Hello and welcome to lecture number 32 of this lecture series on turbo machinery aerodynamics. We have been talking about the different types of turbo machines and with a stronger bias or emphasis towards the axial flow turbo machines, basically the axial compressors and axial turbines. We have already elaborated the reasons why we are sort of giving little more weightage to the axial flow turbo machines, primarily due to the fact that modern day jet engines operate primarily with these type of turbo machines, the axial compressors and the axial turbines due to some of their inherent advantages. Of course, it is not to mention say that the radial flow counterparts are not being used at all. These are also having applications in certain specific areas primarily to do with the smaller sized engines and various other applications. And therefore, with this in mind we also initiated some lectures on the radial flow machines and we started off with the centrifugal compressors. In fact, it must be kept in mind that the earliest jet engines actually operated with centrifugal compressors and for a long time centrifugal compressors were used in most of the jet engines. And of course, once the axial compressors were developed and designed they sort of slowly replaced centrifugal compressors especially in the larger sized engines. But when you look at this smaller class engines, the thrust class smaller thrust class engines centrifugal compressors continue to be used in such applications. So, in with this in mind we had started the previous lecture with discussion on centrifugal compressors. And lecture 31 was devoted towards an introduction towards centrifugal compressors. We discussed the thermodynamics of centrifugal compression process and also the work done and we had looked at power calculations and so on and the governing equations which are involved in centrifugal compressor design and calculations and analysis. We also had quick look at the different components which constitute a centrifugal compressor like the inlet part of the or the intake of the centrifugal compressor, the inducer, the impeller, then the diffuser vanes and so on. So, we also discussed about how one can make calculations and analysis of these different components of a centrifugal compressor. So, that was what we had discussed in the previous class. We what we will do today is to continue some of our discussion which we had had in the last class and sort of wind up our discussions on centrifugal compressor with this lecture. And the next lecture we would obviously be having a tutorial because having undergone two lectures on an overview of centrifugal compressors, it is essential that we understand how one can make analysis and calculations on centrifugal compressors. So, we will devote the next lecture towards a tutorial on centrifugal compressor. In today's class, we will basically be taking up on few important concepts. We will start our discussion with what is known as the Coriolis acceleration. Then we will discuss about the slip factor, the performance characteristics and also stall surge and choking associated with centrifugal compressors. Now, we will start our discussion with Coriolis acceleration. I am sure you must have learnt at least heard about this term called Coriolis acceleration or called Coriolis forces. In your high school classes in your physics, I guess you must have learnt about Coriolis forces and Coriolis acceleration in sort of a very general perspective. We are going to use some of those principles in relation to our current topic of discussion that is the centrifugal compressors. Now, if you remember in one of the slides which I had flashed in my previous class, I mentioned that one of the aspects that distinguishes a centrifugal compressor from an axial compressor is the fact that in a centrifugal compressor, the pressure rise mechanism is slightly different from that of an axial compressor. In the sense that in a centrifugal compressor, pressure rise can also occur because or it primarily occurs because of displacement of the centrifugal or centrifugal force field. And because of that, there is a pressure rise taking place as a result of diffusion in the centrifugal compressor. So, there are these two components which contribute towards the overall pressure rise in a centrifugal compressor. I think I mentioned that the problems associated with the boundary layer flows are not that severe in a centrifugal compressor. This is indeed true that boundary layer separation is not it is still a matter of concern, but it is not the primary matter of concern like we have in axial compressors which also partly explains the fact that axial compressors can develop much lower pressure ratio per stage as compared to centrifugal compressor primarily because of the fact that axial flow performance is impeded by boundary layer characteristics. So, we will also try to explain in the context of centrifugal compressors. Let us also try to look at the pressure rise mechanism and deceleration or diffusion in the passages through Coriolis acceleration as a possible means. So, let us try to analyze what Coriolis acceleration does to this overall performance of a centrifugal compressor. Now, what we will see very soon is the fact that Coriolis acceleration is going to lead towards a certain discrepancy in the velocity triangle from the ideal characteristics that is the velocity triangle at the exit would be slightly different from what it should have been and that is attributed to centrifugal Coriolis acceleration and because of that it leads to certain amount of pressure loss as we will see a little later. So, what we are going to do is that we will consider a certain fluid element which is travelling radially outward in the passage of a rotor. So, before this let me just quickly go through these two bullets I have written here. The one is to do with centrifugal flow field which is primarily not a result of the boundary layer separation and basically that the fact that the pressure change due to centrifugal flow field is not really a cause of boundary layer separation. We will try to explain that with Coriolis forces. So, if you consider a certain fluid element which is let us say travelling radially outward in the passage and we will look at the velocity triangles of this particular fluid element during a certain time period d t. So, this is the fluid element that I am referring to let us consider a fluid element which is passing through these straight radial vanes. Of course, you can see that this is the impeller and these are straight radial vanes a fluid element is passing through the radial vanes which are straight. So, the fluid element obviously has a relative velocity of v and blade speed or rotational velocity omega r where r is the radius at which this fluid element is currently located and omega is the rotational speed. So, if you look at the velocity triangles for this fluid element in addition to v and omega the absolute velocity c is given by the resultant of v and omega r. So, he is the basic velocity triangle is shown by the solid lines and you can see v and omega r and its resultant is the absolute velocity c. Now, after a certain time period well the impeller is rotating that also displaces this fluid element by a certain distance. If we consider the fact that this fluid element is being rotated by this centre that is shown here then after a certain time period d t the fluid element deflects and therefore, the new velocity triangle is shown here by the dotted lines. So, new velocity triangle corresponds to a radial location which is equal to r plus d r where d r is the differential change in the radius with time d t. So, the new speed rotational speed becomes omega omega is unchanged omega multiplied by r times d r and let us assume the fact that there is negligible change in the relative velocity during this time, but because omega has changed c prime also changes that is the absolute velocity changes and it takes a new value which is c prime. Therefore, the net change in absolute velocity is given by d c which is as you can see a tangential component of which is shown by d c subscript w d c w which has two contributions.  So, here what you need to understand is that there are two distinct aspects which has led to this change in the absolute velocity or let us say the tangential component of the absolute velocity. So, there are two contributions here one of them is from the fact that the radius has now changed to a differential there is a differential change in the radius or radial location of the fluid element which is given by d r and that leads to a change in the peripheral velocity which is omega times d r. There is also a change our contribution from the fact that relative velocity being remaining unchanged for the fact that we will assume that it is unchanged because it is change is much smaller compared to the other components. So, v times d theta where d theta is the angular deflection angle through which the fluid element was deflected. So, these two components put together result in a change in the tangential component of the absolute velocity and at the moment we are going to be looking at this change in the tangential component and it is change with reference to time. So, d c w by d t is basically rate of change of the tangential component of velocity with time that is an acceleration and that is basically the Coriolis acceleration and that is primarily because of the fact that there is a rotation given to the fluid element. If the fluid element was displaced simply radially upward without any angular deflection Coriolis forces would be negligible there would be hardly any Coriolis force acting on the fluid element. But because of the fact that in addition to the fact that the fluid element is getting displaced radially outward there is also an angular displacement of the radial element both of these contributions put together results in this acceleration which we will denote as the Coriolis acceleration. Let me recap the velocity triangles once again. So, here in this velocity triangles the default velocity triangle is this. This is shown by the solid lines v and omega r v is the relative velocity of the fluid element omega r is the tangential component or the plate speed peripheral velocity resultant of that is c. When it is displaced we will assume negligible change in v because this magnitude is much smaller than any other magnitudes here. And so we have a new absolute velocity which we have denoted by c prime which is a resultant of omega times r plus dr and v and this change in the absolute component has tangential component which is dc w which has two contributions omega dr and v d theta. So, the sum of these two gives us the dc theta. So, let us add up these two now the magnitude of this change in the tangential component dc w is basically sum of omega dr plus v d theta or dc w is omega into dr we have expressed as v times d t plus d theta can be expressed as omega into d t. So, v into omega into d t. So, this