different flow visualization lines in our last class and we will discuss one more flow visualization line which is called as time line. So what is the time line? If you have a snapshot at a particular time in the flow field where you mark nearby particles. So nearby fluid particles which are located in the flow field at a given instant of time, if you somehow mark those particles by some way then if you now get the snapshot at different times it will give a picture of evolution of the flow field as a function of time and that is known as a time line. So it is nothing but like a snapshot of nearby fluid particles at a given instant of time that is called as a time line. So let us look into a small movie to see that what we mean by a time line. So if you see now this gives a snapshot at different instance of time of nearby fluid particles and in a way it gives a sense of the velocity profiles at different instance of time. You can see that in this example the flow passage is narrowing and as the flow passage is narrowing the fluid is moving faster to make sure that the mass flow rate is conserved. We will see later on that formally this is described by the continuity equation and in may be a differential form or an integral form but at least this gives us a visual idea of what the time line is all about. Now with this background on the flow visualization lines we have now understood that how we can visualize the fluid flow in terms of some imaginary description like through the streamline, streak line, path line or may be the time line. Next we will go into the description of acceleration of fluid flow. So we have discussed about the velocity the next target is the acceleration. Let us say that you have a fluid particle located at a position p specifically the location p1 at time equal to t and how the velocity is described here the velocity described is described here through a velocity vector v which is a function of r1 that is the position vector of the point p1 and the time t. This is nothing but the Eulerian description. If you write it in terms of components you can write an equivalent scalar component description that you have u as a function of x, y, z and t, v as a function of x, y, z, t and w as another function of x, y, z, t. So we are trying to describe it in terms of Cartesian coordinates it is not always necessary to do that but it may be a simple way to demonstrate. One may use other coordinate systems as well. So if you are using a Cartesian coordinate system 3 independent coordinates space coordinates plus time coordinate that together give the velocity at a particular point. So if the fluid particle is located at p1 the velocity at that point is basically the velocity of a fluid particle located at that point and that is given by these components. Now let us say that at a time of t plus delta t these things get changed. Now at a time t plus delta t what happens? This fluid particle is no more located at this point. The fluid particle is located at a different point. So let us say that the fluid particle is located at a point p2. So at the point p2 now let us say that the velocity is whatever some arbitrary velocity. So initially it may be velocity at the point 1 say v1 now it is v2 which is again a function of its local position and time. So you have this v2 this one a function of what?  These are functions of what? These are functions of the new position vector. The new position vector say is r1 plus delta r1. So in terms of scalar components it may be x plus delta x y plus delta y z plus delta z and the time has also now changed it has become t plus delta t. So we are thinking about a small interval of time delta t over which the fluid particle has undergone some displacement which is a change in position vector having components delta x delta y and delta z that is what we are trying to understand. So we can clearly see that there is an original velocity in terms of its 3 components. There is a change velocity in terms of its 3 components and if we want to find out the acceleration see the basic definition of acceleration is based on a Lagrangian reference frame that is the rate of time rate of change of velocity in a Lagrangian frame not in an Eulerian frame all the basic definitions in Newtonian mechanics that we have learnt earlier are based on Lagrangian mechanics. So when you say that it is a rate of time rate of change of velocity then that has to deal with the time rate of change of velocity of may be an identified fluid particle which earlier was at p1 now is at p2. So if we want to find out the change so you can write of course you can write it in terms of the 3 different components but just for simplicity let us just write for the x component similar things will be there for y and z component. So how can you write u plus delta u as a function of u. So u plus delta u is now dependent on the local position of the particle and the time that has elapsed. So it is a function of it depends on what it depends on the original u plus the change.  So again it is a same mathematical problem that there is a function of 4 variables it is known at a given condition. Now you make a small change in each of these variables and you want to find out the new function again you can express it through a Taylor series expansion. Now it is a function of multiple variables instead of a single variable. So we will use the Taylor series expansion to keep in mind that now you are having 4 variables. So let us first consider the time variable may be because it is bit different in characteristic than the earlier one. So this is with regard to the time then with regard to the space plus higher order terms this we have just written the first order term in the Taylor series. Since it is a function of 4 variables you have 4 first order derivative terms. Similarly you will be getting second order derivative terms and so on but we will neglect the higher order terms by considering that these delta x delta y delta z and delta t are very small. So we have to keep in mind that all these are tending to 0 because all they are tending to 0 we are neglecting their higher orders. So you can first thing what you can do you can cancel u from both sides and what is the definition of acceleration along x from a particle mechanics view point or a Lagrangian view point. So you have to find out the change in velocity x component of velocity because we are writing acceleration along x divided by the time delta t in the limit as delta t tends to 0 very simple straight forward Lagrangian description. So when you do that basically what we are doing we are dividing the left hand side by delta t. So right hand side is also divided by delta t and the limit is taken as delta t tends to 0. So the first term is straight forward let us look into the next terms. So first we will evaluate the limit as delta t tends to 0 delta x divided by delta t that multiplied by the derivative with respect to x. Similarly the other terms let us just complete it. So what we are doing is we are trying to find out that because of the changes in velocity component along different directions what is the net effect in acceleration and these terms are basically representatives of that we will formally see that how they represent such a situation. So now let us concentrate on these limiting terms say the first limiting term what it is representing it is representing the time rate of change of displacement along x of the fluid particle over the period delta t. Now you have to keep in mind that we are thinking about the limit as delta t tends to 0. This is a very important thing what is the significance of this limit as delta t tends to 0. When delta t tends to 0 p1 and p2 are almost coincident right that means let us say that p1 p2 all those converts to some point p and that point is a point at which say we are focusing our attention to find out what is the change of velocity that is taking place. So when in the limit delta t tends to 0 we are considering the Eulerian and Lagrangian descriptions merge this is very very important. So we are trying to see what is our motivation we know something and we are trying to express something in terms of what we know what we know we know the straight forward Lagrangian description of acceleration. We are trying to extrapolate that with respect to an Eulerian frame to do that we must have an Eulerian Lagrangian transformation and essentially we are trying to achieve the transformation in a very simple way that as the delta t tends to 0 Eulerian and Lagrangian descriptions should coincide and then what does it represent it represents the instantaneous velocity x component of the instantaneous velocity of the fluid particle located at p that means it represents the x component of the fluid particle located at p. Since you are focusing our attention on p itself and the velocity of the fluid particle if it is neutrally buoyant is same as the velocity of flow we can write that this is same as what this is same as u at the point p. See writing this as u is very straight forward understanding it conceptually is not that trivial and straight forward if the Eulerian and Lagrangian descriptions did not merge we could not have been able to write this because this is on the basis of a Lagrangian description and this is the Eulerian velocity field how these 2 can be same they can be same only when we are considering a particular case when in the limit as delta t tends to 0. So wherever we are focusing our attention at that particular point this represents the velocity