3.5 billion. The ship operations growth from FY17 to 18 is comprised of increases from 13 new warships in the inventory as well as an increase of two ships in our MSC fleet. The increased ship count combined with increased fuel prices leads to a minor growth in this program. And using base and OCO ship operations funds as with the 17 requests, 58 days underway per quarter when deployed and 24 days underway when not deployed. In this submit aircraft depot maintenance is funded to capacity which is 89% of the requirement. This is an increase from last year where we funded the air depot maintenance to 85%. Capacity is limited to different reasons at our fleet readiness centers. Capacity is limited by the hiring of civilian personnel, others by physical space and aging tools and materials. In all cases we are investing to correct these limitations. The flying hour program funds flight operations for Navy Marine Corps squadrons, fleet squadrons, and air training. The flight hour program is funded to the maximum executable level. The growth is driven by increased cost per hour, primarily for repair parts to return non-mission capable aircraft to service. Aircraft are primarily legacy hornets with some MV-22s and CH-53s, ECHOs included. In the past, many of our aviation enabling accounts were under resource to fund flying hours. This out of balance funding contributed to ready basic aircraft gaps and decreased mission capability rates. Executing the training and deployable flight hours requires more than just the flying and depot maintenance funding. It requires sufficient funding for enabling accounts such as aviation logistics, aviation support, and funded in APN aviation spares. The aviation logistics support was increased 6% to a high of 87% of the requirement. These logistic contracts for the F-35, KC-130J and B-22 and E-6B are funded at an all-time high and we anticipate future growth as more F-35 center of the fleet. Aviation support, primarily program-related engineering and logistics, is funded higher in 17, but not to 100%. This account also funds critical chain initiatives to improve depot throughput and increased hiring of planning engineering and maintenance support manpower to align the workforce to the projected work floor. And aviation spares is funded to the highest level in the last 14 years at 91%. The way ahead for the Marine Corps will maintain the equipment they have and prioritize investments in key programs that are aligned to the marine operating concept. The Marine Corps Force 2025 will provide a rapidly deployable scalable force able to succeed across the full spectrum of conflict. In that regard, a 92% reset, the Marine Corps is nearing completion of ground equipment reset from the Sencom Air of Responsibility. Funding remains at 79%, which is executable levels at the depot and is consistent with previous funding levels. Funding for operating forces is indicative of our investment in the marine operating concept. It includes increased investments in net-centric information technology services, funding the fielding and operations maintenance for six additional ground air task oriented radars or Gator, the Marine Corps next generation ground radar, battle space awareness that funds spares for small unmanned aerial systems to include Raven, Puma, and Wasp. The network on the move, which the same systems bought in the last two fiscal years and supports 35 systems being procured in FY18 as we bring this critical capability to our deployed forces. The Navy and Marine Corps installations provide physical environments essential for the individual, unit, and total force training, material sustainment, unit recovery, and equipment reconstitution. This submits funds facility sustainment at 78% for the Navy and 74% for the Marine Corps. While these levels are roughly 7% higher than 17%, they are down from the 85% for Navy and 84% for the Marine Corps funded in FY16. The provided sustainment funding will be prioritized to preserve critical facility components and to perform facility maintenance that affects the health and safety of sailors, Marines, and their families. However, we continue to carry risk and facility sustainment and we will need to closely monitor and manage the material conditions of our facilities. In depot investment, this submit exceeds the 6% legislative requirement. 10% is provided across the shipyards and 8.7% for fleet readiness center and Marine depots. As always, our ability to successfully complete our mission rests on the Navy and Marine Corps team. Sailors and Marine, active duty and reserves, our civilian teammates and all our families. Key to recruiting and retaining the force for the Navy is continued support for the Sailor 2025 program, which is comprised of three main efforts, a modern personnel system, the ready relevant learning system to support modern teaching initiatives focused on providing the right training at the right time in a sailor's career and increased sailor readiness. This submit funds a pay raise of 2.1% in line with the enacted pay raise in 2017. Both services align end strength and force structure. For the active Navy force, the net increase is an additional 4,000 billets to fund a final end strength of 327,900. This increase is due in part to cruiser modification, LCS blue and gold crew concept, the joint strike fighter initial operational capability requirements, support to increase Marine Corps end strength, for example, corpsmen and chaplains, expeditionary staging base four and total ownership costs to include the individual accounts in the TPPH