basically would be equal to 2 into omega v into d t and therefore, dc w by d t is acceleration a theta that is acceleration in the tangential direction or a w or a theta as it is called it is the Coriolis acceleration is equal to twice omega v that is the Coriolis acceleration is directly a function of the relative velocity and the rotational speed. So, higher the rotational speed higher the Coriolis acceleration and higher the relative velocity obviously, that also changes the Coriolis acceleration. Now, this basically requires a certain amount of pressure gradient why is there a Coriolis acceleration in the first phase firstly there is a rotation given to the fluid element there is also a certain amount of pressure gradient which is leading to this Coriolis acceleration. So, if we were to look at the pressure gradient we can express the pressure gradient in the tangential direction as 1 by r del p by del theta that is the rate of change of pressure in the tangential direction which is basically equal to twice rho into omega into v. So, the radial pressure or tangential pressure gradient can be expressed in terms of twice into 2 into minus is basically referring to the fact that the pressure gradient is direction dependent and depends on which direction the rotor is rotating. So, minus 2 rho into omega into v. So, this is the amount of pressure gradient which is acting in the tangential direction and that leads to this much amount of Coriolis acceleration. So, the Coriolis acceleration basically requires certain amount of pressure gradient. So, what we will do is to look at the rate of change of relative velocity in the tangential direction and see how it is related to the or whether it is indeed related to the Coriolis acceleration or not. We have seen that the tangential velocity well Coriolis acceleration is in fact directly proportional to the relative velocity. Let us see the rate of change or is there a rate of change of the relative velocity in the tangential direction. So, if we look at the fact that there is a tangential pressure gradient, then tangential pressure gradient needs to result in a positive gradient of v in the tangential direction because if there is a pressure gradient in a certain direction that needs to also mean the fact that there has to be a velocity gradient in the same direction. And therefore, the pressure gradient in the tangential direction we have expressed in the previous slide.  So, this if you look at if you compare this with the Coriolis acceleration we can basically infer that 1 by r d v by d theta is equal to 2 into omega. And what does this basically tell us? This tells us the fact that there would be a change in the relative velocity in the tangential direction as well. Now, that was in an idealized scenario what would not have expected any change in relative velocity in the tangential direction. But we can now see from our analysis that in addition to the fact that the relative velocity will keep changing in the radial direction because that is what the centrifugal compressor does. There will also be a change in the relative velocity in the tangential direction and that is a very crucial piece of information for us because we will very soon see that this leads to a change in the velocity triangle at the exit of the impeller from what it should have been. So, from our understanding of the Coriolis acceleration we have seen that as a result of the Coriolis acceleration and eventual outcome of the fact that there will be a Coriolis acceleration due to the tangential pressure gradient. Tangential pressure gradient in turn leads to a tangential has to lead to a tangential velocity gradient and this velocity would be affected the component of velocity which is affected is the relative velocity. So, the relative velocity would have a tangential gradient that is it will keep changing in the tangential direction. So, if you look at this aspect in a schematic sense I mentioned that the let us consider the same impeller this is the same impeller we were talking about these are the two straight radial blades and as an outcome of the analysis we just have seen there will be a tangential variation in the relative velocity. So, these vectors which are shown here are basically the velocities relative velocities there is a gradient of this relative velocity in the tangential direction here plus and minus indicate the pressure or higher pressure and this would be the pressure surface and suction surface let us say in the case of an axial compressor blade. So, there is an increasing pressure gradient and correspondingly change in the relative velocity in the tangential direction. So, what happens because of this is that as the fluid element begins to leave the impeller that is if you trace the fluid element which was let us say here and as it leaves the impeller by the time it reaches the tip of the impeller because of this tangential velocity gradient in the relative velocity you can see that the relative velocity is lagging behind the radial direction. So, the relative velocity is actually now pointing in this direction because it is having a gradient in the tangential direction. So, because of the gradient the vector of the relative velocity leaving the impeller is inclined at an angle it is lagging behind the radial direction and therefore, what is the outcome of this? The outcome of this is the fact that ideally one would have assumed a radial velocity relative velocity is being equal to radial velocity that is no longer true therefore, one has tangential component in the absolute velocities scale that is C w 2 which is not equal to u 2. So, if you recall velocity triangles that I had shown in the previous class where I had shown three different types of impellers forward leaning straight radial and the backward leaning blades. For the straight radial blades please go back and take a look at the velocity triangle you will see that I had drawn the velocity triangle with the relative velocity v or v 2 in the radial direction which means that C w 2 would have been equal to u 2 that is an ideal scenario. Now, here we have seen that due to the Coriolis acceleration and its effect and the tangential velocity gradient there will not be a radial of the relative velocity will not really will not necessarily leave the impeller radially. So, there is a change or difference between the tangential component of the absolute velocity that is C w 2 and the blade speed at the impeller exit u 2. So, this change in our difference in C w 2 and u 2 is captured by a parameter which is referred to as the slip factor well slip factor basically tells us the fact that at the exit of the impeller the relative velocity is lagging behind the radial direction resulting in a change or difference in the tangential component of absolute velocity C w 2 as it should have been equal to u 2. So, the ratio of C w 2 to u 2 is called the slip factor and this difference in the relative velocities is basically expressed as a fraction and that is C w 2 by u 2 which is usually denoted by sigma and the sigma is a factor for actual blades it will be less than 1 and one would like to have a slip factor close to 1 because that means C w 2 will be equal to u 2 and it will lead to much higher let us say efficiency and pressure ratios for the same rotational speeds and impeller diameter. Now, slip factor is also a function a strong function of the number of blades you can see I have been I have shown two straight radial blades and you have seen that from one blade to another there is a tangential velocity gradient that means the larger the distance between the blades the velocity gradient will keep increasing and therefore, the slip factor would be or the difference between C w 2 and u 2 would be higher as we increase the blade spacing lower the number of blades the greater would be the difference and as you keep increasing the number of blades the tangential velocity gradient is lower and therefore, the slip factor is also likely to be lower. So, slip factor being strongly related to the number of blades people have come up with empirical correlations for calculating slip factor based on the number of blades one of the most commonly used empirical correlation is given by standards and that is known as the standards slip factor it is equal to 1 minus 2 by n where n is the number of blades which means if there are let us say 10 blades for straight radial blades the slip factor would be 1 by 1 minus 2 by 10 that is 1 minus 0.2 and that is 0.8 and if you increase the number of blades to let us say 20 then you can see that slip factor becomes 0.9 and so on and that is as we increase the number of blades the radial velocity of the change in the tangential direction of the radial relative velocity becomes lesser and therefore, there would be lesser difference between C w 2 and u 2 whereas, for larger spacing or lesser number of blades the variation in the relative velocity in the tangential direction would be larger and larger leading to much larger difference between C w 2 and u 2 leading to poor values of slip factor. And so slip factor being a strong correlation strongly correlated to the number of blades there are different parameters or different researchers have come up with different empirical correlation the most common one is what I have shown which is strictly applicable for straight radial blade for backward leaning blades the slip factor is calculated in a different way and there are different other correlations which are used for such blades and you will find in literature there are many more empirical correlations which are in some way or the other related to the number of blades. So, the basic effect of slip factor is the fact that it reduces the magnitude of the swirl velocity or tangential component of velocity leaving the impeller and since pressure rise is a function of this tangential velocity for lower values of tangential velocity the pressure rise also decreases that for slip factor directly affects the pressure ratio of a centrifugal compressor which obviously is not a good thing that a designer would want to keep for a given rotational speed and impeller diameter try to maximize the pressure ratio and presence of slip factor can bring down the pressure ratio because of the fact that it affects the tangential velocity. So, the out the way out of this is to use more number of blades well more number of blades means you will obviously have higher frictional losses and therefore, it is probably not a good idea to keep increasing the number of blades or other option is to increase the impeller diameter which is for a normal application a land based application may not be a big deal you can keep increasing diameter to some levels, but not for an aero engine application where you know it will increase the drag as well, but larger the diameter of the impeller the stress on the impeller blades also goes up which means then they will have to invest in better materials which can withstand higher stress or the other option is to increase