Hi again Red Hat Developers, this is Jason from the Red Hat Developers Program. Here we are at Summit 2017 at the Dev Zone and we have Dirk Herrmann from Red Hat who's going to talk to us about the Red Hat Container Catalog. As it's stated on the slide I will talk a little bit about the Red Hat Container Catalog in a specific context, so how to identify the right base images you can pick for your application. So in case you are not aware of the Container Catalog at all and haven't heard about it, what are the key challenges? It's got already mentioned some of them in this previous presentation. So the challenge is that there are a lot of public registry out there and everybody can pull images from somewhere and get them and run them and build something on top of it. And we as Red Hat look at this at a certain risk because you typically don't know what's inside, who's updating it, who's maintaining it, who's responsible for providing updates and fix and stuff like that. And this is the whole idea of the Red Hat Container Catalog. So if you're not familiar with what we as Red Hat are doing, we are not only pushing more than 1,500 images in 227 repositories into our registry, we provide a lot of additional value around it. So we have thousands of K-based articles, product documentation. We are regularly updating our images based on our great work of our Red Hat product security team, which provides a lot of additional information around security vulnerabilities around our images. So just that you have some numbers in your mind, last year we fixed more than 97 critical security advisers just in REL. And the good news is we fixed 100% of critical security advisers in REL in less than one day. So if you look at this, you will probably get a better impression. There is much more than just the image itself and the image metadata and the metadata coming out of the repository or registry. So we have security data, we have documentation, we have a lot of other metadata we can provide. And this has been the starting point for the Red Hat Container Catalog, which is a cross-team effort. We work with more than 10 different teams across four different organizations in Red Hat. We followed a design-driven model to develop the thing clearly focusing on user experience. So we started long before we started to develop the final web UI. We worked on wireframes, user stories, target personas and stuff like that. So the key features of Red Hat Container Catalog are the Container Health Index. We made a press release earlier today around this particular piece. We have extensive image and through repository metadata we are automatically adding image documentation surrounding of this image. And of course we are leveraging our Red Hat advisories. So I've added some of the user story and target personas here and also tried to map it better to different life cycle steps. So the first step is typically somebody comes through Red Hat to the Container Catalog or to the customer portal and he just wants to better understand what's inside the Container Catalog, what's inside the Retter Registry, what can I get there and especially I'm searching for a particular Red Hat Enterprise Linux base image. So this is a typical starting point and basically we provide two different options to find images in the Container Catalog. One is the, which is shown on the right side, the Explore Pass where we provide some guidance around popular application categories, image architecture categories, some basic statistics and popular products. The left side you can see a very powerful search where you can use the filter facets shown on the left side to shrink down the search results to exactly what you are looking for. So in case you are looking for a base image, you can either use the filter facets on the left side, the image architecture category base image or you can click on the corresponding tile on the Red Hat Container Catalog Explore page. If you click on the Explore page tile you will see this base image overview page which basically gives you a little bit description what a base image is all about. So this is something Scott McCarty wrote up and we are highlighting the two main base images we as Retter provide and compare them side by side. Below this page you will see the list of all the Retter repositories we ship or Retter Enterprise Linux repositories and this might be a little bit confusing that you see 10 results if you hide better and deprecated repositories and this is something to do with Surrell or Retter Enterprise Linux repository structure. So we ship the latest version into the top-level repository called Well. We have a special repository, Relatomic, we have major release repositories and we have minor release repositories. For the minor release repositories over time those are getting deprecated and we clearly mark them as deprecated in the Container Catalog with warnings and guidance which repositories should be used instead. If you already found what you are looking for you probably want to see a little bit more details, key characteristics, what is the surrounding documentation and what can I do with it, how can I learn more about it. If you go to the repository overview page you will see a lot of details there on an overview table and you might notice the additional tabs for surrounding documentation, for all the text or image versions inside your repository, some technical details coming out of the data inside the image. So if you want to, if you decided you want to pick one particular image you have multiple options to consume this image. So it's much more than just docker pool or atomic run or open-shift, we provide additional guidance for different runtime environments and we have this surrounding documentation tab which also includes a lot of documentation how to pool and use it. So as I mentioned it, the multiple what we call a choir pass provide guidance how to consume those images for different runtime environments and registry. So this is the satellite six template shown here which provides some guidance, how can you synchronize the entire repository or an individual image into satellite six running in your own premise environment that you can consume the images from there. If you already synced it you probably want to better understand how can I use and maintain those images over time. And this brings me back to the search overview page. So you can search for nearly everything. So the search is probably the most powerful element in the container catalog. You can search for images, namespace repositories, you can search for products, you can search for image IDs, for advisory IDs, for categories, keywords and so on and so on. The type ahead options as opposed to support you to find the most relevant items in the container catalog. The filter facets on the left side can be used to come down to the most relevant search result and you get back a list of key data results for the repository shown up. One of the items you might have noticed on the search result is the grade. So if I go back to the previous slide you will see most of the times A and there's one B images which