account. Civil reductions occurred in the major headquarter activity billets and recruiters following the consolidation of the regional headquarters recruiting districts. Lastly for the active component, this request increases funding for the Navy permanent change of station or PCS moves to begin recouping risk Navy assumed in 2017 due to funding constraints and as we work towards the C&O's goal of a six month lead time on written orders for sailors. The Navy reserve shows a modest increase as we complete a period of planned growth that has been in progress over the last six years. The primary growth areas are cyber, unmanned aerial systems and shipyard surge maintenance. Additionally, we are permanently fortifying off installation of Navy operational support centers with armed and trade reserve security personnel to protect our sailors against threats. For the Marine Corps, the Marine Corps is the nation's crisis response force, which provides the nation the ability to respond to unexpected crises from humanitarian assistance and disaster relief efforts to major combat operations. The summit funds an active duty strength of 185,000 Marines and a reserve end strength of 38,500. End strength provides overall dwell ratios of one to two for active forces against the sustained goal of one to three and one to four for reserve forces. The makeup of this force was informed by Marine Corps Force 2025. A year long review which focuses on the changes necessary to successfully operate in the increasingly complex global environment and it builds a balanced MAGTAP optimized for global threats. Several key information initiatives include the establishment of a MEF information group to improve increased offensive cyber operations and communications battalions, increased reorganized aviation intelligence support in its intelligence battalions, new infantry battalion to size, and increased long range precision fires through high Mars rocket artillery battalion. The budget funds the civilian workforce required to restore readiness. To accomplish this, the department's FTE or full time equivalent increased at shipyards to meet schedule maintenance reduced the backlogs that have accumulated over the last decade. Overall, the Navy working capital fund FTE increased for engineering and support for an expanding profile of airframes for STEM personnel at surface warfare centers for NAF sub personnel needed for increased weapon support at spa war for tactical communications and cyber support to handle aviation maintenance backlogs. It also funds an additional 226 civilian guards to protect the Department of Navy installations. The department remains committed to complying with the MHA and the budget reflects a decrease of 310 FTE for headquarters. Overall, the civilian personnel numbers highlighted here reflect the essential role in our civilian personnel play in our mission success. The department appreciates the continued strong support in Congress of Naosha building. Changes in this budget from the President's budget 17 plan reflect congressional action which added an LCS and an LPD. New construction totals remain the same in the submit as were submitted last year. Other construction totals reflect a reduction of 3 ship to shore connectors. Kesha building efforts in this submit are the Columbia Class Program. It continues with its second year of advance procurement funding for the leadership SSBN 826. 826 remains on schedule to meet its first deployment in 2031. Procurement funds for Columbia are requested in SCN however to comply with law any appropriate SCN will be deposited in the national sea-based deterrence fund. We are using two authorities provided by the NSBDF continuous production of common missile compartment components and advanced construction. We plan to award the next aircraft carrier USS Enterprise in March of 2018. CVN 80 is incrementally funded with $1.9 billion requested. Fiscal Year 18 is the final year of funding for the John F. Kennedy with $2.6 billion requested. CVN 79 is on track to deliver within the cost cap. Two Virginia class submarines are requested and they are the final two block 4 boats in the FY14-18 multi-year contract. The department is requesting funding for two destroyers. These destroyers will be funded will be a flight 3 ship funded with the advanced missile defense radar and are requested as part of the shipping operation. One Latorial Combat Ship is funded. We continue to procure LCAS mission packages with two surface warfare mission packages 0205 replacement oil is requested in 18 along with advanced procurement for a future oiler. The oiler contract was awarded in 16 for one ship and five priced options for future oilers. The 18 is the first of those five priced options and the department is requesting a second combined towing rescue and salvage ship with a planned award in January of 2018. The department appreciates the continued strong support of Congress and aviation procurement. Changes in this submit from the 17 plan reflect congressional action which added six total F-35s, 12 FNA-18s, 2C-48 alphas, two AH-1Zs or Zula Cobras, one MQ-4 and four MQ-8s. Procurement totals for the submit decreased from 99 to 91 aircraft. A reduction of two F-35 Charlies, five Zula Cobras and five MQ-8 tritons were cut with one P-8 added. Key aircraft procurement in this submit include 14 F-18 Super Hornets and 24 F-35s with four Charlies and 20 Bravos to address efforts to mitigate our strike for a shortfall while we continue the transition to a fifth generation fighter. On the rotary side there was a