the rotational speed and again if you increase the rotational speed for the same diameter that also affects this stresses on the on the blades and therefore, that again is a constraint. So, you can see that there are all kinds of constraints here in terms of stressing stresses on the blades or frictional losses. So, there is lot of scope for an optimization to be carried out here and to determine what is the best possible configuration for number of blades versus impeller diameter versus the rotational speed and that can give us the best possible efficiency as well as the pressure ratio. So, having understood slip factor and its effect on centrifugal compressor performance let us now talk about the performance of a centrifugal compressor in general. We have already discussed about the performance characteristics of axial compressors as well as axial turbines. Centrifugal compressor performance characteristics would look in some way similar to what we have already discussed for an axial compressor, but problems related to choking is a little more severe in a in a centrifugal compressor as compared to an axial compressor also centrifugal compressors undergo similar problems that we have seen for axial compressors like stall and surge. So, let us look at the performance characteristics of a centrifugal compressor and try to understand how we can estimate the performance of a centrifugal compressor. So, we will evaluate the performance of a centrifugal compressor in a same way as we have done for an axial compressor. We will look at the pressure ratio the dependence of pressure ratio and efficiency on a mass flow rate all of which of course, the pressure ratio and mass flow rate mass flow rate being non dimensionalized for different non dimensionalized operating speeds and we will very soon realize that compressors centrifugal compressors also suffer from instability problems like surge and rotating stall. So, I will make this a little quick because we have already done this for an axial compressor is exactly the same procedure the non dimensional groups are derived from dimensional analysis the exit pressure ratio or exit total pressure p 0 2 and efficiency are functions of variety of parameters like mass flow rate inlet stagnation pressure inlet stagnation temperature rotational speed ratio of specific gamma the gas constant are the viscosity the design as well as diameter. So, if you non dimensionalized this we get these many non dimensional groups p 0 2 by p 0 1 that is the pressure ratio efficiency being functions of m dot root gamma r t 0 1 by p 0 1 d square omega d by square root of gamma r t 0 1 omega d square by nu gamma and design. Now, for a given design and given diameter we can drop a lot of these terms and basically the pressure ratio and efficiency becomes function of mass flow rate m dot root t 0 1 by p 0 1 and n by root t 0 1 this is the non dimensional speed and this is the non dimensional mass flow rate this we will further process for a standard day pressure and temperature. So, we get p 0 2 by p 0 1 efficiency being functions of m dot root theta by delta and n by root theta where theta is t 0 1 by t 0 1 of standard day and delta is p 0 1 by p 0 1 standard day typical values taken for this are t 0 1 standard day is 288.15 Kelvin which is basically 25 degrees Celsius and pressure of standard day is 101.325 kilo Pascal. So, with this set of non dimensional parameters pressure ratio and efficiency being functions of mass flow rate non dimensionalized as well as the non dimensional speed we will now look at how the performance characteristics can be plotted before that let us first look at a very general characteristics which is applicable for any centrifugal compressor and then we will look at a typical performance characteristics in general. So, if you look at the variation of pressure ratio was mass flow rate one can trace characteristic like this ideally one could raise a characteristic like this there are several salient points which I have marked here point a b c d and e. Now, let us take a look at what happens as let us say the compressor was operating at some point e and then as the mass flow is reduced as we throttle the mass of the compressor and decrease the mass flow the pressure ratio across the compressor increases. And as it increases it reaches its peak and eventually you will see that after it reaches its peak the pressure ratio drops and this could this drop of course, could be very drastic as well in some compressors. In the case of axial compressor we have already seen what really happens the fact that when the throttle characteristics become well intersect the pressure ratio characteristics beyond a certain level the compressor undergoes what are known as instabilities. So, the exact same thing happens even in the case of centrifugal compressor beyond this point e where the slope of the pressure ratio mass flow characteristics is positive the centrifugal compressor undergoes instabilities and that is why b is referred to as the surging limit. And any point after the on the left hand side of b between a and b let us say point d would be considered an unstable point and the compressor cannot really operate in a stable condition there. We have discussed the stability in reference to axial compressors in quite detail and all those arguments are very much valid even for a centrifugal compressor. And on the other hand here we have the what is known as the choking limit beyond point e and little later the slope becomes extremely sharp and there is a very sharp drop in the pressure ratio characteristic and mass flow remains more or less constant and that is referred to as the choking limit. So, we will discuss choking in little more detail in relation to centrifugal compressor because these compressors tend to be affected more by choking and as compared to axial compressors and so we will discuss choking in little more detail and limit our discussion on surge and stall because that we have already discussed in relation to axial compressors. So, let us now look at an actual centrifugal compressor map performance map in terms of pressure ratio non-dimensional mass flow rate and for different non-dimensional speeds. So, if you look at the pressure ratio characteristics versus mass flow rate characteristics. So, the previous slide I had shown an idealized curve here we have seen that the curve on the left hand side is not possible and beyond this it chokes. So, the actual performance characteristic is limited between these two points b and e and that is what is shown here by these different lines. So, as you keep changing the speeds the performance characteristics also change and you can see that as a speed reaches its max of the design speeds the performance characteristics become sharper and sharper. For lower speeds one can see one can notice a shallower pressure ratio versus mass flow characteristics that becomes steeper as one proceeds for higher and higher speeds and all these lines are terminated on the left hand side by the surge line and on the right hand side by the choking line. And if you join all the points of maximum efficiency we get the dotted line that is shown here and one would ideally want to operate the compressor very close to this maximum efficiency line provided that of course this line is not very close to the surge line which of course can put the compressor into the risk of surging. Now, if you look at the efficiency characteristic again very similar to the axial compressor that we discussed like efficiency versus mass flow rate for non-dimensional speeds and with increase in speed you can see that the range of high efficiency becomes narrower. For higher speeds we have a narrower band of operation where the efficiency is high and it becomes very sensitive to the mass flow rate. For lower speeds of course efficiency is not is relatively lesser sensitive to the mass flow rate and there is a wider range of operation possible with higher slightly higher efficiencies. In comparison with an axial compressor we can see that even centrifugal compressors have a two aspects of or two lines which basically define the performance on left hand side we have the surge line on the right hand side we have the choking line. Now, between those two points on the map that I shown that is point A and B the compressor may undergo instabilities it could be a rotating stall which eventually leads to surge. Now, we have already discussed these instability mechanisms in fairly good detail I will just quickly mention what happens while a compressor undergoes some of these instabilities. So, basically the operation of a compressor in the positive slope of pressure ratio versus mass flow rate is unstable operation and the compressor cannot operate in that region in a stable manner. One of the instabilities that affect the performance is rotating stall and the more severe one is the surge wherein there is a sudden drop in the delivery pressure and of course, violent aerodynamic pulsations. And in the case of centrifugal compressor it has been noticed that in general the surging begins in the diffuser passages because I think I mentioned in the last class that diffuser passages are significantly affected by boundary layer performance. So, that is one of the weak links in a centrifugal compressor where the performance is very sensitive to boundary layer flow and therefore, surging has been in general observed to initiate get initiated in the diffuser passages. Now, in a centrifugal compressor the pressure ratio or the performance is also a type function of the type of blade that is used in a centrifugal compressor. In the last class we discussed 3 different possible blades blade configurations a forward leaning type a straight radial and backward leaning. Now, if you look at the performance of these 3 different types of blades and analyze the velocity triangles at the exit urge you to go back to the previous lecture and take up that slide where I had shown the velocity triangle for these 3 cases. You will notice that theoretically forward leaning blades produce a higher pressure ratio because if you look at the velocity triangle at the exit you would appreciate this aspect and one would expect forward leaning blades to be much better in terms of performance. But what is interesting to notice is the fact that forward leaning blades have an inherent instability because if you look at pressure ratio versus mass flow characteristic for forward leaning blade the characteristic always has a positive slope and we have just now discussed that operation on the positive slope of pressure ratio mass flow characteristic is inherently unstable and that is the reason I think I mentioned in the class class that forward leaning blades are not really used in centrifugal compressors because of the fact that they are inherently unstable. That is why straight radial and backward leaning blades are commonly used in modern day centrifugal compressor. So, if you look at the performance characteristics either in terms of