of the fluid particle if the fluid particle is neutrally buoyant with the flow then it is like an inert stressor particle moving with the flow and then it would have the same velocity as that of the flow at that point at that point at that instant. However if the fluid particle has a different density then that of the flow then this would be u of the fluid particle. So fundamentally this is u of the fluid particle not u of the flow field if it is neutrally buoyant then it becomes same as u of the flow field if it is an inert stressor particle in the flow which is the definition of the fluid particle then it is definitely same as u at that point but if it is a fluid if it is a particle of a different characteristic different density characteristic then that of the flow it may be different from that of the velocity field at that point. So that we have to keep in mind. So if you complete this description of this term what you will get you will get Ax is equal to that is the straight forward follow up of this expression because the other limits you can express in terms of v and w again with the same understanding as we expressed as we used for expressing the first term. Now if you clearly look into this acceleration expression there are 2 different types of terms one is this type of term which gives the time derivative another gives the spatial derivative you will see that this expression will give you a first demarcating look of how the expression is different in terms of what we express in a Lagrangian mechanics. In the Lagrangian mechanics it is just the time derivative that comes into the picture here you also have a positional derivative and what do these terms represent we will give a formal name to these terms but before that first let us understand that what these 2 terms represent. Today you are located at a point 1 now you go to a point 2 in the flow field. So when you go there there are 2 ways by which your velocity gets changed how one is maybe from 1 to 2 when you go you have a change in time and because of a change and you also have a change in position you have a change in velocity and that is solely time dependent phenomena. How can you understand what is the component of the time dependent phenomena if you did not move to 2 but say you confined yourself to 1 say you are not moving with the flow field you are confining yourself with 1 then you are freezing your position but still at the point 1 there may be a change in velocity because of change in time if it is an unsteady flow field. So because of that it might be having an acceleration. So the acceleration that acceleration component is because of what the time rate of change of velocity at a given point at a given location so that is reflected by this one but by the time when you are making the analysis the fluid particle might have gone to a different point even if it is local velocity that is velocity at a point is not changing with time it has gone to a different point there it encounters a different velocity field. So here it was encountering a particular velocity field because of its change in position so what it has done it has got advected with the flow it has moved with the flow and it has come to a new location where it is encountering a different uvw. So because of the change in uvw with a change in position it might be having an acceleration so that acceleration is not directly because of the time rate of change of velocity at a given point but because of the special change since the particle the fluid particle by the time has traversed to a different location where it finds a different flow field and since we are considering that it is an inner tracer particle it has to have the same velocity locally as that is there in the new position. So because so the next combination of terms it represents the change in velocity solely due to change in position. So the total the net change is because of 2 things one is if you keep position fixed and you just change time because of unsteadiness in the flow field there may be an acceleration the other part is even if the flow field is steady but you go to a different point because of non-uniformity because of a change in velocity due to change in position the fluid particle might have a change in velocity. So the change in velocity in the fluid particle may be because of 2 reasons one is because of the change in velocity due to change in time even if it were located at the same position as that of the original one and the other one is not because of change in time but because of change in position as it has gone to a different position because of non-uniformity in the flow field it could encounter a different velocity and the resultant acceleration is a combination of these 2. So let us let us take a very simple example to understand it. Say you are you are travelling by flight from Calcutta to Bombay. So when you are taking the flight before taking the flight you see that it is raining very very heavily and then say you take 2 to 1 half hours you reach Bombay and you find that it is a very sunny weather. So the question is now if you if you want to ask yourself a question does it mean that when you when you departed from Calcutta it was raining in Bombay or when you departed from Calcutta it was sunny at Bombay or when you have reached Bombay is it still raining at Calcutta or is it still is it sunny at Calcutta. It is not possible to give an answer to any one of these because the net effect that you have seen is a combination of 2 things. You have traversed with respect to time. So you have elapsed certain time by which maybe it was raining at Calcutta but right now it is not raining at Calcutta. Maybe it was sunny at Calcutta and right now it has started raining. So it is like at a particular location the weather has changed because of change in time. But the other effect is that you have migrated to a different location and because of the change in location maybe it was before 2 years raining at Bombay now it is sunny or it might so happen that it was sunny 2 hours back in Bombay still it is sunny. So you can see that individual effects you can maybe try to isolate but what is the net combination of changing with respect to position and time that is the net effect of this and it might not be possible to isolate these effects. So when you think about the total acceleration so it is just like a total change. So when you have the total change it is a change because of position and because of time and that is why this A x or maybe A y or A z this is called as the total derivative of velocity. So it is given a special symbol capital DDT. So capital DDT has a special meaning it is called as total derivative. It is to emphasize that it is a resultant change because of change in position and change in time. So with respect to change in time if you have a change then it is called as a temporal component of acceleration. Temporal stands for time temporal or transient or local. These are certain names which are given again by the name local it is clear local means confined to a particular position only with respect to change in time and this is known as the convective component. So convective component is because of the change in position from one point to the other and this therefore is the total or sometimes known as substantial. So the total derivative is a very important concept mathematically. Here we are trying to understand this concept physically but it is not just restricted to the concept of acceleration of fluid flow. It is applicable in any context. In any context where you are having an Eulerian type of description and it is therefore possible to write the general form of the total derivative as this way where it has a local component and a convective component. So we can try to answer some interesting and simple questions and see and get a feel of the difference of this with again the Lagrangian mechanics. So if we ask a question is it possible that there is an acceleration of flow in a steady flow field that the flow field is steady but there is an acceleration. It is very much possible because if it is steady only the first term will be 0 but if the velocity components change with position then the remaining terms may not be 0. So these are certain contradictions that you will first face when you compare it with Lagrangian mechanics. In Lagrangian mechanics if there is something which does not change with time its time derivative is obviously 0 but here even if it does not change with time the total derivative is it may not be 0. On the other hand it may be possible that it is changing with time at a given location but acceleration is 0 because I mean in a very hypothetical case it may so happen that the local component of acceleration say it is 10 meter per second square convective component is minus 10 meter per second square. So the sum of that 2 is 0 but individually each are not 0. That means it is possible to have a time dependent velocity field but 0 acceleration and it is possible to have a non-zero acceleration even if you have a time independent velocity field. So these are certain contrasting observations from the straightforward Lagrangian description. So you can write the x component of acceleration in this way and I believe it will be possible for you to write the y and z components which are very straight forward and you have to keep in mind that when you write y component this DDT operator will act on v and when you write the z component it will act on w. So you can write the individual components of