small decrease in the Zula Cobras which was for fiscal balancing specifically to fund a comprehensive strategic recovery plan aimed at maintaining combat relevance through capability improvements. The 53K replacement for the CH-53 Echo helicopter completed its milestone C review in 17. Low-rate initial production or L-rep before aircraft continues in 18 leading to an IOC in 20. This submit request funds to procure the first six Navy CMV-22s to replace the C-2 cot. Forecast IOC for the Navy variant is fiscal year 21. This submit includes a requested multi-year authority to complete the production buy for both Navy and Marine Corps MV-22s. For our unmanned systems can continue to L-rep procurement of three MQ-4 tritons. The fleet delivery of early operational capability is planned for this year and the MQ-8 fire scout production was truncated because sufficient inventories on hand to meet planned LCS deployments. The program will continue to be assessed as the LCS and frigate program progresses. In weapons procurement the submit provides a net decrease of 10 weapons with reductions funding and optimal risk of weapons and enhanced capabilities. The Navy begins procurement of the small diameter bomb Block II which adds moving target capability for the F-18 and F-35 aircraft. Amaran quantities were decreased to procure the first lot of form-fit function refresh missiles which will replace 80% of the missile guidance section components. Jagum's Milestone Sea was delayed from 17 to 18. The 17 funding will be used to procure the first L-rep quantities and maintain IOC for 19. Due to the delay no missiles were requested in this submit. In shipboard weapons the Navy added 100 Tomahawk missiles to obtain quantity cost savings. The request includes 66 OKO missiles to replace those expended in the Red Sea in Syria and 34 baseline missiles. 18 also begins procurement of modernization kits to be installed in FY 19 with recertification. The Navy decreased RAM Block II quantities to invest in an upgraded capability to counter emerging complex raid threats. This submit includes initial procurement of the Block II Evolved Seasparrow Missile Procurement and the Harpoon Block II Plus Mods. The Block II Seasparrow replaces the guidance section with an improved seeker and the Harpoon provides an expanded capability to provide more accurate targeting. The Navy increases the buy of the LCS surface-to-surface missile module which is the Longbow Hellfire to provide LCS the ability to protect sea lanes and to move forces quickly through a choke point or other strategic waterway. The submit provides substantial investments to modernize enhanced capabilities that currently feel the systems in order to continue to overmatch our adversaries. It includes key investments in cybersecurity to ensure resiliency of our networks and operational technology, advanced efforts to outpace the threat in C4I electronic warfare and information warfare domains is supported by the Consolidated Float Network and Enterprise Services and the Navy multi-band terminal system. Various ship and submarine modernization efforts include the Summarine Warfare Federated Tactical System which provides hardware and software upgrades to submarine sonar, fire control, imaging, electronic warfare systems, as well as integrating unmanned aerial system and advanced electronic warfare and attack capabilities. The DDG modernization ensures the fleet meets or exceeds at expected service life at 35 years for Flight 1 and 2 and 40 years for Flight 2 alphas. Another enabling count the OPN Spares is funded to 85% of the requirement. The Marine Corps and PMC continues to balance ground equipment, procurement and future development to support the current fight while modernizing to dominate a future fight. It funds major programs including the procurement of 527 joint light tactical vehicles, three gator systems, and the initial procurement of 26 amphibious combat vehicles. Procurement of ammunition Navy and Marine Corps funds munitions and related weaponry that replenishes weapons expended and ongoing contingency operations. It funds major fleet requirements such as general purpose bombs, JDAM guidance systems and airborne rockets. Ammunition also range from the 5 inch 54 guns on cruisers and destroyers to precision guided artillery. While there is general agreement, we must increase the size of the fleet. The urgency associated with budget and certainty and increasing global volatility requires that we implement improvements in concept development, research and development and rapid fielding efforts to accelerate the fielding of advanced capabilities that will provide our fleet a force multiplier effect. In the R&D appropriation, science and technology funding remains steady at approximately two billion per year. The Navy's top program programmatic priority, the Columbia class submarine, supports common missile compartment efforts, nuclear technology development, strategic weapons system integration and ship design efforts, capability assessments to ensure the multi mission frigate paces future threats and aviation and the F-35 is funded to maintain the F-35 Charlie IOC of 2018, the next generation jammer and the F-18 fatigue life expectancy. The request includes $67 million of technology maturation in the unmanned undersea vehicles, needing to increase endurance, payload hosting and payload delivery capability. There's funding for Navy cyber situation awareness, combat system cybersecurity, enterprise workforce and building control systems. The Navy invested $15 million to establish the