pressure ratio or the temperature rise versus either mass flow rate or the flow coefficient a forward leaning blade would have a characteristic which is positive slope throughout. So, this is like the left hand side curve of a centrifugal compressor characteristic where of course this is idealized, but one would still get a positive slope throughout for a forward leaning blade which means that this blade is going to have instabilities irrespective of the mass flow rate and therefore, this is not a favorable type of blade that can be used even though the pressure ratio performance is much better than straight radial or backward leaning. So, these two configurations are the ones which are commonly used the straight radial and the backward leaning blades. So, what I will do next is to discuss about problem of choking which is what is probably little more severe in the case of centrifugal compressors as compared to axial compressors whereas, rotating stall and surge are still the limiting performance parameters on one side. On the other side we also have the choking problem associated with trying to increase mass flow rate and beyond a certain level of mass flow rate compressibility effects will prevent us from operating the compressor beyond a certain level of mass flow rate. So, let us take closer look at choking in more detail because we already discussed about the other instabilities in relation to axial compressors. So, as the mass flow increases in the case of centrifugal compressors the pressure ratio will decrease as we have seen in the performance characteristic and therefore, that also reduces the density. After a certain point one would not be able to increase the mass flow beyond a certain value the compressor is then said to have choked that is on this that is probably we have reached the right hand side of the performance characteristic wherein the mass flow rate has reached its maxima and we are not able to increase mass flow rate beyond that level and that is when the compressor is said to have choked. So, in a centrifugal compressor we have seen the different components which constitute a centrifugal compressor we have the inlet the impeller and the diffuser veins. So, calculation of the choking mass flow is different depending upon whether it is the stationary component or the rotating components. So, we will take a look at the choking mass flow as applicable for inlet the impeller and diffuser veins and see their dependence on the upstream parameters. So, choking behavior because it is different for rotating passages from that of stationary passages. So, if we consider the inlet we know that of course, choking irrespective of whether it is inlet or impeller takes place when the Mach number reaches 1. So, when Mach number is unity the ratio of static temperature to total temperature T by T 0 is equal to 2 by gamma plus 1 because Mach number if in the isentropic relation if we equate m is equal to 1 we get this relation between static and stagnation temperature. So, for the moment if we assume an isentropic flow then the choking mass flow rate is basically m dot a per unit area is equal to rho naught a naught into 2 by gamma plus 1 raise to gamma plus 1 by 2 to gamma minus 1. So, this basically comes from mass flow rate being equal to rho a v and we have expressed rho in terms of stagnation density and velocity in terms of the speed of sound. And here we can see that this mass flow rate is expressed purely in terms of parameters which are the upstream parameters or the inlet stagnation conditions which remain constant. So, as we keep changing the operating condition the inlet conditions are still fixed which means that the mass flow rate also has to remain constant and that is why when Mach number becomes 1 what you can see is that the right hand side of the mass flow rate equation has all the parameters which are basically constants. And therefore, when Mach number becomes 1 one can actually calculate the choking mass flow based on the inlet stagnation conditions. The next component that we will take a look at is the impeller in a rotating passage as we have seen the flow conditions are usually referred through the rothalpy which I had discussed in the last class. And during choking in the case of an impeller it is the relative velocity which basically becomes equal to this period of sound when Mach number becomes unity. And so if you look at the expression for rothalpy we have i is equal to h plus half into v square minus u square. And so and we know that stagnation temperature can be expressed in terms of the corresponding static temperature and the speed of sound. So, here we if we express enthalpy in terms of stagnation temperature and v square because when Mach number is equal to 1 v becomes equal to speed of sound. And therefore, that becomes gamma r t divided by 2 c p because enthalpy is t naught times c p minus u square by 2 c p. So, we have divided this by the speed of sound and therefore, we get t naught 1 is equal to t plus gamma r t by 2 c p minus u square by 2 c p. So, if you simplify that we get t by t naught 1 is equal to 2 by gamma plus 1 into 1 plus u square by 2 c p t 0 1. And therefore, mass flow rate which is rho a v again gets expressed as rho 0 1 a 0 1 into t by t 0 1 raise to gamma plus 1 by 2 into gamma minus 1 which can be simplified further. And what you see is that mass flow rate is equal to rho 0 1 a 0 1 into 2 plus gamma minus 1 u square by a 0 1 square by gamma plus 1 raise to gamma plus 1 by 2 into gamma minus 1. So, this rather complex expression for the mass flow rate once again tells us that in addition to the inlet conditions in the case of impeller we also see that it is a function of the rotational speed. And in the case of inlet we have seen that mass flow rate is purely a function of the inlet parameters and that therefore, mass flow rate gets fixed once the inlet conditions are fixed. In the case of impeller besides the inlet conditions you also have the rotational speed. That means that in principle it should be possible for us to operate the compressor at a different mass for at a higher mass flow than the choking mass flow for a higher rotational speed. Of course, this will also require that if once you start operating the compressor at a higher rotational speed the other components do not choke because if the other components choke the compressor will still remain under choke condition. So, other components permitting like the inlet or the diffuser the impeller performance or impeller choking because it is a function also of the rotational speed operating the compressor at a higher rotational speed may permit us to operate or deliver a higher mass flow provided all other components also are able to operate at this new operating point. Choking mass flow in an impeller is a basically a function of the rotational speed and the compressor in principle should be able to handle a higher mass flow with an increase in speed provided that other components like inlet or diffuser does not really undergo choking for this rotational speed. Now, the last component is the diffuser the choking mass flow in a diffuser has an expression the same as that of an inlet. So, it is again a function of the inlet conditions for the diffuser. So, mass flow rate is function of rho naught a naught into 2 by gamma plus 1 raise to gamma plus 1 by 2 into gamma minus 1. Now, here you can see that the stagnation conditions at the inlet of the diffuser depend upon the inlet of the diffuser itself which is the impeller exit and therefore, mass flow rate can basically be related to the rotational speed of the impeller and therefore, you can see that the operation of the diffuser and impeller are sort of coupled because the diffuser choking mass flow is a function of the impeller exit conditions and impeller exit conditions can basically be changed by changing the rotational speed and. So, there is a certain amount of coupling between the impeller operation and the diffuser operation and so with this analysis it should be possible for us to calculate under what conditions centrifugal compressor is likely to choke and how is it that we can operate still operate the compressor at a probably slightly higher mass flow by looking at the other components involved like the inlet and the diffuser and ensuring that all the three components can operate in under the new rotational speed without undergoing a choke. So, let me now quickly recap our discussion in today's class. We had discussed a few aspects which are an extension of what we had discussed in the last class. We started our lecture today with detail discussion on the Coriolis acceleration and we have derived an expression for Coriolis acceleration. We have seen that Coriolis acceleration leads to a tangential velocity gradient or velocity gradient in the tangential direction and that is what leads to a difference in the velocity that is leaving the impeller that is it leads to a certain amount of difference between C w 2 which is the tangential component of absolute velocity and u 2 and that difference is what is referred to as the slip factor. We have seen that slip factor is a strong function of the number of blades lesser the number of blades the greater the spacing between the blades the greater is the tangential velocity gradient and therefore, the slip factor becomes lower and lower. So, this can be that is with higher number of blades one can reduce the tangential variation in relative velocity and therefore, one can achieve higher values of slip factor. So, slip factor and its dependence on the number of blades we have seen the Stanitz formula where one can approximate slip factor as 1 minus 2 by n where n is the number of blades and of course, that is true for a straight radial blade. We have then discussed about the performance characteristics and of a centrifugal compressor of course, we did not discuss too much of the details of the performance characteristics because it is very similar to that of an axial compressor. We spend much less time discussing about surge and stall because we already discussed that and we have discussed slightly more details about the choking condition which is affecting which might affect a centrifugal compressor performance and how one can estimate the choking mass flow for the inlet the impeller and the diffuser and the interrelation between choking conditions for these three different components. So, this were the topics that we had discussed in today's class and so, this will sort of wind up our discussion on centrifugal compressors and therefore, the next lecture as I mentioned in the beginning we will basically take up few problems for solving. So, we will have a tutorial session in the next class. We will discuss about how we can solve problems pertaining to centrifugal compressors and at the end of the tutorial, we will also have a few exercise problems for you to solve based on the discussion during the last few lectures. So, we will take up a tutorial in the next lecture which will be lecture number 33.