acceleration vector and the vector sum will give the resultant acceleration. Now you can write these terms in a somewhat compact form. So this you can also write as v dot del where del is the operator given by and v is the velocity vector you know that is ui plus vj plus wk. So if you clearly make a dot product of these 2 you will see that this expression will fall. So it is a compact vector calculus notation of writing the convective component of the derivative. So we have got a picture of what is acceleration of flow, how we describe acceleration of flow in terms of expressions through simple Cartesian notations and may be also through vector notations. Next what we will do? We will start analyzing the deformation of fluid elements. Why this is very important because we have seen that fluids are characterized by deformation. They undergo continuous deformation under the action of even a very small shear force and the relationship between the shear force or the shear stress and the rate of deformation is something which is unique to the constitutive behavior of different fluids. So we must first understand that how to characterize deformation of fluid elements in terms of the velocity components. Once we understand that it will be possible for us to mathematically express different types of deformations in terms of the velocity components say u, v and w. When we do that we have to keep in mind that we will be essentially bothering about 2 types of deformations. One is the linear another is the angular deformation. When we talk about the linear deformation it may eventually give rise to a change in volume of the fluid element also because if you have a length element and the length element gets changed a volume element is comprising of several such length elements. So if length linear dimension gets changed the volume is also likely to get changed. Initially we will think of how we can say estimate the linear deformation. So we will start with the linear deformation. To understand or to get a visual field we will consider a fluid element like this. Maybe we may consider even a 3 dimensional fluid element if you want but that will not make the thing more complicated because at the end we will be dealing with linear deformations in individual directions. See why we use coordinate system for analyzing a problem. The reason is like say when you think of x, y, z is a Cartesian coordinate systems. These are independent coordinates a combination of which describe the total effect in the system. So when you are thinking of a linear deformation along x you may be decoupled from what is the linear deformation along y and z and these individual effects you can super impose because you are dealing with linearly independent components and these vector components actually give you linearly independent basis vectors like components along x, y or z. So similar concept whenever we are considering a change along x maybe we are bothered only with respect to like what is the change in the linear dimension along x. This regarding what happens along y and z. So let us keep that target. Let us say that delta x is the length of the fluid element which is originally there and now what is happening? Now we are having a change in time and because of a change in time now you see that let us consider the front face of this cuboid. So this left face over a time interval of delta t will traverse a displacement will undergo a displacement. What is that displacement? If u is the velocity at this location simply u into delta t. We are considering the time interval delta t to be very small so it is like just a product of the velocity into delta t. The right face will also undergo some displacement what is that? So if this is the x direction the new u here is not the same as the u at the left face but this is because of change in u due to change in x. So this is the new u times delta t. So if you consider only the front face and only subjected to this motion say we freeze all other events just for a clear picture. So maybe now it is having a new configuration shown by this dotted line. So what is the change in its length along x? That is the final length- the original length. So what is the final length? So what is the net change? See the right hand face has got displaced by this amount. The left hand face has got displaced by this amount. So the net displacement is the difference between these 2. So what is that change in length? So change in length along x. This is the change in length along x. What is therefore the strain along x? The change in length per unit length. So the strain along x this is the elemental strain because we have considered only a small part of the fluid which is having an extent of delta x. So this is elemental strain along x. As we have discussed earlier we are not just interested about the strain for a fluid because if you allow it to grow in time the strain will be more. See if this delta t is larger and larger and you integrate it over a large interval of time this will be trivially more and more. So measuring strain in a fluid is nothing that is important. It is just a function of the time that has elapsed. What is more important is the rate of deformation or the rate of strain. So the rate of strain along x what is that? It is basically this divided by delta t as delta t tends to 0. So when we say rate that means the time rate we always implicitly mean that. So that will be simply the partial derivative of u with respect to x. We may give it a shorthand notation say epsilon dot x. Similarly just from your common sense you can say what will be epsilon dot y and what will be epsilon dot z. So what is epsilon dot y? Epsilon dot z is this. So we have been successful in finding out a very simple thing. What is the rate of linear deformation along x, y and z in terms of the velocity component. So if you are given u as a function of position v as a function of position and w as a function of position by simple partial differentiation it will be possible to find out the rates of change. Now we are interested not only just in terms of the rate of change in the linear dimension but may be rate of change in the volume. So to understand that what is the rate of change in the volume let us say that we are having this fluid element which has dimensions along x, y, z as delta x, delta y and delta z. So we set up coordinate axis as this is x, this is y and this is z. So delta x, delta y and delta z. Now what is the new length? So we are interested to get the new volume. So what is the new volume? The new volume is new length along x into new length along y into new length along z. So what is the new length along x? That is the old length plus the change. So the old length is delta x plus the change is this one. So we can take delta x common and write this one. Similarly it is possible to write what is new length along y and new length along z. So let us complete those expressions. So the new volume is product of these 3. So what is the new volume minus the old volume? Yes. So what you have to do? You have to find out the product of these then subtract the old volume that is delta x into delta y into delta z. You will see that the first the delta x into delta y into delta z that term will go away will get cancelled. Then out of the remaining terms you have to neglect the terms of may be higher order in delta. So like if you have products like delta t square or delta x into delta t square that type of term you tend to neglect because those are higher order terms. So retain only the leading order terms because you have to keep in mind that you are dealing with the situation again as delta x, delta y, delta z, delta t all tending to 0. Then what will be the term that is remaining here? So obviously a product of these 3 is there. Then what is the remaining term? This plus higher order terms will be there. That into delta t. Other terms will be of order higher than delta t. So what is the volumetric strain? The rate of volumetric strain. So the rate of volumetric strain is the change in volume per unit volume per unit time just like what we found out for the linear strain. So when you say find out per unit volume you are basically dividing it by this delta x delta y into delta z. So this is like the original volume. Let us give it a symbol v with a strike through. So that is the original volume. So what is the rate of volumetric strain? This change in volume divided by volume divided by delta t and take the limit as delta t tends to 0 when all other higher order terms in the limit will be 0. So it is not that we are neglecting. The one delta t here will remain even after division by delta t that will be tending to 0 as in the limit delta t tends to 0. So then what will be the final expression of this? Some of these 3. So we may write it in terms of the total derivative. See the volumetric strain it may be due to many things change in time, change in position and a combination. So we are not bothered about that what is the individual effect? We are bothered about the total effect. What is the net change in the fluid element volume because of this? So this should be expressible in terms of the total derivative. So it is capital DDT of the volume with per unit volume. So this is the rate of volumetric strain and in terms of the vector calculus notation you can also write it as the divergence of the velocity vector. This leads to a very important definition. The definition is with regard to incompressible flow. So when we say that a flow is incompressible. So incompressible