digital warfare office whose priorities include setting requirements, prioritizing resources and leading efforts related to information and systems operability. We've increased investments in laser technology to accelerate delivery of more laser capabilities to the fleet. It builds on the Navy's successes with lasers with funding for the surface naval laser weapon system in a low power module with a future investment of $107 million. The Navy is focused on increasing the speed with which we provide warfare war fighters with critical war fighting capabilities. To facilitate this, the Navy implemented emergent needs and accelerated acquisition policies for the Maritime Accelerated Capabilities Office or MECO program and the rapid prototyping experimentation demonstration or RPED projects. The Marine Corps major R&D initiative continues to be the amphibious combat vehicle. For military construction and family housing, the Milcon submission reflects a 13% increase compared to 17 and funds 35 projects, 18 for the Navy and 17 for the Marine Corps. The program focuses on target investments that provide maximum readiness and war fighting capability to include shipping repair training facilities, paint blasts and rubber facilities, repair facilities for avionics and lift fans, and ammunition recapitalization for Chambersfield, Indian Island and Mayport for missile magazines. Construction of four projects in Guam supports relocation of Marine forces in Okinawa and the family housing budget includes the operation maintenance and recapitalization leasing privatization and oversight of the department's family housing worldwide. Overall, this budget provides the investments required for the Navy and Marine Corps to execute its missions as assigned against the backdrop of complex global security and challenging fiscal environments. It affects the best balance of investments across our readiness inputs of people, equipment, supply, training, ordinance, networks and infrastructure. Balance resourcing across readiness generation efforts provides a wholeness to the force that will allow us to maintain the capabilities and capacity to accomplish the missions of today and the future. This completes my review. I look forward to your questions. We have about nine minutes, so I'll be quick with the ground rules. Of course, this is on record for attribution. When I point to you, go ahead and please state the name and the publication and please also limit your questions to today's brief. Hi, sir. Megan next time with the US Naval Institute News. So you spoke of this year being a readiness year and not necessarily a growth year. But Navy and industrial based folks have talked about for the LCS program meeting three ships to keep the base healthy and for the LPD program meeting that LPD 29 Hall to help with the transition to LXR. So I was just wondering what the discussion was as you were putting this budget together around those two and how industrial based health played into your talks. So as you said, the guidance was fixed, filled the holes for 18. And but the industrial base is a consideration for the shipyards, for airplanes, for weapons. So we the direction was clear, filled the holes first. And then as we go forward for the future, we will look at the industrial base and and we will conduct a review to ensure that we understand truly what a minimum sustained rate is for an acquisition program. And then we will review and what is the sustainable. The goal for the Navy is to have both shipyards available to compete for the FFX competition down the road. So we would respond accordingly in the out years if it was necessary. Hi, Admiral Sydney Friedberg breaking defense. Just to get the big picture right of not a growth year, compared to the Obama plan from last year for Foyight 18, when this was an out year, we're still the same number of ships being built and the exact same types of ships being built. And I believe the aircraft are also very similar. I think you said different sort of 99 in last year's flight. The airplanes, 99 to 91. What type was was was coming coming down to that? The type of airplanes that that came down. Yeah, we reduced some F-35s were reduced. And as I mentioned the Zulu, there's five Zulu Cobra's, but they self-funded their main modernization program. So they took quantity and then bought capability with that. We truncated the buy of the fire scout because we have sufficient inventory on hand to address that. I think those were the three major ones. Hi, I saw a man with aviation week. So two quick aircraft questions. Number one, why, what was the reason for the decrease in F-35Cs this year? And two, I didn't see any mention of the next generation aircraft fighter, FAXX I think. Can you just explain why there's no mention of it and what's what's the plan for that? Has it been delayed? I'll start with the first. So to continue the theme of 17, we had to make hard choices and so we maintained our readiness accounts and we had to balance somewhere. And so we tried to hold the line as best we could in our procurement accounts, but if there was something. So reducing just two F-35s allowed us to maintain the IOC in 18 for the F-35. So we made a hard choice and but maintain the risk to allow us to maintain IOC. So that was a cost-benefit analysis on that one. Or it's deferred? The F-35s? Well we'll look at that as we go forward with the defense strategic review. So all the out years and I and you know I think Mr. Roth mentioned this earlier, right? So the as we go through those 10 mission sets will be examined. Those 