Recently, I discussed the denial of racism from black people. I wanted to analyze what's happening because I'm obsessed with understanding denial, self-deception, and delusion. Similar to the denial of racism, I've also been blown away about the denial of white privilege from white people. In 2020, like millions of other people around the world, I saw the video of what happened to George Floyd and it messed me up. Whenever there are these like earth shaking events, I just sit there and ask, how does this happen? It wasn't just that another unarmed black person was killed by police, but the whole thing was filmed. These cops were fully aware that people were filming them and it didn't even phase them. Around this time, it was months after a Maude Arbery was murdered while jogging, but we were just hearing the news about it. This black man was murdered in broad daylight for the crime of exercising. As the conversations, debates, and protests began to erupt around these events, as well as the death of Breonna Taylor, I did what I always do when I have questions that won't leave my head. I started reading as many books as possible and doing additional research. And when I really want a different perspective and to understand, I read books by people from that specific group. For example, to better understand feminism, I read books by women who are feminists. To better understand what drives people on the opposing side, I read books by conservatives. So I started reading a ton of books from black authors and it just hit different. Why? Well, for those of you who don't know, I'm half black, but I look pretty damn white. It's extremely rare that anyone realizes I'm half black. And I usually have to show pictures of my dad and show other evidence just short of providing a DNA test. But for some reason, black people know that I'm half black, which I still don't know how they do it. But I always find that pretty interesting. So although I'm half black, as I read these books, I realized there are just so many things that I've never had to worry about. As someone of my complexion, I don't have to worry about police kneeling on my neck until I suffocate while they're being filmed. I don't have to worry about some hillbillies chasing me down and shooting me while I'm going through a neighborhood. Even in the case of Breonna Taylor, I am far less likely for a no knock warrant to happen. And if it did happen, the research says it's highly improbable that the police would see me as a threat and shoot me in my bed. This, amongst many other scenarios, is white privilege. I can't even imagine how cognitively taxing it must be to worry about so many different situations that black people who have a darker skin color than me have to worry about. As I write this, I just remembered what happened to Philando Castile as well.   With so many Second Amendment loving people running around and open carrying, how many of them have ever had to worry about this? But when I started to research white privilege and observe the conversations around it, I was blown away at how many white people refused to admit that white privilege was a thing. Although it was clear as day to me, I kept asking, why can these people not see what I'm saying? So today, I wanted to break it down and see if we can understand what's going on. We'll start with asking, what is white privilege? Then we'll discuss how it works. I want to understand why people deny it exists and we'll go over a paper that has what I think is the best theory about this denial. Most importantly, I really wanted to discuss why so many white liberals will acknowledge white privilege but won't actually do anything about it. Before we dive into the weeds about the denial of white privilege, I wanted to welcome all of you beautiful new subscribers. My last video on the denial of racism did really well and I actually thought it was going to be this dud that nobody saw nor cared about. And I personally, I try to write about and make videos about different topics that I don't think are getting nearly enough attention or they aren't covered in a way that I think they should be. So I'm super duper grateful for everyone who took the time to watch it. But one comment that I kept seeing on that video was that it wouldn't get recommended by the algorithm and not get nearly enough views. And as somebody who makes YouTube content, it's really interesting to me that even viewers recognize how these algorithms don't do much to promote like these types of videos. So aside from subscribing so you don't miss any of my future videos, I'd really appreciate if you like any of these videos, if you think they deserve more attention, just do me a big ol' favor and share them. It's absolutely free to you, takes two seconds, just share it on social media, email it to a friend, post it on Reddit, whatever you got to do. And yeah, stuff like that actually shows the algorithm that people care about these topics. So not only are you helping my videos reach more people, but you're also helping other creators who make these types of videos. Alright, so anyways, if you're not yet, make sure you're also following me on Instagram and Twitter. Not only do I love chatting with all of you and getting like book recommendations, but that way you don't miss any upcoming videos. But I also do a lot of writing and other types of content and stuff. But yeah, follow me over on Instagram and Twitter at the Rewired Soul. Alright, so let's jump into this thing and let's start out by asking, what is white privilege? Alright, so in short, white privilege is the advantages and individual experiences due to the fact that they are white. It's not super complicated, but for some reason, it's extremely hard for people to grasp. As I mentioned in the intro, I realized that there are just so many things that I'll never have to worry about. If you really want a good reference for white privilege, I just started an amazing book that I've been binging. And it's called Black Fatigue, How Racism Arrows the Mind, Body, and Spirit. And it's by Mary Frances Winters. And actually, when I wrote this, I was still reading it, but I actually finished the book this morning. It's phenomenal. Alright, so the author explains all of the different things that Black people have to worry about and deal with on a daily basis, from racism in the workplace to getting an education and getting proper healthcare, the book is filled with research, studies, and statistics. Alright, and as I mentioned early on, right, if I don't understand something, if I'm not in that position, what I personally try to do is read books, alright, or consume content by people who are from that demographic. Okay, so if you if you're right here in the video, and you are like, yo, white privilege isn't a thing, whatever, do me a favor, grab the book. Alright. And one of the reasons I say this, and any of you who do believe white privilege exists, like recommend it to other people because when you read an entire book, right, an entire book on a topic, it's hard to deny that these people are experiencing something, especially a book like this that has so many facts and data and just research, right, because as you keep challenging it and questioning it and making up these excuses, you start to feel like you're gaslighting the author. So I really recommend you read books by people you don't agree with, to get different perspectives, and just like if you're interested in understanding a topic better. But I think one of the best examples of white privilege that a person can't deny is just the policing of black hair. Alright, so did you know that black people literally have to pass a law to prohibit discrimination of their natural hair? Alright, so the Crown Act was introduced by Senator Cory Booker of New Jersey in 2021. And black people are waiting to see if it's cool that they just grow out their natural hair. Do you know how insane that is? If you're white, how many times have you had to worry about just the simple act of growing out your hair? Employers see black hair as quote unquote wild or unprofessional. Imagine for just a second that your straight hair was seen as wild and unprofessional. This is where the white privilege deniers come running in screaming. Well, I can't just do my hair however I want. I couldn't just come in with a mohawk or dye my hair purple in a professional setting. But the thing is, what those people are talking about is actually doing something to your hair. This is completely different than its natural state of being. And it's one of the mental gymnastic routines white people do to deny that this is an issue.  They're just trying to not have their Afro police. Alright, imagine just for a moment if white women actually had their bosses tell them that they could not grow their hair out. Maybe some professional settings won't let men grow their hair super long unless it's in a ponytail. But this is still different than a well kept Afro or dreadlocks. Anyway, go get Mary Frances Winters book. It's amazing. But aside from just the fatigue black people have to deal with, there are some white people who legitimately think that they are the ones being oppressed. They refuse to acknowledge that white is the default in the United States and it comes with its advantages. One of the first reasons I think that there's so much denial around white privilege is the same reason that nepotism babies refuse to admit that they were handed anything. You've seen these people who were born into rich families, raised in good neighborhoods, had their tuition paid for by their parents and get that great job. And then they say, I did this all on my own. And trust me, the media doesn't help either. Every time they call someone a quote unquote self made millionaire or billionaire, nobody wants to admit that they got anything handed to them or that they had any type of advantage. This is a form of self deception because we want to believe that we've earned every single thing that we have. The reality is that you can work hard and have an advantage. What privilege does is give you a head start and additional resources to make your outcomes a little bit easier to come by. White people don't have to worry about any of the biases that happen when you're a black person and are trying to just simply make a good life for yourself. And this is when even more denial comes in and white people start telling you about all of the disadvantaged white people who also struggle. This is an extremely weak but extremely common argument. And I wanted to dedicate an entire section to this topic. One of the common things you'll hear when white privilege is discussed is that there are so many disadvantaged white people and how dare you say that they are privileged. I cannot tell you how many times I've heard people say, this is why people turn Republican. Do you know how offensive it is to tell a white person who grew up in poverty and in an abusive household that they're privileged? While I'm not Robin D'Angelo's biggest fan, I think it's important to note that this is exactly what she's talking about when she says white fragility. If you are literally too sensitive to have this conversation, you're being extremely fragile and you need to chill out. So if you are incapable of having this adult conversation, you may want to leave now. Nobody is saying that some white people don't have it bad. Hell, nobody is saying that white people don't face their own biases. I think the best example is lookism. If you're conventionally attractive in this world, you have it better than most people. I have been overweight for most of my life and I always have to wonder how much my weight plays a role when something doesn't work out in my favor.  The reality is that in literally any situation, if you put a white person and a black person side by side and both were identical on every single metric, the white person has the advantage. So yes, there are millions of white people who grew up in traumatic environments with alcoholic or addicted parents who abuse them. There are millions of white people who are also homeless or are in poverty. But if I took a white person in this situation and a black person in this same situation, who is going to have an easier time crawling their way out and getting up on their feet? Which of the two is more likely to be seen as lazy? Which one is more likely to get an entry level job? If both of these people got an entry level job and worked equally as hard, which one is more likely to get a raise? Which one is more likely to get government assistance? Which one is more likely to get mental health care if they're struggling with a psychological disorder? If you're still not sold yet, let me introduce you to the moral, legal and political philosopher, John Rawls. John Rawls created a thought experiment that showcases white privilege perfectly. It also shows all of the other issues of inequality in America when you run this experiment. Rawls was interested in justice and fairness. So he created a thought experiment called the veil of ignorance. Here's the veil of ignorance, but with my own little twist on it.  