you can see in the middle. And this is what we call the container health index. So we made a press release earlier today around the container health index. So basically if you look on container images, container images are static content bundle which means if we ship them into our registry by definition they are getting outdated over time. It's automatically nothing can prevent you that the image gets outdated over time because the static content bundle met security issues which immerse frequently. And I put some numbers in there that you can better understand what we are doing with the container health index. So basically we have more than 2,000 images in our registry and we will add ecosystem images very soon and more than 500,000 RPM packages are inside those images. On the other hand we have more than 3,000 advisories with more than 5,000 unique CVs we can compare those image content bundles against. As a reminder last year 97 critical security advisories came out and if a critical security advisory comes out this immediately shows up in the container catalog nearly in real time so we need some time that we can process it. But you will see that this image is affected by this particular content update inside and the grade goes down to B immediately. So the health index indicators are on the one hand the age of the image on the other hand the unapplied updates where a CVE is attached to it. So we are focusing on security data it doesn't matter if it's a security advisory also there are bug fix enhancement advisory CVs are attached to it and we are parsing them as well. So basically again we develop this as a cross-team effort of course with the help of our product security team who by the way developed the initial prototype of this piece and the idea is to reduce complex or to provide complex security data in a simplified way with one leather health index grade. And we are leveraging all the Reddit security data we provide so all the advisories for all RPMs inside the images for all products and this provides actionable scan results and I will explain a little bit better what does it mean. So if you look on the tech index page where you see all the image versions inside the repository you might notice the health index history graph over time which shows what we as Reddit are doing. So if there's a critical security advisory coming out which impacts one of the images you will see that the freshness grade goes down to B but at the same time we are starting to respin this image which probably as you see in this screenshot probably in most of the cases we are able to bring it back to A with shipping a newer image version just because we have all the data we need to maintain those images and then you can see that all the versions inside the same repositories have a worse fresher spray so in this case C and this is typically so this is true for all the images. Again you can search for an image ID you will see which freshness grade the image ID or the image version you are currently using currently has. If you search for an image ID and come to the particular tech details page or on this particular tech or image version you will see by default the security details tab if it's not the current version you will see a warning pointed you to the most current version inside the repository you will see the health index with a short summary of what exactly this particular letter grade means you will see the applicable vulnerabilities by advisory severity and you will get a full list of the advisories and the most powerful thing is on the bottom right side besides having the list or the advisory of the RPM content inside which helps you getting rid of the fix we provide an information in which all this image version this fix is contained as well so basically if you want to get rid of one of the security advisories listed at the bottom of this page you can apply the image version or at least this image version which is shown in the applicable updates table so this is the reddit container look could look a very brief summary there's much more we can talk about if you have any questions, want to file a feature request or have some other feedback please don't hesitate to step by at the UxD booth it's right over there I will be there most of the time together with Dash Copeland who is one of our leaders thanks a lot for your patience


What's going on everybody got Kyle here relating sports cards and we are ripping this is one box of contenders optic basketball for Kato One moment Dude, yeah, I've heard I've heard some horror stories so far Spencer for sure some people selling a little too early on those I mean, there is no way that there's no way to know that that would happen But I've heard a couple Josh was saying one earlier where a guy intercepted a package on ebay after he had already sold the card He intercepted it from the once the thing came out. He went back and grabbed it Alrighty. Good luck. Kato one box of contenders optic basketball. I backs are serious man. There's some serious prices on those for sure Alrighty, good luck. Kato. We got a lottery ticket to start us off Jabari Smith, Jr Jabari Smith, Jr Behind that we have a blue blue ice Jabari Smith, Jr to 75 Going back to back on the Jabari's Third pick in the draft for the Rockets got a season ticket Chris stops Got a um hallowed de mar de rose in the season ticket. Oh nice and short print is black pandora It is season ticket of devon vasel on the short print black pandora not numbered on these but do love the design man black pandora is one of my favorites And on the back we have two 99 it's going to be red rookie ticket on card auto of trevor keels working for the nicks The variation ticket the horizontals are the variations Rookie ticket red to 99 All righty there Kato that'll do it quick one there um optic basketball. Thank you. Thank you. We'll get it right out to you


Hello and welcome to lecture number 30 of this lecture series on introduction in on jet aircraft propulsion. We have been discussing about the components of aircraft engines and the last lecture we had devoted exclusively for discussion on one of the components which constitute an aircraft engine that is the nozzle. And I think during the last lecture we had some detailed discussion on different types of nozzles. We have discussed about subsonic nozzles and supersonic nozzles and various types of these nozzles like fixed geometry, variable geometry, axisymmetric nozzles and two dimensional nozzles and so on. We also had some chance to discuss about what are the functions of a nozzle besides the fact that nozzles are primarily meant to generate thrust. Modern day nozzles have various other functions some of which are for thrust reversal which is used for breaking an aircraft when it is landing then thrust vectoring used popularly in combat aircraft. And besides that it also has to keep noise control and some of the aircraft have to like the military aircraft also have to keep in mind that the nozzle exhaust should have as low an IR signature that is infrared signature as possible. So, that it can escape enemy radar from being detected. So, these