10 mission sets are the driver for the utilization of the forces. So if something comes out different that says, hey we need a different force sizing construct, then that may drive. My expectation is that we will continue to fly airplanes off aircraft carriers and we'll look at what the demand signal is and then procure the aircraft appropriately to the DSR when it comes out in August or September. For your FFX, I'll have to, I don't have that off the top, so I'll get back to you on that. You said that or eliminating those aircraft allowed you to get to IOC in 2018. Can you just be more specific on that? No, we maintain IOC and to maintain IOC, right? Where does the money go, like how does that work? Well I can't take you as a, you know, this is a dollar and fund it through but I will tell you in the aggregate we increase funding as I mentioned for example in aviation spares. So aviation spares at a high level. We went to those enabling accounts, so PRE, PRL. So we bought engineers to do dispositions for the maintenance. We bought Navy One Capital Fund people to do to handle the IOC for the JSF. So the two airplanes for the JFF that may have been programmatically to balance the increased requirements in other accounts. Okay, Justin. Hey, Justin, don't believe inside defense. I just was wondering, I think it was about a billion dollars it's going to be requested for just one LCS. The ships have been coming in around 500 million. So why do you need that much money for just one LCS? I'm not familiar that we ask for a billion dollars for one LCS. Oh, is it about six? Excuse me. Well, in the second part of that question, how does this budget set up the transition to the frigate going forward? So as I mentioned earlier, we'll take a look to maintain an industrial base that remains competitive. And so in the R&D effort, we're funding the capabilities assessment to assure we know what the FFX needs. And then we are on pace to do a fourth quarter 2020 award for the FFX. So that's the end state that we want to do. You mentioned in brief that 4,000 sailor plus up, how it's going to be apportioned. And I was wondering if you could go more granularly, say this many sailors will be part of the blue and bold concept, this many for the expeditionary If you give me a second to get to it, I can. Actually, it's this is a delaying technique. Let's go to the other brief. I know that approximately 2,000 are in our IA and TTPH, the overhead associated with friction so we can we can get sailors to their ships on time. There was a thousand for cruisers modification 450 for the LCS balloon gold concept, 373 to support the IOC for the JSF support for the Marine Corps was 163. And the expeditionary staging base was 100. And that adds up roughly to about 4,000. Sir, Richard, with regard to that single LCS for 2018, does that represent a down select to a single hull design? It does not. The intent is to have two shipyards competitive in 2020. We maybe it seeks to have a competitive bidding process. Okay, Chris, last question. Chris Cab's defense news, actually following on the LCS, my understanding is that OMB wanted to add another LCS into this budget to make two. But but the the submission here is for one, which is the Obama request. Are you is there the possibility of the Navy submitting an addendum to this or a modification to this request and going up to two ships? As I know today, we are not submitting an amended budget submission for a second LCS. Do you plan on submitting a amended budget submission right now? As of right now, I have not been directed to create nor submit an amended budget submission. Okay, thank you everyone. You have follow-up questions. You can direct them to me. We up here with Kerry as well.


Hello again Bradford City fans, me James Mason here at the Northern Commercials Stadium and of course you all know by now about our Matter of Heart DVD, the latest film to document Bradford City over the last 12 months. I'm sure you've got your DVD by now but what about the chance to meet Eddin Rahage in person? Yes the chairman, the focal point along with Stefan of the DVD. Yes you can meet him but not only can you meet him you can join us at a very limited exclusive question and answer session here at the stadium next Thursday evening. We've got the premiere of the film on the 14th in in Bradford City Centre and on the 16th you can have your own audience with Eddin, a two-course meal here at the stadium followed by an exclusive preview of the film itself. Not the whole film, just the most important salient scenes.  Have you got a question for him? Of course you have. What's the first 12 months being like with Eddin? Book now if you want a chance. £47 for the two-course meal, the preview of the film and the chance to ask Eddin Rahage, the chairman of Bradford City, a question that you've wanted to ask him if you ever had the opportunity. Next Thursday book now limited availability £47 for next Tuesday night starts at seven o'clock in the McCall Suite. Book now, hope to see you there.


We're training for the next enemy. I mean, whoever comes next, trying to make sure we're prepared for whatever they have to give to us. Make sure we're ready at a moment's notice. You can work out as much as you want, but you're not going to be prepared to hike up a huge hill, you know, put a gun up there. It's prepared immensely. It's more of a confidence in my whole squad, my whole company, the Marine Corps in total. You grow together and you work together. It's the cohesion. I trust them with my life. I jump on the grenade for them.