There's a person or some celestial being there who says, Welcome to death. There's no heaven or hell. You just get reincarnated. You're going to be born in a brand new body, but you get to choose the exact circumstances that you're born into. From there, this being basically gives you a menu where you can choose whatever you want. Here are some of the categories on the questionnaire that you get to choose from. What race do you want to be born as? What country do you want to be born in? Do you want to be born in a rich or a poor family? Do you want to be disabled or able-bodied? Do you want educated or non-educated parents? And so on. Let's focus on the race question real quick. Knowing everything that you know about the world, what race would you want to be born as? Well, if you would want to be born white, it's because part of you recognizes the advantages there are to being white. If you'd want to be born anything other than white, ask why. And if you're lying to yourself, you really need to work some things out. Another topic that I'm extremely passionate about is wealth and opportunity inequality. So I'll be revisiting Rawls' veil of ignorance again. But the point Rawls is trying to make is that if you cannot be born into any circumstance and have the same opportunities, something with our society is definitely wrong. And we need to address it. If the majority of people know for a fact that it's better to be born white, then we clearly have a white privilege problem. Again, most people recognize that it's advantageous to be born white in America as well as many of the other successful nations around the world. So why do they deny it? And more importantly, why don't we do anything about it? So I was actually first introduced to the concept of white privilege way back when I was about 14 years old from one of the first stand-ups that I ever watched. And still to this day, it's one of my all-time favorites. It's Chris Rock's 1999 stand-up, Bigger and Blacker. I actually just had my girlfriend watch it with me the other day. I haven't watched it in a few years. Still hilarious. But anyways, this clip kind of summed it up for me. And while hilarious, what Chris Rock just said is extremely true. Regardless of how many people lie during the veil of ignorance thought experiment, we know that many white people would prefer being white. Why? Because it comes with its advantages. One must wonder how far off Chris Rock is when he makes the joke about a one-legged bellboy. Sure, having one leg is rough, but is it rougher than being black? Since my main area of interest is psychology and human behavior, I started searching to see if anyone had done any research on white privilege. Specifically, I wanted to know if there was any research around why people are in so much denial about it. Well, not only did I find some research, the authors of the research have a separate study that I just recently found that provides some evidence-based solutions. So this research has been conducted by Dr. L. Taylor Phillips and Brian Lawry, PhD. Lawry is a professor of organizational behavior and senior associate dean for academic affairs at the Stanford Graduate School of Business. He's also a social psychologist by training. Phillips is a professor of management and organizations at NYU Stern School of Business, who focuses on diversity, equity, and inclusion. I first came across their work when I read their paper titled, Heard Invisibility the Psychology of Racial Privilege. In the abstract, they say, despite overwhelming evidence of its existence, white privilege has received relatively little attention in psychological science. However, given the chronic and pervasive benefits tied to racial privilege, it stands to reason that living with such privilege affects white's everyday psychology. Here, we explore the psychology of privilege, connecting white's everyday experience and behaviors to underlying motivations, i.e. innocence and maintenance, shaped by the privileged position in the social hierarchy. So these two researchers wanted to understand what the motivations are behind the denial of white privilege from white people. And if you're familiar with how economists think, economists do this regularly because they're always trying to show how humans are driven by incentives. As rational as we think we are, there's always an incentive at play. And sometimes these incentives are unconscious. It's important to highlight that these can be unconscious because most people aren't purposely racist, nor do they want people of other races to be mistreated. The other issue that we face is something called identity protective cognition. We all have an image of self. We have an idea of who we are and what type of person we are. When something challenges that self-perception, we go into this protective mode that causes a ton of dissonance as we try to rationalize the situation in order to avoid disrupting who we believe we are. Lowry and Phillips theorized there are two main motives at play when white people deny their privilege. We suggest that this strained relationship with reality, while not in the same league as that of our church-going ancestors, requires management of the obvious existence of racial privilege. However, privilege is often experienced as invisible to those who have it. How can this be? Here we suggest that individual actors motivated to maintain their positive self-regard, innocence motive, or privileges associated with their group's dominant status, maintenance motive, will engage in behaviors to cloak their privilege. As a result, invisibility emerges at the societal level and can thus protect both the privileges and the innocence of individual privileged actors, even when they do not individually engage in these protective actions. This right here explains why it's so dang difficult for white people to see their own privilege, and it's probably the best explanation that I've seen for what's going on. The innocence motive is basically the identity protective cognition that we just discussed, but I think the one that's much more difficult for people to face is the maintenance motive, and honestly, I do not know what the solution is. The researchers go on to say whites want to maintain privilege and racial privileges depend on the stability of an unequal racialized social system that tends to provoke resistance. So what they're saying is that it's good to be white. And unfortunately, this is a zero sum game. For every advantage that a white person has, in order to have a truly equal society, these white people would have to lose that advantage. This script was like 10 pages long, and I could honestly write another 20 pages on this topic alone because it's the same exact challenge that we face with wealth and opportunity hoarding. It's why there's so much slacktivism in the world today. It's easy to sit back and talk to talk and say that you want people to have it better, but the second that means that we're going to have to give something up, the mental gymnastics begin. A few weeks ago, some of you watched it, some of you didn't if you haven't go watch it, but I made a video about Hassan Piker being a fake socialist, and this is the exact same issue. Although his fans came out in droves to attack me, what I'm saying is he can sit back and scream about progressive ideas and equality so long as it doesn't mean that he has to give up that sweet, sweet lifestyle that he has. But I digress. In the case of white privilege, think about the opportunities afforded to white people when it comes to going to good schools and getting good jobs. Schools only have so many openings, and it's the same for jobs. For white people to give up their privilege, they're basically shooting themselves in the foot. Due to identity protective cognition, you will rarely see a single person admit this. Everyone sees themselves as a giving, altruistic person. So you will hear every excuse in the book to not actually make our society equal. Although I'm a leftist, this is much worse when it comes to white liberals, and I would argue that it's worse because white liberals virtue signal by saying that what they want is equality. But when it comes down to it, they aren't willing to make the sacrifice. That's why we get so many nimbies. People saying, yeah, I would love for underprivileged black kids if they can go to a better elementary school, but just not the one in our neighborhood. Or they'll say something like, yeah, I believe in equity, but I don't think someone should get into a good college or get a good job because of their race, if that'll affect me. Chris Rock's bit actually ends with him saying, for white people, the sky's the limit. But when you're black, the limit is the sky. So what's the solution? Well, while researching this, I realized that Laurie and Phillips actually have more papers that they've co-authored. In a separate paper titled The Hard Knock Life, whites claim hardships in response to racial inequity. They found a way to actually get white people to tune down their denial just a little bit. The abstract starts off by saying the following. What happens when white people are faced with evidence that their group benefits from privilege? We suggest such evidence will be threatening and that people will claim hardships to manage this threat. Sound familiar? It should because it's what we were just discussing a little bit ago, when white people respond by saying, oh, so you're saying that even poor white people who grew up in abusive households are privileged? This is that defensiveness that they're talking about. So the authors go on to say in the abstract, these claims of hardship allow individuals to deny that they personally benefit from privilege while still accepting that group level inequity exists. Again, this is extremely common.  All of them believe that they worked hard and that they have had an extremely difficult life. In a previous video, I discussed Netflix dating shows and lookism about how none of these dating shows will have any overweight or fat people. And something that I regularly notice as I watch these shows is how these beautiful people who also grew up in rich families, they have to they just something in their brain makes them have to find something in their life that was difficult. And they'll have a big dramatic scene where they're having a one on one conversation with somebody and talking about how they've been hurt or how something was rough in the past, even though for anybody who's grown up underprivileged or without privilege sees that they had it much better than the viewer did their entire lives. It's like as humans, it's for some reason impossible to state that we had it pretty easy. Well, Laurie and Phillips were able to figure out a hack to get white people to recognize their privilege. What they did was run two different experiments. In the first, they show white people evidence of privilege and inequality. The first group got defensive and within state the personal hardships they experience. But in the second experiment, the experimenters had the participants do self affirmations. Once these white people were feeling all good about themselves, not only did they recognize more personal privilege, but they also showed increased support for inequity reducing policies. Pretty cool, right? So you just need to make white people feel good and then we'll get more equality. I'm just kidding, but this is really interesting research because it shows that when people are feeling good and they're in a good headspace, they recognize this a little bit more. Alright, but the thing is I am extremely skeptical of these results in practice. I'm not skeptical of the results. I'm skeptical of the results being used in the real world because there is a major difference between supporting something and actually going through with it. While these people may have vocally supported these inequity reducing policies, I would personally be curious to see them put their money where their mouth is and actually take action. What would happen if you had these people do the self affirmations and then immediately vote on something that would take away some of their advantages? Would they still support these policies that promote equality or would they snap out of it? I'm usually a pretty bright eyed optimist, but based on my experience, it's extremely hard to get people to make a sacrifice for the greater good. We can't even get universal health care when we're basically the only advanced nation that still doesn't have it. Why? Because people would have to pay more taxes to give equal access to medical care to everybody. People don't like their money messed with and I get it. We all have families and we all want the best for ourselves as well. Trust me, as someone who thinks about this stuff all the time and rants about people I could saw on piker as well as every other rich person in the world, this is regularly on my mind. I think that if we hope to get anywhere near an equal society, we all have to start asking ourselves what we are willing to sacrifice. Are you willing to potentially not get a great job with great pay so an equally qualified black person can get it?  Like these are really tough questions to ask ourselves and it's even tougher to make the noble choice. But until we start recognizing our privilege and getting past our denial of that privilege, it's impossible to make progress. So hopefully now that you're armed with the information, you can start considering what you're willing to sacrifice so we can counteract the inequality that black people are still facing. And like I said, this is something regularly on my mind and I'm constantly challenging myself to say, what am I willing to sacrifice to make our society more equal? All right, everybody, that's all I got for this video. I've been dying to make it. I was actually hoping to get it out sooner, but this has been a crazy, crazy week. Make sure you subscribe because I'm hoping to get to a point where I can release at least two videos a week. I have just a laundry list of topics. I really want to dive into more racial issues, but also issues around like capitalism, wealth inequality, opportunity inequality, so many other things. I just I have a whole document just filled with outlines and ideas. All right, so make sure you're subscribed. Okay. And if you're not yet, make sure you're also following me on Instagram and Twitter at the rewired soul. I love chatting with all of you. If you got good books, send them my way. I love to read. Okay. And then as I mentioned, like a lot of you notice, these videos don't necessarily get promoted by the algorithm. So do your boy a favor. It costs you absolutely nothing. Just go share this shirt on Twitter, Instagram, Facebook, Reddit, send it in an email, whatever you got to do, just share this thing far and wide. All right. But anyways, that's all I got for this video. I hope you have an amazing rest of your day and I will see you next time.