are some of the functions that a modern day nozzle has to satisfy with the fact that it has to also work as a unit as a single unit along with the rest of the other components like the intake, the compressor, the fan and the compressor, the combustion chamber, the turbine and the jet pipe and so on. So, all these components put together constitute the engine and when an aircraft is operational it has to operate over a variety of operating ranges and all these components need to be matched. And so you would also be looking at matching process between various components in the next few lectures you would also be discussing about matching of these components separately and matching is obviously a very important aspect. Even though individual components may be designed for highest possible efficiency it should be ensured that when they are all put together and when they form an engine then they all work as optimum as possible and that is where the importance of matching comes into picture. So, nozzle obviously is all another component the last component of an aircraft engine which also needs to be matched with the other components. So, in today's lecture we are going to discuss about the function while we have already discussed the functions we are going to discuss about the working of these nozzles the different types of nozzles from a very fundamental thermodynamic sense. If you have undergone thermodynamics or gas dynamics course you probably would have discussed about you would have already learned little bit about how different nozzles work that is subsonic nozzle and a supersonic nozzle work and how the pressure ratio across these nozzles can be controlled and so on. We will discuss some of these aspects in today's lecture. So, today's lecture we shall be taking up some of these topics we shall talk about the working of subsonic and supersonic nozzles. We will be very briefly discussing about the performance parameters of these nozzles and towards the end of the lecture we will also discuss some of the issues which nozzle expansion will have like if it is not correctly expanded or fully expanded then there could be some problem with the flow that is coming out of the nozzle. So, before I start discussing details about the subsonic or the conversion nozzle and subsequently the convergent divergent nozzle let us review some of the concepts which I presume you would have learned in either the gas dynamics course or if you have undergone one of our earlier courses on introduction to aerospace propulsion some of these topics have already been covered there in detail. We will quickly review some of these concepts before proceeding towards understanding of the working mechanism of these nozzles. Now, in the last class I think I mentioned that in a conversion nozzle there is a certain limitation to the Mach number that can be achieved that is if we keep varying keep reducing the downstream pressure the back pressure so called back pressure. The flow will accelerate in a subsonic flow will accelerate in the nozzle and what is the maximum Mach number that it can reach the maximum Mach number it can reach in a conversion nozzle as you probably know is Mach 1 that occurs when the flow or the flow rate has reached its maximum level of the throat of the nozzle throat is the area that is the minimum cross sectional area of a conversion nozzle. When the mass flow reaches its maximum then at that instance the Mach number at the throat would be unity and under this condition the flow or the nozzle is said to be choked. Now, if you want to reduce the Mach number further one might intuitively want to reduce the area further that is we will attach let us say another conversion nozzle to that. What you will notice obviously is that that is not going to help it is not going to reduce the it is not going to increase the Mach number further. If a Mach number increase has to indeed take place after the throat of a conversion nozzle we will need a divergent section and that is why we have conversion divergent nozzle wherein we can achieve supersonic flow which is not possible in conventional simple conversion nozzle. So, in a conversion nozzle as I am going to illustrate here now this is an illustration of a conversion nozzle. So, in the first one we have a conversion nozzle which has upstream pressure stagnation pressure P 0 or P naught and stagnation temperature T naught as the flow accelerates through the nozzle it reaches sonic Mach number that is Mach 1 at the throat. And of course, this occurs only for certain back pressures it does not occur always if there is a sufficient pressure ratio then the nozzle can be choked and you get a sonic velocity here. Now, if you want to increase the Mach number further and after that is after this we want a supersonic Mach number it will not help if you put in another conversion nozzle here. Let us say we put another conversion nozzle with this as the inlet area of that nozzle and in area which is much smaller than this at the exit. What will happen is that the sonic point of the throat will shift. So, as you attach this additional portion here the throat will shift to a new location which means that the location which was the throat for the first nozzle where you had Mach number unity will now longer be sonic Mach number you would have a subsonic Mach number here sonic Mach number would have shifted. Of course, this will not keep happening if you keep increasing the area I mean the area ratio further then it will obviously result in losses there will be increased losses in the nozzle and it is not a feasible proposition. So, this requires that we attach a divergent section after the throat attaching a divergent section is the only solution that we can get a supersonic Mach number in a nozzle that is conversion section ending in a throat followed by a divergent section. Now, in your gas dynamics course you must have derived what is known as the area velocity Mach number relation right where we must have seen that when Mach number is less than 1 then when there is an increase in area we have decrease in velocity that is we have a diffuser and if there is a decrease in area we have an increase in velocity. Whereas, if it is supersonic Mach number then the trend is reversed and increasing area will actually give you an increase in velocity and vice versa that is a decrease in area will result in decrease in the velocity this is for a supersonic flow. Which means that if that is to be true for this conversion nozzle which has attained a sonic Mach number at its throat you can achieve a supersonic Mach number further if we attach a divergent section that is in a at the end of a convergent section where it has reached its throat. If we attach a divergent section there then it is possible that we can get supersonic Mach number in the divergent section and little later we will see that it does not always happen it requires certain conditions to be satisfied like the pressure ratio the back pressure has to be low enough for you to achieve supersonic flow even in the divergent section that we will discuss a little later. Now, in the next slide