hey friends so now we are going to deal with the problem solving on herons formula what is herons formula herons formula is nothing but a formula herons formula is nothing but a formula given or which is used to find out the area of triangle which with three sides given and the formula looks like this s times s minus a times s minus b times s minus c where a b and c are the side lengths side length side length of a triangle okay so let's now do the sum it says find the area of a triangle very good two sides of which are 8 centimeter and 11 centimeter so hence it's given a is equal to let's say 8 centimeter and b is let's say 11 centimeter two sides are given c is not known but other information given which is perimeter is 32 centimeter what is perimeter so if you have a triangle like this so perimeter is let's say this is side a this is a b and b and this is c so perimeter is given by perimeter p is a plus b plus c right so hence from here this from this information you can find out c so that means p is equal to a plus b plus c so hence c is equal to p minus a minus b which is equal to 32 minus 8 minus 11 which is equal to 13 centimeter is it so hence what did we find out the third side is now known to us now simply deployment of formula and finding out the result what is s s is p upon 2 semi-perimeter that means a plus b plus c by 2 now perimeter was already given and that was equal to 32 isn't it so hence it will be 32 upon 2 which is 16 centimeter right so what is the area of the triangle now before you find out the you know the area you it's better to find out all the values separately so hence s is now known now let's find out s minus a so s minus a is 16 minus 8 which is 8 centimeter s minus b is 16 minus 11 which is 5 centimeter and s minus c is 16 minus 13 which is 3 centimeter yep so these are the three sides so 8 5 and 3 are the three sides now so hence the area of the triangle area of the given given triangle will be equal to under root write the formula s minus a s minus b s minus c which is equal to under root 16 into 8 into 5 into 3 and now your factorization skills will come to play so let's see let's try to factorize this prime factor is it so it is 2 to the power 4 into 2 to the power 3 into 5 into 3 so now we can pull off some powers of 2 isn't it so we can say 2 to the power 6 into 2 into 5 into 3 can we say that yes we can say that so hence this is nothing but 2 to the power 3 times under root 2 into 5 into 3 which is 30 so hence area is 8 root 30 centimeter squared by centimeter squared area unit will be meter squared or centimeter square or inch square or you know any dimension of length square so since the values were given in centimeter so hence the unit is centimeter square please do not forget to mention the units is that okay so this is how you have to find out the area if the sides are given so now the learning is in this in this case it was not a direct question that means all the three sides were not given but an extra information of perimeter was given so you have to use that information to find the find the third side and then find the triangles area okay so hence you know you should be knowing the meaning of perimeter to solve this question


What's up everybody jason for jazby's case breaks calm 2021 panini national treasure's baseball just sold out This is a four box case break pick your teams number four So again guys we do have The customer names that bought in actually sorry. Why does this a number three? Come on man? Come on man One say window guys One moment one moment Reprint this one. I'll just read right over this one So there you go. That's number four. These are the r&b spots right there for those teams Brett fava right number four There's a customer name right there that bought in straight up Really appreciate you guys. We got done with four cases number five is on the website and You know little by little people are taking teens guys. Someone just took the podgers Eric I mean, I'm not trying to rule it out, but you guys want to do another one We're at 15 left now our first r&b. We did of the day was a 13 spotter So we're more than enough close to potentially do a fifth case of NT tonight so Luke Walton number four Luke Walton The number four is now so if you guys really want to run one back show me grab some teams in number five He said I can always r&b of The remaining teams that people don't want to buy You missed my comment or all over earlier. What happened? What happened to Fox? I believe Fox is number five, right? What happened the door defense too much? It's a great play by the door Kyle Lewis eight out of 99. That's gonna go to Seattle's part of the r&b eight It's going to Oliver. It's okay Oliver. You're gonna get some hits in this break to make up for that Sacramento Fox turnover Noah Senegard to 99. I Actually didn't watch the game so but I just seen that I Gotta try to like download NBA game pass or something Senegard 86 at a 99 that's gonna go to the New York Mets When a Joe survivors Game gear Don Maddingly 83 out of the 99 For the New York Yankees and Noah under playing some good ball right now the man. They started off like oh and six They won like five out of the last seven games Jamiah Jones for the Los Angeles Angels of Anaheim 10 out of 25 Maron with the Angels We have Ryan Jeffers for Minnesota Minnesota to 99 Minnesota it's gonna DIY and whoa Printing play one-of-one RPA of Mario Feliciano Uno of Uno from Milwaukee And then it's going to Brian I know that was like they're only two wins of the season up until then Oliver They beat the makers and both of them were like 20 point comebacks or something great Oh back-to-back one-of-ones Ronald Acunha Jr. Wow Look at that with the heat And we have an out of 10 legendary materials Tommy Heinrich for the New York Yankees and look at that I was gonna touch the patch Very nice. Let's run it back guys. I wanted to number five Let's run it back R&B of the remaining teams. Let's just sell maybe two more. It'd be so worth it And he's such a great product. I don't care what people say. It's not licensed. Who cares who cares?  