flow by the name it is clear that we are looking for a case when the fluid element does not change in volume. So incompressible flow it will have what signature one and only important signature 0 rate of volumetric strain because the fluid element may not be changing its volume that is the meaning of that is even the literal meaning of incompressible that you cannot really compress it. So 0 volumetric rate of volumetric strain and that boils down to the divergence of the velocity vector is equal to 0. So if you are given a velocity field and you are asked to check whether it is compressible or incompressible flow then it is possible to check by looking into the fact whether it is satisfying this equation or not. If it satisfies this equation we say that it is an incompressible flow. Keep in mind the distinction between this definition and incompressible fluid definition. So earlier we also introduced the concept of incompressible fluid and we said that a fluid is incompressible if its density does not significantly change with change in pressure. So that is incompressible fluid. Now we are talking about incompressible flow and these two are again related but different concepts that we have to keep in mind. So when you are having an incompressible flow it is possible to characterize the particular flow in terms of its mechanism by which it satisfies the overall conservation of mass. To understand how it does let us try to write an expression for conservation of mass of the fluid element. So we will now write conservation of mass for fluid, a fluid element. Let us say that m is the mass of a fluid element. You can express it in terms of the density and the volume. Let us say that rho is the density and b is the volume. Since the mass is conserved of a fluid element so there will be 0 rate of change of mass. So since we know already the expression for the volumetric strain and in that volumetric strain 1 by v appears it may be useful to utilize that expression by taking log of both sides and then differentiating because then 1 by v will automatically come out. So let us take the log of both sides and then differentiate with respect to time. When we say we want to differentiate with respect to time it has to be a total derivative. So because it is a fluid element now it may have change with respect to change in position time whatever we are bothered about now the total effect because the conservation of mass is not for individual effects. It is a combination of total effects that gives rise to a mass of a fluid element is conserved. So when we differentiate it with respect to time by keeping that in mind we have the left hand side like this which again becomes 0 because the mass of the fluid element is conserved. The right hand side 1 by rho so you have 0 equal to 1 by rho d rho dt plus 1 by v dv dt is what is the divergence of the velocity vector or if you write in terms of the Cartesian coordinates. Till you write it in a vector form it is coordinate system independent but when you write it is corresponding say components then the components depend on how you take your reference. So in a Cartesian reference it is this. Now let us write this one what will be this use the definition of the total derivative okay. Now you can multiply both sides by rho because density of the fluid is not 0. So you can multiply both sides by rho and then if you multiply both sides by rho what you get you get now you can combine these types of terms and write them in a compact form by using the product rule of differentiation. So this equal to 0 will imply this equal to 0 okay just by using the product rule of differentiation. It is again possible to write it in a compact vector notation this becomes divergence of rho into velocity vector that is equal to 0. This equation in a general understanding is supposed to be the most fundamental differential equation in fluid mechanics because no matter how complex or how simple the flow field is it should satisfy the law of conservation of mass. So this is a differential equation expressing the law of conservation of mass for a fluid element and this is known as continuity equation. So if you are given a velocity field you must first check whether it is satisfying the continuity equation. If it does not satisfy the continuity equation it is an absurd velocity field. It may be mathematically something but it does not physically make any sense because it has to satisfy the mass conservation. Now briefly let us look into certain special cases of this. So what are the special cases? The first special case we consider as steady flow. So when you consider a steady flow then how this equation gets simplified to? So steady flow means the first term at a given remember what is the definition of steady at a given position any fluid property will not change with time. So at a given position that is why the partial derivative with respect to time that means keeping the position frozen you are trying to find out the change in density with respect to time. So that is 0 if it is a steady flow. So steady flow will have that term equal to 0 so that will boil down to but that does not ensure that rho is a constant. Rho might not be a function of time but might be a function of position. So still rho remains inside the derivative it does not get disturbed. Let us consider a second case incompressible flow. We have to keep in mind that there is a very big mis-concept that we should try to avoid. What is that? Many times we loosely say incompressible means density is a constant. It is a special case of incompressible flow but it is not a general case of incompressible flow because general case of incompressible flow is what? The divergence of velocity vector equal to 0 that is the definition. Now where does it ensure that rho is a constant? That basic definition never ensures that rho is a constant. At the same time it can be shown that if rho is a constant then this will be satisfied. So the converse is true that means rho is a constant is a special case of incompressible flow but it is not a general case. What is the general case? Let us look into that. So when you are looking about the general case you have to see the continuity equation. So when you look at the continuity equation look into this primitive form that is not the compact form but the form before that. So here when you have an incompressible flow which terms will go away? These terms will go away because divergence of the velocity vector is 0. So then what you are left with is the total derivative with respect to total derivative of density with respect to time is 0. So that means incompressible flow means d rho dt, capital d rho dt equal to 0. See a very interesting thing it does not mean that rho is a constant because rho might be a function of position and time in such a way that this collection of terms eventually gives rise to 0. If rho is a constant this collection will definitely give it to be 0 but that is a trivial solution. That is a trivial solution to the case that is rho is a constant therefore any derivative of rho with respect to time or position is 0 but even if any derivative of rho with respect to position and time is not 0 still the net effect may be 0 and then even though rho is a variable we will say that the flow is incompressible. So a variable density flow may also be an incompressible flow. This is a very important concept. So incompressible flow need not always be a constant density flow. So a typical example is let us say that you have a domain like this. Within this there is a fluid. Now this fluid changes its phase say it was in a particular phase say it was in liquid phase now it becomes a vapour phase. So when it becomes vapour phase it becomes lighter. So the same mass now cannot occupy this volume. So there is so it wants to occupy an extra volume but given a particular volume what it will do some extra mass will leave because you are constraining the volume and if you are having a change in density you must have a flow to accommodate that change in density so that whatever fluid is there now is accommodated within the volume that was given to you. So you can see that you might have a change in density at a fixed position with time because maybe with time the phase change has triggered. So with time the density has changed. So this has to be now adjusted with some uvw so that the net effect may still be 0. So it might also happen that now here the net effect it may be 0 it may not be 0. So let us let us take an example where the net effect is 0. What is that example? Maybe there was a fluid now it is getting frozen and because of freezing its volume gets changed so it is possible. So its density has got changed but we do not call say liquids or solids as compressible fluids. So what has happened because if with freezing there is a shrinkage then there will be a deficit in volume here. Maybe to satisfy that deficit in volume there might be a material supply from all sides. So it is possible that to make a balance of what is happening locally and what is happening over the volume element you might have to adjust these things with velocity across the different phases of the element. So in summary we can say that incompressible flow definition is the total derivative of rho with respect to t0 but not just rho is a constant. We will stop here today we have just seen one way of deriving the continuity equation but we will learn more by having different ways of deriving the continuity equation and that we will do in the next class. Thank you.