Item No. SCP-764 Object Class Safe Special Containment Procedures SCP-764 is to be kept in Hazard Vault MT with unlocking mechanisms only operable by two Class-1 researchers or higher working in tandem. No personnel are to enter without proper safety precautions, and no personnel would be in Hazard Vault MT unless under the direct orders of Level-4 personnel or as part of an approved destruction attempt. Personnel entering Hazard Vault MT are to wear the locking gauntlets and containment supply 313, size 14, and a key is not to be brought into the vault. The gauntlets physically prevent attempts to don SCP-764 due to their size and therefore permit SCP-764 to be handled with a modicum of safety. Description SCP-764 is a pair of punch and judy puppets that display no exceptional characteristics upon visual inspection. When observed by individuals with no barrier between them and SCP-764-1 and SCP-764-2, a compulsion comes over a single person to put on a show, utilizing the puppets, even if none present have any skill, talent, or training regarding puppeteering. Others feel an overwhelming urge to watch the show regarding all events taking place as the height of entertainment until the show is over. As the subject on SCP-764-1 and SCP-764-2, and no circumstances of SCP-764-1 and SCP-764-2 been seen placed on separate performers, any individual without physical barrier between themselves and SCP-764 will find themselves compelled to sit and watch the show. The show begins with a normal punch and judy show, with light slapstick comedy and violence occurring between the puppets. After a period of three to five minutes, the individual will be chosen from the audience and brought forward, participating at a part of the show, typically playing as a police officer or constable, but at an incident 764-34D, the subject played as E-Class Agent Jonathan ████████, an individual who was part of the team responsible for recovering SCP-764. A light-hearted exchange will occur between the volunteer and the puppets before the violent slapstick resumes, but after this exchange, both puppets will brandish appropriately sized weapons and begin to viciously attack the volunteer. The remaining audience will find it even more amusing than the previous antics of the puppets, and even the volunteer will laugh until SCP-764-1 inflicts the final and invariably fatal wound, quipping, that's the way to do it. Another short delay will ensue as the puppets banter until another volunteer is brought forward in the process repeated, with the roles assumed by those coming forward becoming more and more bizarre as the show progresses. The show will conclude with the puppeteer's death, or after four to eleven individuals were killed, at which point the puppeteer will begin removing the puppets and ask, did you enjoy the show, and receive as a response from all surviving audience members, yes, Professor. A show concluded in this manner will negate SCP-764's ability to mentally influence individuals for anywhere from eleven to twenty-six minutes. Addendum ████████, Incident Log 764-23B This containment breach occurred when a D-class personnel in the process of moving SCP-764 opened the crate containing SCP-764. The door to hazard vault MT-█████ was immediately sealed and locked. A recording device was brought in after approximately two-and-a-half minutes to record the remainder of the incident. SCP-778 laughs, D-8778 replies, That's ridiculous, you're so, then begins coughing. SCP-764-1 says, Oh no, he's sick, we'll have to operate. SCP-764-2 responds, But punt, you're not a doctor. Has that stopped me before? D-88778 laps again but resumes coughing. SCP-764-1 brandishes a scalpel about half its length. He begins humming to itself as it cuts into D-88778's throat, who seems to be stifling a laugh. He then reaches into the incision and fumbles around before grabbing onto something and tugging, and he says, I think I've got it, there's something in his throat, we'll save you yet. SCP-764-2 shakes its head. SCP-764-1 pulls out the hyroid bone and shakes in the air triumphantly, and says, Told ya I could do it.  D-88778 makes a noise that might be a laughter. SCP-764-1 says, Al, stop it, I'll fix him, you'll see woman. SCP-764-1 puts the scalpel back into the incision and begins sawing the blade. After a moment, he reaches in and begins pulling as blood begins to spray, approximately four inches of the keratin artery are pulled out of the wound, and he quips, that's the way to do it. Full pump is sucked to the ground, as D-88778 collapses.


My name is Andrea with Foodimentary Adventures in Food.  On our channel, you'll find simple and tasty dinners using everyday ingredients. So for dinner tonight, Howard grilled out some short ribs that I had in my freezer and this is what I use to marinate the short ribs and they are really good. We really like this brand. With it, I made some fried rice and this is a fried rice seasoning mix that I used. I got this from H Mart which is a Korean grocery store. You get five packets in there and then it tells you that you can use it for soup or fried rice and I followed the fried rice directions but I did not put any chicken so it's just a little bit of green onion in there and then we are having a side salad and this is a side salad. This is the kit that I used and it comes with seasoning, dressing, bacon, lettuce of course, croutons as well. So this is it. So this is what we are having for dinner tonight and we will see y'all next time. So for dinner tonight, we are having taco salads using these taco salad shells that I love so much. I've been eating them ever since I was a child. They are really hard to find now but my mom found me some a while back ago and I just put them in my freezer. You get four flour shells and formers and you bake them and they turn out really, really crunchy. So crunchy and flaky. They taste like they are fried but they are not. Then I am trying out this nacho and taco blend shredded cheese. I've never seen this before. It came from Kroger. You get cheddar and Montre Jack and it is blended with spices. Then my favorite taco seasoning is this one from Trader Joe's. One packet seasons two pounds of meat and it gives you directions on the back how to use the taco seasoning. It is spicy. So if you have kiddos that are sensitive to spice, it may be too spicy for them but I always pour mine out in a jar and then I just use it that way. So this is what it looks like. Lots of herbs and spices in there. So this is my taco salad on the bottom. I have lettuce. I have the taco meat and I'm actually using ground turkey. We're trying to eat a little bit healthier. Then I've got cheese and salsa and this is Howard. He has the same thing except he added sour cream. His avocados were not ready to use so he is very sad about that of course. Then the salsa that I am using is this Mateo's. I like it. I find it at Kroger. I mean not Kroger, Costco but you can find it anywhere. Of course it's a lot cheaper at Kroger. Costco, sorry. You can find it anywhere but it's cheaper at Costco. Alright so this is what we are having for dinner tonight and we will see y'all next time. So for dinner tonight I am making turkey thighs in the crock pot. So at the bottom of my crock pot I've got two onions that I chopped up and then on top of that I added two turkey thighs that I browned on top of the stove. So in Texas and I'm sure other places that you can just buy turkey thighs by themselves and I got these at Walmart and I had them in my freezer and so now I'm getting ready to add a package of onion soup mix. I've never made my turkey thighs like this but just wanted to give this a try and I'm just going to sprinkle this onion soup mix right on top and then I'm just going to cover these and let them cook on low for probably about seven, eight hours. I forgot to mention the garlic butter so I used this Kerrygold garlic and herb butter. I've had it in my fridge for a while. I had probably like six tablespoons so I just decided to throw that on top of the turkey thighs. Okay so here are our turkey thighs. Like I said I let these cook for eight hours on low. That darkness you see on top is the Lipton onion soup mix. It kind of caramelized in there. With it I am serving some mashed potatoes and then I was going to make a green vegetable. I just didn't feel like it. I just made some corn to go on the side and so these turkey thighs are really big so Howard and I are splitting one and then let me show you there's one left in the crock pot and you can see all that juice that it made all that gravy. I didn't add any water to it at all. Now we've got one more to eat. So this is what we are having for dinner tonight and we will see y'all next time. So we are having a pantry and freezer meal for dinner tonight. My pantry is starting to get way too full so I need to get back on track. So we are having this tempura shrimp from Costco and this is what the box looks like. But I threw the box away to make room in my freezer. In my pantry I had this package of cheddar and broccoli rice sides which I really like a lot. I spent my pantry for a while and I needed to use it.  So quick and easy dinner tonight and we will see y'all next time. So I am kind of making up a dinner tonight. I don't have a recipe for this. I am kind of throwing it together but I will make sure to write down what I do in the description box. So in my freezer I had some beef smoked sausage and all I did was just chop it into rounds.  I am not going to use all of these but I am going to use some of them.  I am going to use some garlic powder and onion powder to season.  But I have this bouillon so of course I will add water to it. But that is all I am going to do. It is going to be a really quick skillet meal. Okay so I fried up my sausage and veggies and got them all nice and brown. I did add a little bit of olive oil in there as well too. So now I am adding in my water and going to add in my bouillon. And I am just going to give this a good stir. I am going to cover it and adding just a smidge more. Going to cover it up and let it simmer probably maybe for about 20 minutes. I am not sure. Kind of making this up as I go along. Okay so here is dinner all plated up. I did not feel like making a vegetable so we are just having this. But it is really good. And like I said I will make sure to write down what I did in the description box. It is very tasty. This would be good with turkey sausage or chicken sausage but I will definitely be making this again. So this is what we are having for dinner tonight and we will see y'all next time.