It doesn't matter You save money this way. Anyways, love these boxes this year, too Retro materials start us off and that is a Omar Viscale Seattle additional Marvis scale. Don't see that too often to 99 Seattle's 14 spot for Martin Also, have I been missing any names? No, right? These are all teams that customers bought We have Buster Posey to 99 for the G-man Giants. That's going to Martin We have a Roger Clemens relic 15 out of 25. That's a Yankees edition. Buy a box low We have them available on Jaspies.com Daniel Johnson to 99 That is for Cleveland No down Like a bunch of like 10 15 year old kids came in early when it was really loud And we had at least like 12 boxes of NT out there. They took them all, you know, we give them away for free to the kids This is gone always royal Brady singer out of 49 look at this patch autograph to 25 Tyler Stevenson for Cincinnati regular patch and autograph 23 out of 25 Cincinnati Reds that is going to Dennis Good way bogs on card for Boston. What a Christopher? 24 to 49 and Dual booklets chipper Jones Andrew Jones legendary silhouettes for the Atlanta Braves. What a break for the Braves 7 out of 25 Nice on Matt.  It's for kids No, yeah, we give away all that stuff Hollywood. We just don't ship it out to customers If you're local if you want to come in the store, you can definitely take some Sometimes we don't have the box dimension sizes for it. So Yes, it's not like tricks or you need to be a kid. So during flawless season like this upcoming Wednesday, actually This upcoming Wednesday, we're gonna have flawless collegiate. So you'll be seeing a lot of those outside It's like Liam Neeson and what was it? What movie was that Ted? Is it true? These are exclusively for kids Uh Michael Lorenzen to 49 Cincinnati. I'm good. Why? 69 out of 90 now Jared Kellenick No, Hollywood. That's the one thing we tell people is that we do not offer that service whether you pay for it or not You just don't do it. Oh If you want one you can come pick it up in the store and a one out of five Do I good and little doc? Two-color patch All the bat relics right there For the Mets going to Joseph. We have Vladimir Garo, Jr 77 out of 99 spots seven going to Laurel last Balmogel RPA Not RPA. Tim Anderson actually veteran patch autograph one out of five Look at that patch. Good Lord colossal one out of five Chicago White Sox is going to Christopher Butler Very nice hit Dr. Sticks Is that his nickname? Tristan McKenzie. Is it because he's really skinny Karusha That is for Cleveland. We're gonna know Dalton Varshow to 49 for Arizona That's part of the R&B 23 spot three going to John. There you go four-color patch as well go about the name of chef Curry We have a eight out of 99 Edgar Martinez that is for Seattle eight Going to Oliver Martinez and we have a Bill Dickey Signature cut materials one out of five. Wow. Look at that class of 54 beautiful hit Bill Dickey Slider box for that. So I'll put that right over there in the corner. Yeah, very nice. I have one more box left guys Again, if you guys want to get those fillers done, let's work on those One of them does sell out contenders the obsidian filler got to sell that one out plus one more so Work on those fillers work on formula one or if you guys really want to try to do another NT Give me a show of hands who would get spots in an R&B if I ran a number block through remaining teams And maybe we can try to get that rolling Not like I said, we'll just save it Randio Rosarania to 99 for Tampa Bay and you Darvish for San Diego Adam Harper we have Houston Jeff Bagwell Hall of Fame materials to 99 and we have hail or haul sorry new and howl sir howl new and howl sir for Cleveland and Sam Huff rookie material signatures gold gold and material signatures kind of a 175 Gold would be out of 49. It looks like Texas Rangers let's go to the main hits here guys. Good luck First one is Omar the Skelfer Cleveland 23 out of 49 Cleveland that is going to Noah Ian Anderson RPA for Atlanta three out of 99 Lana having a great break. We have Jose Reyes and remember Jose Reyes 80 out of 99 for the New York Mets Mets that's going to Joseph and last one here is Josh Fleming to 99 jumbo material signatures for Tampa Bay There you go TB And there you have it folks that was the break so we did get that one out of five cut autograph here of Bill Dickey, which was really nice And a lot of really nice stuff here Edgar Martinez Some nice RPAs appreciate it guys no randomizes do here though So again number five is in the store if you guys want to potentially run it back We are down to 15 if we can probably get another team or two sold I'll arm be up all these teams and we'll do a little amount of number block Just expected to be a little over a hundred and I think we did a 13 team R&B for number one And I think it was around 140, but again, you're getting a piece of almost half the league Right if we do the all 15 you're getting half the league So yeah Dodgers really haven't been so hot man. Maybe it's a fresh maybe number five is a charm Number five is a charm Dodgers a little pricey, but they have a huge checklist guys So I appreciate you guys and again no randomized to do here. This was NT Baseball Pikachu number four and make sure I don't think there was any randomized to do here, right? No, that was a duel. That was the same team fine rank That's it. Appreciate it guys


Hi everyone, Joe for Jaspy is doing a recap video for our Sunday fund a three box football mixer random team number two on Sunday the 10th did a box of 2023 elite a box of 2023 fanatics under wraps mini helmets and a box of 2022 putting you one football Football season is in the air. It's good to do some NFL with you on the fanatics live stream Thanks, everyone Nice a Bijan Robinson die cut Got it Kendra Miller pen pals autograph the Clayton tune auto a epic materials relic for T. Higgins and The hit from Panini one was Desmond Ritter nice RPA and a win for the Falcons earlier today the mini helmet was This is for break to yes Was for the Patriots It was a Christian Gonzalez the corner It's 25 right there as well the defensive back the corner back that they drafted in the first round There you go. And so that went to the Patriots. I went to Adrian. All right. Thanks for watching everyone. I'll see you next time for the next one