This is stock number 10232. We are here at Summit Automotive in Fond du Lac, Wisconsin near new and used heavy-duty truck headquarters. Today we are checking out this super clean 2010 Ram 2500 crew cab short box. This truck has the 6.7 liter Cummins diesel and from this HD video you will be able to tell just how clean this truck is all the way around inside and out. Bright silver metallic is the color we shoot all of our videos in 1080p so if you have HD capabilities on your computer tablet or smartphone device, whatever you may be watching this video on, turn them on right now because it is like you're right here looking at the truck with me and definitely your best way to check out the vehicle before seeing it in person. Lower rockers look really good as factory chrome step bars, factory polished aluminum rims, BF Goodrich Rugged Trail LT2 6570R17 tires with about I'd say 70 to 80 percent of the tread left. Frame and underbody is really good looking on this truck. I didn't see any dents or dings on that front fender. The headlight lenses are nice and clear. The front bumper is in excellent condition. I didn't see any dents or dings. The lower valance is in nice shape. The grille is in nice shape and I didn't see any dents or dings on the hood. Passenger side rim, really nice condition. I didn't see any corrosion, no scuffs. As you go down this side of the truck you can see just how clean the body is, how reflective and mirror like that paint is. Didn't see any dents or dings on the box. Cab is in excellent condition. We take these HD videos so if you are far away or even if you're close by and just cannot make the trip down you can still see the truck, hear the truck and have confidence in the vehicle that you're looking at before you even get here. And for a 2010 for the rockers to look this good you know it was well cared for in a very low corrosion environment. Has all the remaining factory exhaust has not been modified in any way shape or form and the back tires have just as much tread as the front tires. This back rim, nice condition as well. As you come around to the back of the vehicle rear bumper is in pretty nice condition. One tiny little ding that I saw but other than that that's really the only imperfection I saw on the entire outside of the truck. Tailgate in nice shape, does have some reflectors on there. Not sure the brand of this rolling tonneau cover but it's a nice condition and it does have a curtain sliding fifth wheel back here that is included with the truck. A drop in bed liner and yeah some really nice condition. Tailgate truts nice and solidly. As you go down this side of the truck just as clean as that passenger side. No dents or dings on that box side. And for full disclosure this back rim is an excellent condition as well. Yeah it doesn't really say a brand name on the tonneau cover here. My guess would be like a retract or a pace Edwards or something similar to that. Driver side doors are in excellent shape as well. It does have the fold out tow mirrors so they go like so. They are heated and they also fold in. They have built in directional signals and they are power, power windows, power locks, power mirrors. The SLT package gives you the gray cloth interior. There are no rips, there are no tears on the seats. They are in really nice condition. Power driver's seat with lumbar, factory floor mats throughout. This one does have a factory brake controller, auto headlamps and power pedals, audio controls on the back of the steering wheel. And as you hop inside the truck here you can see instrument cluster is very nice and clean. This one has 85,156 miles. Unbelievable for the condition of the truck. How many miles are on this truck but just really nice condition. Has an outside temperature, compass display, can do fuel economy on there as well. Leather wrap steering wheel that's in really nice condition. Cruise controls on the right and information center controls on the right and left as well. Six speed automatic transmission. This one has the 430 radio, AM, FM and Sirius XM radio capabilities. You do get turn dial four wheel drive, factory exhaust brake and all your climate controls right there. 115 volt, 150 watt plug-in. Passenger seat is very clean as well, no rips or tears on that. The headliner is in excellent shape. This truck's never been smoked in, smells very clean. You do get map lights, power sliding rear window and an auto dimming mirror. We will take a quick look at the back seats and then we will check out under the hood. The back seats are just as clean as the front seats as you'd expect. Has latch child safety system, power sliding rear window. That latch system is right there, those are the hooks. Storage under the rear seats, very clean as well. Has factory floor mat back here and the carpeting is very clean too. In-floor storage bins which are removable for easy cleaning, you can put ice and drinks in there and it's like you have too many coolers wherever you go. Also has child safety locks for the back doors and we will take a quick look under the hood. I would personally like to thank you for checking out the video today. Hopefully from this HD video you'll been able to tell just how clean this truck is all the way around inside and out. Under the hood we have the 6.7 liter Cummins diesel engine bay is very clean, runs very smooth. This truck has been fully safety and inspected by our service shop has a fresh oil and filter change. All the fluids have been checked and topped off. The truck has been gone through mechanically 100% and is 100% ready to go. I would highly recommend this truck from a quality and condition standpoint. And to see more pictures of this truck or one of our other 450, new and used cars, trucks, SUVs, minivans, wranglers, halftones, three quarter tons, one tons, you name it we got it go to our website www.summitauto.com. Full pictures and descriptions of every single vehicle from two locations all at summitauto.com and if you'd like to check out more HD videos you can go to youtube.com slash summit auto. Remember to like, subscribe, and share on this video and all the videos that you see there. In fact in a second you will see a link to subscribe to our YouTube channel on your left. A link to more heavy duty truck videos like this one on your right. If you have not been to our website on the bottom link to this vehicle on our website click those check us out and we really look forward to helping you with this super clean 2010 Ram 2500 crew cab short box. Thanks again.


The use of antibiotics in livestock farming has been increasing globally, leading to increased antibiotic resistance in both humans and animals. This study found that global antibiotic usage will continue to rise unless more stringent regulations are put into place. The authors suggest that countries should make their own antibiotic usage data publicly available so that it can be monitored and regulated.