what I shall show you is probably something you would have learned in gas dynamics or in the previous course which is a direct outcome of the area Mach number velocity relation which is what I had just described that what happens for subsonic flow and what happens for supersonic flow are entirely opposite when it comes to nozzles and diffusers. So, let us take a look at what happens there. In a subsonic flow let us say the first two diagrams the top two pictures or illustrations are true for a subsonic flow subsonic flow Mach number upstream Mach number is less than one decrease in area results in decrease in pressure and temperature static pressure and temperature it at the same time results in increase in velocity and hence the Mach number. If we put the nozzle the other way around that is Mach number is still less than one upstream, but area is now increasing then the pressure and temperature static pressure and temperature increases velocity and therefore, the Mach number decreases. Therefore, the first one is known as a subsonic nozzle second one is known as a subsonic diffuser. Now, the reverse exact reverse of this happens when the flow is supersonic if Mach number is greater than one then an increase in area as you can see here will result in decrease in static pressure and temperature and therefore, velocity and Mach number and therefore, this is a supersonic nozzle and Mach number greater than one that is in supersonic flow if there is a decrease in area it results in increase in static pressure and temperature and therefore, it will results in increase decrease in velocity and hence Mach number. So, this is basically supersonic diffuser.   So, this gives us some idea on how we can proceed now we are stuck with the fact that in a in a convergent section we can only achieve sonic Mach number. So, what do we do if we have to get a supersonic Mach number beyond the throat. So, after the throat now if we need to get a supersonic flow the best way to do that is or well rather the only way to do that is to attach a divergent section. So, a divergent section as we have seen now will get us a supersonic flow because a divergent section in a supersonic flow is a nozzle for a supersonic flow. So, if we have to get achieve supersonic flow we will need a divergent section. So, all supersonic nozzles will have a convergent section which will end in a throat which is the minimum area of that entire nozzle followed by a divergent section where we can get supersonic flow. So, in a supersonic nozzle we normally refer to supersonic nozzles as convergent divergent nozzle because it has a convergent section it also has a separate divergent section and in between these two there is a throat where the area is minimum. So, supersonic nozzles will be basically convergent divergent nozzle. So, today's lecture we will discuss in detail about how a supersonic nozzle can work and we will see very soon that it cannot work in under any circumstances there needs to be a certain pressure ratio across the nozzle which has to be maintained. So, let us begin our discussion with the discussion on the subsonic nozzle first. Let us see what happens in the case of a convergent nozzle. So, in a convergent nozzle what we will discuss begin with is that convergent nozzle as we have seen can give us the maximum of Mach number of 1. So, beyond that obviously we cannot increase the Mach number that is a convergent nozzle. So, before we look at the convergent nozzle let us look at one set of equations which will be used in both the cases whether it is subsonic or supersonic flow. So, we will look at one of the governing equations for this where we will derive an expression for the mass flow rate which can pass through these geometries whether it is convergent or convergent divergent nozzle. So, mass flow rate as we know it from continuity is equal to the product of the density the velocity and the area. So, from product of these three we can calculate mass flow rate. So, let us express mass flow rate in terms of parameters like the upstream parameters the staggeration pressure and temperature and some of the other parameters including Mach number. Let us express or derive an expression for mass flow rate which we can use in our subsequent discussion on convergent as well as c d nozzle that is convergent divergent nozzle. So, let us basically consider flow of a calorically perfect gas through a nozzle which could either be a convergent nozzle or convergent divergent nozzle. So, mass flow rate as we know it is product of density velocity and area density we know is pressure divided by r t p by r t velocity is Mach number times square root of gamma r t and area. So, here we have we are going to simplify this we have now Mach number times area p by p naught which is p naught is a stagnation pressure multiplied by p naught into square root of gamma divided by square root of r t into square root of t by t naught this basically comes from this expression here because we have a square root of r t here and r t. So, this becomes square root of r t and t by t naught. So, this again we can simplify we now have square root of gamma into p naught which is stagnation pressure divided by square root of t naught into r multiplied by Mach number into area. In the numerator we have 1 plus gamma minus 1 by 2 m square and where does this come? This comes from the temperature ratio that is t t naught by t is 1 plus gamma minus 1 by 2 m square and that is why we have the square root 1 plus gamma minus 1 by 2 m square raise to 1 by 2 because it is square root of this. Similarly, pressure we have expressed in terms of Mach number we have 1 plus gamma minus 1 by 2 m square raise to gamma by gamma minus 1. This we can again simplify this after we simplified we get an expression mass flow rate is equal to area times stagnation pressure divided by stagnation temperature square root square root of gamma by r which are properties of the gas multiplied by Mach number m divided by 1 plus gamma minus 1 by 2 m square the whole raise to gamma plus 1 divided by 2 into gamma minus 1. So, this is a simple expression which relates mass flow rate and some of the other parameters which are involved mass flow rate then the inlet stagnation pressure temperature and Mach number besides of course, the gas properties like the ratio of specific heats gamma and the gas constant r r. So, what we have here is an expression which tells us that what is the mass flow rate which a given area can give. So, here again the area comes into picture once we know the stagnation pressure temperature and the Mach number or vice versa if we know the mass flow rate and of course, the area we can actually calculate what Mach number we are operating it. And so, from this expression which can be used for both subsonic and supersonic nozzles we can basically relate mass flow rate with the other parameters like stagnation pressure temperature Mach number and so on. So, with this background in mind we will now try to analyze flow through a convergent nozzle, but we will look at an isentropic flow through a convergent nozzle. When we talk about isentropic flow we