What was your first job after university? Well my first job was working at a company called Public Affairs International and I worked in government relations. I didn't work in public opinion research but the company that was affiliated with it, I was a company owned by Alan Gregg called Decima Research and by the way Alan another Carleton graduate, another alumni and he brought me in to do the 1988 federal election and my career in polling started with that. I really didn't have a plan when I graduated from high school. My twin brother and I were the first in our family to go to university. I just knew that I wasn't going to stay in Cambridge, Ontario. I was nice to town as it was. I knew that there was a bigger world for me to experience and I thought that the best way to do that would be to go to university. So I started my university career at Wilfrid Laurier University where I did my BA in my MA and then I went to Carleton for my PhD. What attracted me to political science is I was always interested in politics. It seemed to be very immediate. It was a pretty vibrant time in politics back then and I originally actually started in history and I thought it was a little more contemporary in my focus and I was really more interested in what was going on at that time day to day. The reason I got into polling was because it was factual. I found when I was going to university there was a lot of people who had a lot of opinions on stuff but there wasn't a lot of people who had a lot of facts. So the thing I really liked about public opinion research was its precision and its finality. It tended to settle a lot of arguments back then really quickly. And the whole scientific method I found really appealing that you had a very specific question that you were trying to answer that you could structure a study in a certain way and you could come up with that answer by the end of it. The whole package really worked for me. Well, it didn't just help me along the way that I took a political science degree. It helps me every day. It is absolutely true that everything that I learned when I was going to Carlton and then previous to that Wilfrid Laurier that I still use it today. I mean, I work in an environment in which the statistical methods that I learned, the scientific method that I learned, what I learned about Canadian history and sociology, what I learned about everything that you can imagine about this country, not only do I apply it when I'm talking about Canada but I also bring it to the rest of the world where I use the same methods, the same ideas, the same concepts, and the same skills to explore public opinion in all those places. I think the most important lesson that I've learned so far, really the biggest one, is that you need to keep learning. Things are keep moving so fast in the world of business. They keep moving so fast in the world of social science that I think it's really easy for people to get uncomfortable with change and to sort of sit back and compare the future with what they know in the past. And I really do think that you need to continue to build on the shoulders of what you already knew before but continue to change and modify what you do based on everything that's new out there, whether it's new technology, whether it's new ideas, whether it's new people that you meet, you need to continue to be inspired by what's happening out there and what's contemporary. And it just makes you, I think, a better researcher but more importantly I think it also makes you yourself contemporary and interesting and relevant. So I would say that the thing that I really learned was keep learning. The biggest advice I would give students, and it's something that I wish somebody had told me when I was going to school, was to own it. You're not there to satisfy professors. You're not there to satisfy your peers. You're not there to get grades. I mean all of those things obviously are part of what you do but you really need to own what you're doing. You really need to accept that this is where you are going to find satisfaction in terms of your future career and you really need to feel that you are part of what's going on rather than somebody who's just participating as a student. Really own what your future is. Really own your professional positioning. Really take it seriously. I think too often what happens in university is we treat it as a basically a checklist where we go through school and we have to take these various courses to get these various grades to get to the next level. But the truth is if you're really serious about this, all of these things are just part of the process. What you're becoming as a person is ultimately what you're trying to achieve. And when you own it and you learn to satisfy your own conditions rather than the conditions of the academy or grant funders or whatever it is, else it is that you're going to be confronting in the future, the more that you're really trying to satisfy your own standards, I think the more satisfaction that you'll get out of what you're doing. So I would say own your experience when you're at Carleton. Own what you take out of there and then own the responsibility that you have for crafting your own career and being somebody who plays an important part in the world. Well, I think my colleagues and I at Ipsos are changing the world. I mean, we're living in an era in which we can, for the first time in human history, construct something that looks like world public opinion. And public opinion and the measurement of public opinion is an extremely powerful force. It creates change in the world. And sitting in the seat that I have the privilege of sitting in at Ipsos, I have the smartest people, the best technology, the most creative minds to work with in order to answer that question, you know, what does the world think? And the more that we do of that, the more that we bring the voice of the public into the conversation that some two, I would say, sometimes is far too dominated by elites, I think the better world that we have. So I'm really excited about about what I do in public opinion research. I'm really excited about what we do at Ipsos. And I'm very grateful that I had the opportunity to go to Carleton University to learn a lot of the skills that I'm still using today.