Okay. Good afternoon and welcome to Vermont House Judiciary Committee. And it is Tuesday, February 16th, and we are considering continuing our discussions on age 87, which is an act relating to establishing a classification system for criminal offenses. During our discussions, the issue of restitution and when restitution is paid and how that works has come up a number of times in terms of considering the sentencing commission's recommendations and age 87. So I've asked Chris Fenno from the Center for Crime Victim Services to come and testify and explain to us how the program works. And thank you, Chris, so much for your patience. I think we had to cancel you one day and you've been waiting a long time already. So anyway, thank you. And I know that Robin Joy is also here to chime in. So good afternoon and welcome. And for the record, this Chris Fenno, I'm the executive director of the Vermont Center for Crime Victim Services. And I just want to preface my remarks by saying I think that issue that the impact that this kind of a bill and reorganizing fees and fines has on victim services in the state will make an impact. But this is what we're talking about in lots of different places. We saw and we have seen continuing declines in that revenue. And Vermont really funds victim services a lot through special funds and through these funds. So that said, when I came to the center four years ago, I had never really worked around and didn't really understand restitution. And I think people often get restitution and compensation confused. So I'm going to start with the easy one, which is compensation. And the compensation program here gives financial assistance up to $10,000 and there is a cap on that. For crime victims in Vermont who have uninsured crime related expenses arising from a violent crime. And this program is running in conjunction with the federal government who reimburses the state 60 cents for every dollar that we spent. So we get revenue from it. And then we give that out. But the important thing about victims compensation is that it's not to fix anything that might have gone wrong in the commission of the crime, unless it is physical, unless it's somehow affects the victim. So if they need mental health counseling, they need a broken leg fixed. Victims compensation is also the payer of last resort. So if they have insurance, the insurance is going to pay. If they have a copay attached to that or deductible, then victims compensation can pay that. All of our payments are to providers. They're not, it's about things that have happened to an individual or to a family. But what we do is we pay providers who on their behalf. There's something that has greatly increased in my time here with compensation. And I, and, and maybe Robin knows the answer to this I don't know but we have, we pay out a lot for homicide victims families. And it has became it has become quite pricey because a lot of times they they're out of state. We had to bring somebody in from Alaska.  But when there's a homicide, any of a group of qualified family members can get $10,000 each. So we may have five men family members that need to come in, and they each could do up to $10,000. There are limits placed on travel there are limits placed on funeral costs, crime scene cleanup and those kinds of things. But, but it's victim compensation is really about having this benefit. Folks of violent crimes who have things that they need to have physically done. So if they get robbed. If they get their tired slashed. If they get their door broken down. These funds can't be used for any of that at the center we have four and a half staff positions that work in this program for full time people the halftime person runs our sexual assault program. And the other thing that's important about this is that there has to be probable cause established. So we actually, if it's not reported to law enforcement that and this is a federal regulation that we can't assist because there really does need to be probable cause that it's a crime related injury or loss. That's the easy one. And maybe restitution is easy to I don't know, but restitution is really about the courts who order restitution on sentencing. And they order it based on loss. So I, I got my door broken in down and it's going to cost $300 to fix it. But the judge can order $300 and restitution to be paid. There are, you know, I got robbed and I lost my paycheck that I just cashed and there was $500. They could order $500 restitution at at sentencing. Judgment has to be issued by the court. And there are only certain. Well, let me go back one second. There's two kinds of victims that get served through restitution individuals and businesses or companies. We help both of those groups. We are restitution unit manages all of the restitution for crimes in the state. And it's collected for all crime types. So with businesses, it could be a state agency, commercial business stores, banks, that kind. And then there's the individuals who are crime victims. If you're an individual and a crime victim, oftentimes the restitution ordered is under $5,000. And if there are qualifying items that need to be replaced. We don't we don't replace money, but we do replace things like. I don't know my phone. And you know you need a new cell phone. So as long as we can get a cost associated with that. We, through the center will upfront the restitution to individual crime victims up to $5,000. And at that point then the victim is done. And it goes to our collectors, who then work to get that restitution paid back into our fund. We don't do it for businesses. But we do do it for individuals. We have the ability like collectors of child support. For instance, we have the ability and the power to attach wages to take lottery winnings to take cash that they've forgotten that they have that is held by the state. We actually do all of that. We also have the ability to place leans on property. And we work should the perpetrator die. And there's an estate we will work with that estate to recoup the restitution or to get the restitution for business. We have six staff that work pursuing unpaid balances. And each one has about 700 cases that they're working on at any given time. They reach people by phone they make payment arrangements. We have people who on, you know the same day every month we run a credit card for them because they can pay $20 a month on that credit card. We have a victim liaison and supervisor, and that's to work with victims so that they understand what we can reimburse them up front. They get all their restitution ultimately but if it's over $5,000 they don't get it, or if it's money or jewelry. They don't get that part back until the offender pays us. Right now, we have 9,924 active accounts for 4,922 offenders. Under law, we can seek any monies owed to the state by the offender. And so that is exactly what we take as our mission for the restitution unit. We certainly give prior notice around tax returns and all of that we have to follow. There's lots of rules and regulations that we have to follow so that people know that we're taking their money. But it is a way that people can get reimbursed at sentencing. At sentencing, they do take, my understanding is that they do take into account ability to pay back the funds. We have people, especially if they leave the state, we're unable to find them. They do a lot of skip tracing the collectors do. But if somebody moves out of state, it's really pretty impossible to do collections. Sometimes we get repaid when somebody applies for a job, we had somebody who applied for a federal job, and they were going to do a background check. So, he sent us a check for $12,000 to pay off his restitution, so that that wasn't on his record anymore. So, oftentimes it's done like that. If we have a lien against a property and they want to refinance, they'll pay us back, well, they'll pay us then. But many, I mean, many people who are paying restitution don't have a lot of money. And so, we really try to work out what is going to work for them. It's, you know, we're not like those credit card agencies who hound people. We really, we don't hound people, we make up plans. If they don't stick to the plans, we'll try to reach out. But it is kind of the Wild West is how I feel when they're all over there working, because they all have headsets, they have automatic dialers, they, you know, the whole thing. The interesting part, which I want to bring back to the center, is that this ultimately is a victim's service, because for anybody who has been, who has gotten an award under $5,000, they can be done with what has happened to them. And it is an important thing, because if they had to negotiate themselves, go back to court because, you know, they're not getting paid for whatever. And this happens a lot in domestic violence cases. The truth is they don't ever have to deal with that person again, we get to. So, so it really is a victim service that we offer. And it, it does pay for itself through the victims, restitution, special fund. So that's the easiest way I know how to explain those two things but certainly questions. Thank you very much and I'm actually going to ask representative Norris because Bob I know you had, you had questions. So I want to make sure that you, that you have a better understanding now. I do have questions yes thank you. Great. I have a lot of questions and I'm not going to try to take up all of your time here because other folks may have questions also so it's my understanding that you are funded through the state of Vermont. We're a small state agency, a small state agency funded. Pardon, are you funded again. Well, we, we, these are just two of the things that we do. We also have grants program that we administer a lot of federal money for victim services. It's probably about $6 million or $7 million a year that we, we grant out to nonprofit and minds of organizations to do victim services. And then we support the victim advocate program which is having an advocate in each of the state's attorney's office. All of it's through all of that on the federal funds on the federal funds we are, we're allowed to take about anywhere between 5 and 10% of the pack of the money and pass through the rest. So that covers part of our administration. And then we also pay the out of the restitution fund, the cost of the restitution unit under the compensation fund, the cost of the workers under that, and then part of our administration. We don't get any state general fund to support the center.  