are inherently assuming that the flow is adiabatic and of course, it is reversible. Well adiabatic flow is true in this case because the amount of change in pressure that occurs across the nozzle is much larger than the amount of heat transfer which may take place across the walls of the nozzle. So, with that assumption in mind we can keep we can safely assume that the flow through these nozzles are adiabatic there is no heat transfer really even though there would be heat transfer that is very small compared to the pressure drop which occurs in the nozzle. Therefore, it is safe to assume that the flow is adiabatic and so with for an isentropic nozzle flow or isentropic flow across a nozzle we will now look at what happens in a convergent nozzle. How the pressure changes? How the mass flow rate changes and so on in a convergent nozzle which is basically a subsonic nozzle which we will very soon see that the max Mach number which we can get and the reasons behind that is unity you can get a Mach number of 1 at the throat of the nozzle. So, we will look at a convergent nozzle first in a subsonic flow which means the convergent nozzle in a subsonic flow will have to have a decreasing area along the flow direction. We will now consider the effect of back pressure on the exit velocity mass flow rate pressure distribution etcetera and we will also assume that the flow is entering the nozzle from a reservoir in such a way that it is stagnation pressure there therefore, inlet velocity will be 0 and stagnation pressure and temperature will not change in the nozzle that is stagnation temperature cannot change because it is adiabatic there is no heat transfer across the nozzle walls and the stagnation pressure we will assume does not change because we will assume that there are no pressure losses. Let us take a look at what happens? So, I have here a very simple schematic of a convergent nozzle. So, this is a convergent nozzle in subsonic flow it has to be increasing area. We will now see the effect of back pressure which I have denoted by P subscript b on the flow properties in the nozzle the upstream pressure that the reservoir pressure is P naught which is stagnation pressure it also has a stagnation temperature of T naught. The nozzle exit pressure is denoted by P subscript e or P e. Let us look at the ratio P by P naught that is pressure at any instant versus the reservoir pressure for any value of back pressure. The first instance is if back pressure is equal to the reservoir pressure what happens? Well if the pressure at both ends are same obviously, there is no flow taking place across the nozzle. So, there will not be any flow. Let us see what happens if we decrease the back pressure we have decreased the back pressure now, but it is still greater than the critical pressure critical pressure is denoted by P star critical pressure tells us or denotes that pressure at which we get a sonic flow or choked flow at the exit of the nozzle. So, second instance we have P b which is greater than P star, but it is still less than these reservoir pressure.  Now, we have P b by P naught less than 1 there, but it is still greater than the critical pressure. Now, if you further reduce it we reduce back pressure and now it is equal to the critical pressure critical pressure refers to the pressure where we get sonic flow at the throat. Now, when P b is equal to P star that is when the flow has attained the maximum mass flow rate that it can pass through we get choked flow here mach number is equal to 1 and mass flow rate reaches the maximum value possible.  Any further reduction in P b if it is P b less than P star it will still lead us to the same flow rate that we are talking about whatever be the flow rate here we continue to get the same mass flow that we get at this particular point. So, it does not change the pressure characteristic it is the same because the way the pressure drops in the nozzle will continue to remain the same even after we reduce back pressure any further than the critical pressure. So, this is how pressure ratio varies across the nozzle let us look at how mass flow rate varies we have discussed about pressure ratio already. The first chart here is for the mass flow rate the second one is the pressure ratio exit to the inlet stagnation pressure. So, we are beginning our flow right here where mass flow rate is 0 which occurs when P b is equal to P naught that is ratio P b by P naught is equal to 1 that is when we have 0 mass flow rate. Now, as the ratio decreases as P b by P naught is reducing mass flow rate is increasing as you can see here from 1 it goes to 2 when P b is equal to P star which is the critical pressure then we have the mass flow rate which reaches its maximum value which is m dot max. If you look at the corresponding pressure ratio plot here we starting from here where P by P naught is 0 is equal to 1 and as that ratio continuously decreases we reach here which is P star by P naught any further reduction does not change the mass flow rate and it does not change the pressure ratio as well P star by P naught remains the same mass flow rate has reached its maximum value. So, this particular condition of the flow which we have seen just now discussed that is at state 3 and beyond is known as the choked flow we are saying it is choked well literally choked means that whatever we could pass the maximum that one could pass has reached and that is known as choked we cannot take up anything more than that is known as choking. So, the nozzle has choked means that it has passed the maximum mass flow that it can and any further increase will not change the mass flow rate that the nozzle can handle that is known as the choked flow. So, for a subsonic nozzle a convergent nozzle choked flow is the limit to which it a nozzle can operate beyond which nothing can happen it will continue to it will in fact lead to more losses or if one tries to increase the mass flow because mass flow cannot increase beyond that level. So, a nozzle when operating under choked condition will have mass flow rate is equal to maximum mach number is equal to unity sonic mach number pressure will be equal to the critical pressure which we have denoted by P star. So, from the above figure that we have just discussed now the back the exit pressure P e will be equal to the back pressure for all back pressures greater than P star exit pressure will be equal to the critical pressure for any back pressure which is less than the critical pressure itself. So, for all back pressures lower than the critical pressure exit pressure will be equal to critical pressure mach number is unity and mass flow rate is maximum that is we get a choked flow back pressure lower than the critical pressure cannot be sensed in the nozzle upstream flow and it does not affect the mass flow rate. So, any back pressure which is lower than critical will not be sensed by the upstream flow and therefore, it does not change the mass flow rate. So, before we discuss a little more on how we can analyze the flow, let us look at quickly look at nozzle efficiency. We have already derived this in one of the earlier