I guess out of the gate, I'll just ask you maybe with a week to work with before you really know who you're going to play, what maybe you do hope to accomplish this week, what will be your focus before you turn to game prep. I think it's a great opportunity at this juncture of the season to focus on us, you know, what we need to do better and and things that we can improve on. We're continuously having that improvement mindset and looking for ways to get better at the task that we're asked to do and, you know, also take a peek at schematically what we're doing in some areas and so good, good self reflection and and commitment to working on ourselves. Hey Todd, where where do you feel like Ryan is coming off of these two games, how much momentum maybe does he have and and how important do you feel like that is for him personally. Yeah, you know, I think he's had a good good couple of games, you know, I think he obviously had some production in this in this past game and, you know, we realize that there are some opportunities that are near misses as well and so, you know, we try to take it on a week by week basis of how we're going to approach each game plan and I think Ryan went out and executed the game plan well last week. Hey coach you guys have been really good on third down all year long and particularly in the last three. What do you kind of attribute that to and how much does the offensive line being able to you know start and finish a game as healthy as possible have to do with that as well. I think the lines been doing a nice job of working through different protection schemes and, you know, different blitz patterns that we've seen on third down and certainly guys done nice job of, you know, getting open and being available for Ryan in a timely fashion. I think there are tight ends and backs have done a nice job of their protection responsibilities as well and getting some chips, you know, and help and slow the past rush and then Ryan's distributed so, you know, it takes it takes a village and I think that those guys are committed to executing our bread and butter schemes, you know, just doing it out of their formations and looks and, you know, I'm pleased with, you know, some of the production we've had out there down but I still feel like we're leaving some meat on the bone. Hey, Todd.  Yeah, I think each guy's different, you know, and it'd be a case by case basis of what guys can handle and certainly Coach Brable and the training staff, you know, and strength staff will let me know what workload, you know, can be expected from him each day and, you know, I'll just take that as we go and see how Derek's doing. David will help. Todd, I'm curious, given the different players you kind of had available week to week, were you able to learn about guys maybe a little further down the depth chart to the point that maybe along the way you added some things to the playbook to take advantage of this guy's particular strength or that guy's particular strength that maybe you didn't know they had initially?  Guys were, you know, maybe you move them around and run different types of route concepts or different, you know, branches of the route tree with those guys or emphasize something here or there, but we truly do ask everybody to be able to embrace that next man up mentality and we expect you to be able to go execute most of the playbook if not all of it. Uh, John Russia, kind of following up on that Todd, is there any particular, you know, pride I guess this year and staff or team and the fact that you guys did, you know, have 91 different guys play and is there is there an art to making that work beyond you know everybody be ready is there something that maybe you guys even learned along the way. I'm sure there'll be a time for reflection on this season where you're able to kind of digest and take a broader scope view of some of those types of things but you know, really try to work diligently to keep a week by week focus and look at the task at hand so I'm sure there'll be a time to look back and think about those kind of numbers and things like that but as we're in the midst of it, you know, the routine is the routine. Steve Lam. It's odd when Ryan was struggling a bit earlier in the season with guys coming out of the lineup and turning over the ball there are some critics out there, certainly the thoughts. Okay, this is who he is or he's not living up to what he's played in the past. Did you ever doubt him during that time or what did you see from him that kind of tuned all that out stayed steady and a leader for you and has now played really good football over the past few weeks. Yeah, I definitely never doubted him, nor will I, and I'm sure some of the same critics had some issues with me so you know we try to tune out that kind of stuff and focus more on what we can do and what we can control. And I think Ryan's been a great example of just staying steady in his business like approach to things and you know, we, we believe that that'll pay off and continue to propel us where we want to go. Corey. Hey Todd, is it just coincidence that things have opened up for FERC with with AJ back or does AJ indeed open things up in the in the middle of the field for other guys. I'm sure he garners a little bit, you know, more attention but you know Anthony's production has been because Anthony's hard work. He's, he's worked diligently to improve on areas of his game that we've asked him to and you know I think that that has bred some confidence and that repeated action has bred confidence in him and he's playing a little faster and taking advantage of his opportunities and went up, made two nice plays on the football on Sunday for us and you know obviously was shining on the spot where we needed a touchdown so proud of, proud of FERC you know I obviously know him well working with him past couple of years and and you know not surprised that he found his way. Ben. Hey Todd, I'm sure kind of with with Julio's kind of lack of availability was maybe a struggle for him just throughout the course of the regular season but for him to get his first touchdown with you guys. And how encouraging was his showing in this past game and how much do you think that you guys can maybe build on that with him getting a season high in targets in this in the last in the regular season finale. And certainly we're excited when anybody can find Peter there but you know I think, you know we were able to connect on a couple things that previously we weren't able to and, and I think that bodes well for going forward. Emily. Yeah as you await an opponent Mike Raples said that you know the key this week is really focusing on you guys and you know working on things in particular on offense what are some things that you can get done this week. And I think you know just more time on tasks with you know spacing and timing in the past game being able to work, you know combinations and things like that up front, you know, you know, being able to take some time in the meeting room to look at yourself and not just in a in a game recap mode but take a peek at some things that we've done over the past few weeks and how we might want to quarter turn or adjust those so it's a great opportunity for us at this spot in the season to do some reflective work and also put it to time on tasks on the field.


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What did they see in the sky and how does the progression of thought assimilate over time as these witnesses pass the information on through the ages, a test to remember the power of thought, wait to hear this. The Thunderbird is a widespread figure in Native American mythology, described as a supernatural being. The enormous bird was a symbol of power and strength that protected humans from evil spirits, apparently so-called the Thunderbird because its flapping of its powerful wings sounded like thunder, and lightning would shoot from its eyes, the Thunderbirds brought rain and storms which could be bad or good. Good when the rain was needed but bad when rain came with destructive strong winds, floods and fires caused by the lightning. If you haven't already guessed it, the Thunderbird was a squatter man event as witnessed in the sky by the Native American ancestors, and this figure that they saw in the sky was said to be so large that it would engulf the entire planet and they lived in the clouds higher above the tallest mountains, and just as the Greek gods lived on the highest mountain, the Thunderbird 2 was perceived in this way. Various tribes have oral traditions about the magical Thunderbird, which they both highly respected and feared. Each story of course is a perception of thought exaggerated over time but important fundamental details remain. In Grovant traditions, it was the Thunderbird who gave the sacred pipe to the people. Some plains tribes, including the Arapaho, associated Thunderbirds with the summer season, while the White Owl represented the winter season. In other Indian mythologies, the Thunderbird controls the upper world, while the Underworld is controlled by the Underworld panther or the Great Horn Serpent, from which the Thunderbird protects humans by throwing lightning at it and we can connect this venture with the Sun God Ra, sailing the solar bark and defeating the Serpent Apophis each night to ensure the light would prevail. These details from America and Egypt are closely connected because this is how they saw it in the sky. Their perceptions across the planet are the same because they saw the same thing, the Taurus Field. According to the legends, the Thunderbirds were the ancestors of the human race and helped to create the universe. The Menominee of Wisconsin tell of a great mountain that floats in the western sky, upon which the Thunderbirds live, and it's from there that they control the rain. They are the enemies of the Great Horned Snakes called Amisagenevig, which they fight with to prevent them from overrunning the earth and devouring mankind. They are the messengers of the Great Sun himself and delight in the deeds of greatness, the Great Sun having once existed alone before descending into catastrophe. Other tribe versions of the stories remain similar in that the Thunderbirds fight underwater spirits, their traditions also say that the Thunderbird is responsible for punishing humans who break moral rules. The Native Americans state that the Great Bird was created by Nanobozo, a high spirit and a cultural hero, and that the birds lived in the four directions and migrated to Ojibwe lands during the spring with other birds. They stayed there until the fall, when the most dangerous seasons for the underwater spirits had passed, at which time migrated south with other birds again. Some believed that they were shapeshifters who would often change their appearance to interact with people. The shapeshifter description is also accurate as the manifestation went through discrete phases over a very long period of time. In some tribes Thunderbirds were considered extremely sacred forces of nature, while in other tribes they were treated like powerful but otherwise ordinary members of the animal kingdom. Many legends reference the anger of the Thunderbirds as something fearsome to behold, which could result in harsh punishments for their observers. And in one story, an entire village was turned into stone for their wrongdoings, this was out of their control and it was indiscriminately bombarding the earth at random with plasma. This was the anger of the gods and a traumatised people tried and vain to understand this cataclysmic happening in the sky. Throughout their history, the Thunderbird symbol has appeared on totem poles, pottery and petroglyphs, and from these petroglyphs linked all across the world, Anthony Pirat has shown a global connection of perception, but these are not abstract figures, these are details of events once witnessed in the sky, but what do you guys think about this one anyway? Comments below and as always, thank you for watching.