We do and we, we, we also administer one other fund, which is the domestic violence sexual assault fund, and 100% of his pass through to the network programs. Okay, but it appears as though that when restitution is ordered that you simply front the money for victims. Yes, and then attempt to sell on a six month basis on a yearly basis or whatever. What is your accounts receivable look like as far as recouping these monies that are ordered through the courts. Okay, I have I do have an amount. Last year in 20 FY 20, a total of not quite a million dollars 987,648 dollars was ordered in restitution. We advanced about a $257,000 to victims. And by actually yesterday. We had collected $52,000 of that. So that's not good. Well, it's not but our, our restitution fund is pretty robust because it, it is fines and, and people who get sentenced through the remote process. Right, but, but part of the restitution is, is for the lack of a better term, a sentence handed down from the court to an individualist says, you must pay this and then as it turns out, probably two out of 10 do it would appear. You're looking at $50,000 on receivable. They actually do pay it. It may take a while. I'm sorry. So why are your accounts receivable so high, Chris. We're dealing with a population that doesn't have a lot of disposable income. So the judge has taken that into account when they ordered it. And then we take that into account as we're trying to collect it. So it truly might be $10 a month, and they may owe, you know, $7,000. It takes a long time. Okay, I'll, I'll ask one more question in case someone else has a bunch of questions here. Over the course of a year or two years, whatever else, what do you actually write off, as far as we're not going to get this.  So it could be just forever until until they pass 20 years. Yeah. Every, every month we actually have a report given to the board. I would say it states how many offenders have died in and if we're writing anything off then. Now sometimes, especially if it's a large amount that has been ordered. And somebody dies. We will make an arrangement for to take less. So, you know, we are, we do have some flexibility to. All right, so I know I said I was from my last question, but this will be my last question. So, in the terms of, does everybody pay. Most people pay people who leave the state, we have a hard time collecting from until they move back to the state. Okay, so so those are the monies that I'm concerned about those monies are left in a limbo, shall we say. That's what I was trying to get a figure on that. But that is because we just we always try to get payment, even if they leave the state will try tracking them out of state. But it's very different. Okay, I think it's great for the victim. So I think it's a great program for the victim to social. I just want to make sure that the other end is living up to their responsibility sort of speak. Yes, and the, the thing with it is that at one point, we also were fronting up to $5,000. Actually, I think it was 10,000 then up to $10,000 for businesses to, but it became too costly for us, because a lot of the businesses were big businesses and what we really wanted was the mom and pop stores that that kind of restitution that got ordered but we couldn't do that we had to say okay we're only going to do individuals, because if we said we were going to do some kind some types of businesses then the banks and the grocery stores and everybody else could come in and demand that we give them that money to upfront. My experience is it's the small businesses, whenever we do public events where we're looking for feedback.  Okay, thank you all that somebody else chiming here thank you Chris. Yeah, thank you because we just have very few minutes left I do want to adjourn on time so Barbara and then Martin. Hi Chris sorry I'm just beginning. So, I want to, and you're presenting I know Thursday right in. Yes, I will be there so that's good, but you said a few minutes ago that your state agency, and I would say, you're not state employees. We're not. So you're not a typical state agency that gets funded like a state agency and I think it's just important we kind of set that stage you're not like the defender general's office or the. So, when you're doing your budget. You need new software are your, your bills called how are you funding your general operating expenses. A lot of it is from this 5% on the federal funds, and our special funds, and you're right, we, we are not state employees. When the center was tasked with victims compensation, and the legislation shows this is that it's in statute that we couldn't be state employees. So we are not state employees however, because we're a state agency. We work with we just recently because of coven needed people, all of our staff when coven hit, we had to lay off a lot of people we had to furlough them because they couldn't work from home. So we just got a virtual private network through the state and upgraded our speed and so all of that goes through the state. But we, you are correctly are not state agent, we are not state employees. And your subcontracted victim advocates are state employees now right. They are, well, they are, I think, doors their state there, they receive those right okay. Yeah, they do. So, it's interesting, because again, I think you're the best deal in town I don't know anyone that charges 5% admin. I mean, so, in a way, you have an unsustainable I think Bob is on stuff like on all fronts you have a very unsustainable business model. And I don't know if that's government ops that looks at your structure, but I was just thinking about the forfeiture bill that we were talking about the other day and how, in certain cases, we, and people in this room know that we really have this thing about towers being able to get people's cars. So in some cases, we are allowing people to take people's money. Same thing with like child support. So, I'm, I'm not saying we should open the floodgates and do that here but it's just again like quite a tale of two different ways that you're really helping victims and that's not your fault I feel like you're doing everything you can, but I'm really concerned about the structural setup of your, of your office like it feels like as hard as it is for any of the state offices like you've got like a mountain to climb to get, you know, something so I love to figure out who is that government ops Maxine, because it is yeah I think I think it is and, and we can, we can just you know continue with discussion. I don't know about another time offline but I think it really is, is government operations and right now we're focusing on age 87 and have restitution comes does or doesn't come into play but but no and at some point we'll have the discussion about use of fees and so fun, you know, right, because it would seem that they would need at least some grant that sort of buffers your, your, you know, your bad payments and I'd love it if there's another state that is, you know, set up in a different way that we should be looking at because this is really like, you know, not a good model. Right. Yep. Yeah, and we're going to talk about that on Thursday too. All right, well, thank you and Martin you get the, you get the last word. I have a couple questions and kind of focus on on some of the property crimes that we're looking at in age 87. So you talked a little bit about businesses and small businesses. The courts, the courts still order restitution you don't have anything to do with the actual ordering of whether there's an order for restitution or not right. No, I guess the question is, since your organization has the ability to collect through wage garnishment and one of the things you mentioned through lottery winnings through probably I assume tax returns as well. I mean, are those things available to businesses and how would they be if they don't have an entity like is like yours to be able to provide that collection component or so. We still collect for them. Okay, all right. We collect for businesses. Okay, it's just that we don't advance them money. Gotcha. All right, that's great. Thank you. And how often do you use wage garnishment to. We're the last one on the list so we don't that's not usually a place we go because child support is the number one piece that they're taking off. And, and so it really, it's mostly surprisingly enough lottery winnings unclaimed property and tax returns. And you only can take so much from a wage garnishment. There's a like a cap or, or a floor I should say on that is that correct. That is correct. All right. I think that was all the questions I thought I had one more but that I think that's my main questions. Thanks. Great, and I have written testimony that I'll send to you all that talks about all of this. Thank you. Thank you. And we certainly can, can get back to this at, at another time I do like I said just want to keep to schedule because other folks have have meetings. Coming up very soon has been a long day so thank you and Robin I'm sorry we didn't get to you but we will definitely see you again when we take this bill. Again. Okay, so. So Barbara is your hands still up or is that from before. Okay. All right. So, so committee we did obviously did not get to our budget discussion but we'll do that with Barbara tomorrow afternoon. And any questions before we go off YouTube and adjourn. Just procedural questions or anything like that. Nope. Okay, well thank you very much.