lectures, but let me quickly review that nozzle efficiency. We are talking about a process this process which is shown by the dotted line where the nozzle inlet pressure is been denoted by P o that is P naught stagnation inlet and exit condition is denoted by P e which is static pressure. So, this is the actual process. The solid line here shows the isentropic process which will be denoted by P e s where s stands for the isentropic flow. Now, the corresponding exit stagnation pressure would be P o e or P naught is the stagnation pressure subscript e is for the exit. Now, what is to be also kept in mind is that there is no change in stagnation temperature because it is an adiabatic flow stagnation temperature cannot change unless there is heat transfer. So, T o T naught i which is stagnation temperature inlet will be equal to T naught t which is stagnation temperature at the throat that will also be equal to stagnation temperature at the exit T naught e. So, this is how the process will look like. Now, with that in mind we have defined efficiency earlier nozzle efficiency is H naught i which is stagnation enthalpy at the inlet minus H e static enthalpy at the exit divided by H naught i minus H e s which is static enthalpy for an isentropic process where H e s is the static enthalpy for an isentropic process. We express this in terms of temperatures. So, efficiency will be equal to T naught i minus T e divided by T naught i minus T e s which is 1 minus T e by T naught e because T naught i and T naught e are the same divided by T e s by T naught i. So, this we will now express in terms of the Mach number and the pressure ratios. So, for a choked flow what happens is that Mach number is equal to 1. So, this temperature ratio that you see here T naught e by T e is 1 plus gamma minus 1 by 2 m e square and since m e is equal to 1 when we equate that equal to 1 we get 1 minus 2 by gamma plus 1 divided by 1 minus p c or critical pressure divided by p naught i raise to gamma minus 1 by gamma. So, from this if you simplify we get the critical pressure ratio or just the pressure ratio p naught i by p c is equal to 1 by 1 minus 1 by eta and the nozzle efficiency multiplied by gamma minus 1 by gamma plus 1 raise to gamma by gamma minus 1. So, if we see that in this case when Mach number is equal to unity the pressure ratio the critical pressure ratio is only a function of the gas and of course, the nozzle pressure ratio. So, if we get this number p naught i by p c less than the actual pressure ratio p naught i by p a or the ambient where p a is the ambient pressure the nozzle is operating under choked condition. So, if this pressure ratio that we have seen which we can calculate based on the gas properties and the nozzle efficiency if that is less than the pressure ratio corresponding to the ambient pressure the nozzle is operating under choked condition. And so, given a certain nozzle geometry and some of its properties the type of gas which is normally either air or combustion products from the pressure ratio we can actually find out whether the nozzle is going to operate under choked condition or not. So, if that pressure ratio which we have just now derived p naught i by p c comes out to be less than p naught i by p ambient then it means that the nozzle is choked. In most of the aircraft which use subsonic nozzles or convergent nozzles the nozzle will most of the time at least under the design operating condition we operating under choked condition because that gives us the maximum mass flow which can which the nozzle can handle. And of course, this choking condition can be changed by changing the area ratio which is one advantage which adjustable or variable nozzles have. So, if the nozzle exit area can be changed then the choking condition can be changed. So, the nozzle can be un choked and then depending upon the operating condition the nozzle area can be changed to get again a choked flow at the exit. So, that is obviously one of the advantages of a variable area nozzle. So, for a convergent nozzle let me summarize what we have just now discussed. So, in a convergent nozzle if it is operating under choked condition the exit Mach number is unity as we have seen. The exit flow parameters will then be defined by the critical parameters that is the exit pressure will be equal to critical pressure exit temperature will be equal to critical temperature exit density is critical density and so on all exit properties will be equal to critical parameters. This also we have discussed when we were talking about the cycle analysis real cycle analysis or even ideal cycle where we have actually calculate the pressure ratio. And then see just see if the nozzle is choked or not if it is indeed choked then we have to equate the exit conditions to the choked parameters. So, if the pressure ratio is greater than the critical pressure ratio the nozzle is said to be choked in which case the parameters at the exit of the nozzle will be equal to the critical parameters that we have which we can calculate because critical temperature for example, T e will basically be a function of gamma that is it will be 2 by gamma plus 1 into T naught and so on because T naught by T is equal to 1 plus gamma minus 1 by 2 m square for critical condition m is equal to 1. So, you get T naught by T e is equal to 2 by gamma plus 1 and so on or gamma plus 1 by 2. So, based on this we can actually calculate the exit conditions of the nozzle which will only be purely a function of the upstream stagnation conditions and the ratio of specific heats that is gamma. So, having understood operation of a subsonic nozzle let us now take up a supersonic nozzle that is a convergent divergent nozzle. Let us now look at how an isentropic flow behaves as it passes through a c d nozzle a convergent divergent nozzle. We will analyze the flow in a very similar manner as we have done for subsonic flow that is we keep changing the exit back pressure and see how the flow varies in the nozzle. Of course, in this case the flow is going to be slightly more complicated because of the fact that we are going to deal with supersonic flows there will be presence of shocks. So, some of these aspects we are going to discuss very soon. So, in a c d nozzle the basic advantage is that we can achieve supersonic Mach number which can be achieved in the divergent section. Well, but divergent section alone cannot guarantee a supersonic flow we need to ensure a certain back pressure. So, that is what we are going to discuss now. So, for that let us again take up a very simple c d nozzle it is a linear c d nozzle just for the sake of simplicity. We have a convergent section as you can see here which is very similar to the convergent nozzle we have seen in few slides earlier followed by this throat this is the throat section we have the divergent section. Convergent nozzle ending in a throat followed by the divergent section this constitutes a typical convergent divergent nozzle upstream pressure that is stagnation pressure the reservoir stagnation pressure is p naught exit pressure static pressure is p e we have a back pressure p b. So, let us now