In this presentation we will discuss what will be included or should be included in inventory costs. So when considering inventory costs clearly we have the cost of the inventory which would be included but there are other components that we want to keep aware of and keep in mind that could be included in the cost of inventory as we record that inventory cost that purchase price or the amount in dollars of inventory on the financial statements. One is going to be do we have to pay for the shipping costs and that typically will have to do with the terms of FOB shipping point or FOB destination. It's going to be a common question that is asked and a common factor in practice that we need to consider if we're saying that something is FOB shipping point for an onboard shipping point then we're saying that the inventory is trading hands and is the responsibility of the person purchasing or the company purchasing at the point in time that it is being shipped and typically then the person purchasing would be in charge of the shipping costs to get to the point of destination or warehouse. If that is the case if we're paying for the shipping costs in order to get the inventory in place it's the same kind of circumstances as if we are purchasing a property plant and equipment in that we need to include those costs into the cost of the inventory as we would to the cost of property plant and equipment if we were purchasing property plant and equipment. Anything that we had to pay for the cost of basically getting that inventory to us and ready and it's prepared for the sale should be a cost that is part of the inventory. If on the other hand we're saying it's FOB destination then typically the person purchasing or the company purchasing is not responsible for the shipping costs and therefore it's not an issue. A typical question however on it on a multiple choice question will be on the shipping cost how do you record the shipping costs and one of the answers will typically be you're going to record shipping costs as freight expense and the other would be that you're going to record it as the cost of the inventory and freight or shipping expense sounds really correct if you paid for the freight. However you paid for the freight in order to get the inventory which has not yet been sold and in accordance with the matching principle then we can't record the expense or should not record it until we have used that cost in order to help generate revenue. We hadn't used the cost yet in order to help generate revenue we only used it in order to acquire an asset inventory which we will then use to generate revenue in the future and then expense that shipping costs as part of the cost of the inventory in the form of the expense of cost of goods sold. A consignment is another thing we want to keep in mind we might get a couple questions on a consignment and certain types of industries would benefit from this kind of arrangement so a consignment would mean for example if we had someone that had a farm and they were producing wine then they could sell that wine of course to something like a restaurant directly the restaurant then paying for the wine and then selling that wine to their customers if that's the case then the producer of the wine would record revenue at the point of sale. However it is possible to have a different type of arrangement it is possible for our producer to go to the restaurant and say hey I would like to sell the wine here if you if you sell it great you can pay me at that point in time if you don't sell it then that's okay we won't charge you for it at that point in time and if that's the case then we're saying that we're only going to have the wine in other words the wine although it's located at the restaurant is still the inventory or the property of the owner of the wine the producer in this case of the wine and the restaurant is just there to provide the sale and at the point of sale as they sell the wine then they would take some of that take you know a cut of that and give the difference to the consignor so in this case we're saying the wine producer is the consignor giving the wine to the restaurant and the restaurant has possession of the wine however it's not the restaurant's inventory and that's the key points here the inventory although it's located at the restaurant would be the inventory of the consignor the producer in this case of the wine the consignee is just going to be holding on to the wine and at the point of sale typically we'll get some type of payment of course for the service of the sale transaction and give the consignor that the revenues for the sale of the wine as well next we have the discount the purchasing discount now note this also often gets confused in terms of what is a purchasing discount between the sales discount if we're the owner and we're purchasing the merchandise that we are later going to sell then the vendor that's giving us the merchandise could give us a discount and the terms might look something like this 2 slash 10 in dash 30 meaning we're going to get a 2% discount if we pay within the discount period 10 days otherwise we need to pay within 30 days if we do take that discount if we get the discounted amount then that's going to affect the inventory meaning if this was the sticker price and that's what we were going to pay but we get a 2% discount we have to then decrease the inventory of course by the amount that we actually paid for the inventory so we need to keep that in mind to to reduce the inventory for that discount when we record that it could be a little bit confusing because students often get or we often get mixed up when we have a sales discount and a purchase discount the purchase discount will reduce the inventory a sales discount the discount will go to sales returns and allowances so this is a common question common multiple choice we'll ask about the discount and a journal entry related to it and it's a common mistake that will happen that we don't we often miss the fact that we need to reduce the inventory by the amount of the discount some other costs that we need to consider would be tariffs if we have tariffs we're going to consider those in terms of the cost of inventory that's related to our inventory purchase storage also something that's going to help us to get the inventory ready for the point of sale and therefore a cost of the inventory insurance on the inventory against something that's necessary for us to get that inventory and get it ready for sale therefore it is a cost of the inventory if we have damaged or obsolete inventory then we're going to have to go through kind of a thought process and say well what happened to the inventory what are we going to do with it so it would look something like this we can say well can the inventory be sold if it was damaged inventory or if it's obsolete in some way is it still something that is sellable if we say that it is sellable then we're still going to include it in inventory but at a reduced price we're going to use what they call the conservative and principle conservative principle meaning we don't want to overstate our books we want to we want to make sure that we're basically recording at the lower price the realizable price realizable price that we could get on the market to sell that inventory if it cannot be sold then we're going to have to not include an inventory we're going to have to write off the loss at the point of time that it's been determined that the inventory cannot be sold note that this is a huge component all these are huge components but this one in particular is a huge component to inventory this idea of the conservatism principle because note that we typically record the inventory as most assets at the cost of of the inventory and if the inventory is damaged or goes down then that could be one something that's not as easy to determine and two obviously the company doesn't really like the idea of having their inventory be marked down and may not have the best method or know exactly what the realizable price for the inventory that is obsolete or damaged would be and it could be a significant factor on the financial statements to have these this inventory be written down to the appropriate price whatever that net realizable value is


Hi, I'm Walter from Hannover, Germany. I'm part of Medinetzernurfer, an NGO which helps people without or with limited access to the regular healthcare system. We support especially undocumented migrants to get adequate medical treatments. Undocumented means that they have no permit to stay in Germany. In Germany, although it seems to have one of the best healthcare systems in the world, there are hundreds of thousands of people who can benefit from this system. People who ask for our help are for example undocumented migrants, but also unemployed EU citizens and even some German citizens can't visit a doctor or receive medical treatments. The situation of the people who contact us is already difficult in normal life, but with the spread of COVID-19, their situation has worsened. Our clients have a lack of information about the situation, often problems to build up an effective care routine and inadequate access to tests and medical help. Therefore, they are in an even more threatening situation than the general public and especially undocumented migrants are in fear of becoming visible for governmental institutions and ultimately being deported to their countries of origin. This situation requires a humanitarian reaction of the governmental institutions in charge to improve the situation of these vulnerable groups and beside, it's not only a humanitarian decision, but also an element to interrupt the spread of COVID-19. From this point of view, it could save lives in several ways.


Dear pandemic backslash S readers had diverse information needs during the COVID-19 pandemic. Question box submissions were categorized into six overarching themes, scientific and medical basis of COVID-19, COVID-19 vaccine, COVID-19 mitigation strategies, society and institutions, family and personal relationships, and navigating the COVID-19 infodemic. Topics related to viral variants, vaccines, and mitigation strategies followed the news cycle and reflected the anticipation of future events. As time went on, more submissions focused on how the virus affected family and personal relationships. This shows that readers' information needs evolved as they navigated the COVID-19 pandemic. This article was authored by Alexandra M. Golos, Sharith Chandra Guntuku, Rachel Pilchlobe and others. We are article.tv, links in the description below.