look at how the flow would vary as we keep changing the back pressure initially when p a is equal to p b which is the equal to the stagnation pressure there is no flow taking place. Now, as we decrease the back pressure we have now new pressure which is p b which is less than p naught, but it is still greater than the critical pressure in a convergent section the flow will accelerate which means there is a drop in static pressure from inlet to the throat from the throat till the exit it is a divergent section in a subsonic flow. So, there has to be diffusion or deceleration leading to increase in static pressure. So, the static pressure increases, but it reaches a value which is lower than the stagnation pressure upstream. We further increase it we reach a point where which is basically corresponding to the joked condition we still have subsonic flow because when p b is equal to p star which is the critical pressure at the throat we get sonic flow at the throat and that is indicated by p star. So, you can see that for all these three cases we still have a subsonic flow at the nozzle exit. Now, our objective here is to get a supersonic flow which means that we have to now furthering decrease the back pressure. Now, what happens is for a back pressure which is lower than the critical pressure there are different conditions which can exist that is as the back pressure is lower to value which is lower than the critical pressure which means that the flow is no longer well it becomes sonic at the throat, but since the back pressure is lower than critical pressure then we have a divergent section here which will act like a nozzle in a supersonic flow. So, we have a divergent section. So, the flow becomes supersonic which is why you can see the static pressure continues to drop because the flow is accelerating and that happens in a supersonic flow. So, after the throat it the flow becomes supersonic and under certain conditions if the back pressure is not low enough you might have a normal shock within the divergent section of the nozzle itself. So, there could be a normal shock here which means that downstream of the normal shock the flow is subsonic. So, after the normal shock we have a subsonic flow which means that the divergent section will now behave like a subsonic flow a diffuser. So, you can see there is again an increase of static pressure. So, this occurs till a point where the back pressure is low enough to ensure that there is a supersonic flow that is we have to continuously decrease even we are now at a back pressure which is equal to p d we have to decrease further even if it is p e we continue to have a subsonic flow in the nozzle exit which is not the objective. So, the back pressure has now is now supposed to be lower than all these pressures. So, if back pressure is further reduced we now have we can ensure that the normal shock that was existing here can be pushed out of the nozzle. So, that we get a supersonic flow at the nozzle exit which is basically our objective that we need a supersonic flow at the nozzle exit. So, for back pressures which are not as low as this, but it is lower than critical pressure we might end up having a shock within the divergent section of the nozzle which is obviously not a good thing. So, if you look at the Mach number plot for these conditions we had the first case that is for subsonic flow we have Mach number increasing from the inlet all the way to the throat, but it is not Mach number equal to 1 at the throat after which again the Mach number decreases. For critical pressure when we have sonic flow at the throat Mach number increases reaches Mach 1 and then again it decreases their decelerates because it is subsonic. For back pressure is equal to p d we have Mach number equal to 1 at the throat it continues to increase, but only up to the shock after which it becomes subsonic and it decreases below 1. For Mach numbers for continuous supersonic Mach number all the way up to the nozzle exit we need to ensure that the back pressures are low enough so that there is no shock within the divergent section of the nozzle. So, this is the basic operation of a CD nozzle a convergent divergent nozzle where we can achieve a supersonic flow under certain operating conditions that is depending upon the nozzle pressure ratio one can ensure that we can achieve supersonic flow in a CD nozzle. So, simply fitting a divergent section at the throat of a convergent nozzle will not suffice we need to ensure that there is a sufficient pressure ratio which can lead to supersonic flow within the nozzle. So, with this background in mind we shall now derive some expression as we did for convergent nozzle also to evaluate the performance or some of the parameters like mass flow rate through a supersonic nozzle and so on. So, what we will do is we are going to assume as we have done for convergent nozzle that the flow is adiabatic because heat transfer per unit mass is much smaller than the difference in enthalpy between inlet and outlet. The flow can be assumed to be isentropic up to the throat, but from the throat to the exit it may not really be isentropic because there could be possible shocks specially under certain operating conditions. So, the nozzle efficiency we have already derived for the subsonic nozzle which is h naught i the inlet stagnation enthalpy minus h e divided by h naught i minus h e s which we can express in terms of temperature ratios 1 minus T e by T naught e divided by 1 minus T e s by T naught i. This will now be expressed in terms of the pressure ratios.  So, here we will now express P e by P naught e in terms of the nozzle efficiency and the other pressure ratio. So, the exit pressure to the exit stagnation pressure ratio is equal to 1 minus eta n which is nozzle efficiency into 1 minus P e by P naught i raise to gamma minus 1 by gamma the whole thing raise to gamma by gamma minus 1. Now, we can now express P naught i by P naught e as P e by P naught e multiplied by P naught i by P e. So, from this we get P naught i by P e P naught e is equal to P 0 i which is a stream stagnation pressure divided by P e into this term that is 1 minus eta n into 1 minus P e by P naught i raise to gamma minus 1 by gamma raise to gamma by gamma minus 1. So, the exit velocity so, which we have also derived for the cycle analysis is u e which is square root of 2 into h naught i minus h e which in terms of efficiency becomes 2 into eta n into h naught i minus h e s and this again in terms of temperature is 2 C P eta n into T naught i minus T e s this is on simplification 2 gamma r by gamma minus 1 into eta n into T 0 i multiplied by 1 minus P e by P 0 i raise to gamma minus 1 by gamma. So, this combined with the previous equation that we have seen we will now express that in terms of the Mach number. So, the exit Mach number as we know is M e square of that is u e square by A e square that is u e square by gamma r T e. Now, we know that T e by T naught e by T e is 1 plus gamma minus 1 by 2 M e square which is T naught i by T e. Therefore, we can express M e from what we have seen in the previous equation that is u e square and this equation we get 2 into eta n by gamma minus 1 multiplied by 1 minus gamma minus 1 by 2 M i square where M i is the inlet Mach number multiplied by 1 minus P i by P naught i raise to gamma minus 1 by gamma. This of course, can be simplified and written here in terms of the pressure ratio 2 by gamma minus 1 into the nozzle efficiency 1 minus P e by P naught i raise to gamma minus 1 by gamma divided by 1 minus eta n into 1 minus P e by P naught i raise to gamma minus 1 by gamma. So, here we have expressed the Mach number in terms of the pressure ratio that is the exit pressure to the inlet pressure. So, this will be useful in determining whether we get a sonic Mach number or supersonic Mach number especially in a supersonic nozzle one would want to have supersonic Mach number at the exit. So, we can find out what is the pressure ratio that will be required if we have to achieve a supersonic Mach number let us say we want to achieve a Mach number of 1.2. So, given the exit Mach number is 1.2 we can now find out what will be the pressure ratio that the nozzle will have to develop if one has to achieve the supersonic Mach number with a certain nozzle efficiency. So, nozzle efficiency in mind one can actually find out what will be the kind of pressure ratio that is needed to achieve that Mach number. So, the second part that we are going to look at now is to see how we can also derive expression for the area ratio we have now just derived the equation for the Mach number we will now look at how we can derive an expression for the area ratio. So, we have already discussed about the mass flow rate or the governing equation little earlier we will assume again isentropic flow of the up to the throat. So, we can express the throat area and the exit area as a t by a e which is throat area by exit area expressed in terms of the corresponding pressures and Mach number p naught e by p naught t which is the stagnation pressure at the throat multiplied by m e by m t Mach number of the throat into 1 plus gamma minus 1 by 2 m t square divided by 1 plus gamma minus 1 by 2 m e square raise to gamma plus 1 into divided by 2 into gamma minus 1 this also can be expressed in terms of the inlet pressure. Now, if the throat is choked where we have Mach number m t as equal to 1 the throat area becomes a star which is the critical area a star by a e would now be equal to p naught e which is exit stagnation pressure multiplied by exit Mach number divided by inlet stagnation pressure which leads to the choking multiplied by gamma plus 1 by 2 by 1 minus gamma minus 1 by 2 m e square the whole raise to gamma plus 1 by 2 into gamma minus 1. So, from this we can actually find out what is the critical area ratio area ratio between the throat and the exit of the nozzle which can lead to a critical flow that is choked flow at the exit of the nozzle. So, this is one of the expressions that one can use we have also seen how we can calculate the pressure ratio that is required to develop a certain supersonic Mach number at the exit of the convergent nozzle. We will also look at what is the mass flow rate that one can achieve especially if it is under choked condition what how we can calculate the mass flow rate. Because we already derived general equation for mass flow rate in terms of the inlet stagnation pressure temperature the Mach number and the area and we now know that for choking the Mach number at the throat becomes 1. So, from that we can actually calculate the mass flow rate in terms of the throat area and the inlet parameters. So, mass flow rate we can calculate using the equation we have discussed earlier where we substitute m is equal to 1 we now get a star which is the throat area multiplied by p naught i inlet stagnation pressure divided by t naught i square root the gas properties gamma by r square root 1 by 1 plus gamma plus 1 by 2 raise to gamma plus 1 by 2 into gamma minus 1. So, here we see mass flow rate is function of the inlet stagnation pressure temperature and of course, the throat area. Now, another aspect concerning the designer is that he would like to always try to keep the exit area the area ratio that is a i by a e as close as possible to unity. Because if the exit area is very large then it has other implications like it might lead to high levels of external drag. Because obviously, the entire nozzle and the engine is housed in casing in a nacelle. So, if the nozzle area is increased very large if we have an exit area which is much larger than the inlet area then the possibilities of external drag increasing would be very high. But if he does not do that if he tries to keep the area ratio as close as possible to unity then the nozzle may not be operating under what is known as the fully expanded condition that is fully expanded condition is 1 where the exit pressure is equal to the ambient pressure p e is equal to p a. If p e is not equal to p a then the nozzle could either be operating as an under expanded nozzle or an over expanded nozzle both of which has certain issues which we are going to discuss now. That is if a nozzle is under expanded what are the problems if it is over expanded what are the problems. So, we will take a look at how we can how a designer can keep this in mind in under these conditions. So, an incomplete expansion is a result of a difference between the nozzle exit pressure and the ambient pressure. Incomplete expansion could be either over expanded nozzle where the exit pressure is greater than the ambient pressure if p e is greater than p a it means that the flow is capable of additional expansion that is the flow has potential for expanding further and this is now carried out using expansion waves which will originate from the lip of the nozzle that is because the flow is having enough energy to further expand and that is why it will carry out that expansion because the pressure has to eventually become equal to the ambient pressure. So, that expansion takes place through nozzles through the formation of expansion waves. The other extreme case would be over expanded nozzle that is if p e is less than p a that is the nozzle is expanding more than what it should and how can that be taken into account well that can happen if there I mean in the instance where the exit pressure is greater or is less than ambient pressure there would be shock waves which would again be originating from the nozzle. So, across the shock wave the pressure would change increase a static pressure would increase. So, that you have exit pressure of finally, equal to the ambient pressure well the ideal case one would like to have of course, is a fully expanded nozzle where the exit pressure is exactly equal to ambient pressure. So, there are no shock waves or expansion waves here now if the exit pressure is much less than the ambient pressure then the shock waves will actually occur within the divergent section of the nozzle we have already seen that when we are discussing about the nozzle performance and behavior that if p e is much less than p a shock waves may actually occur within the divergent section of the nozzle. So, these are the illustrations of all these 4 cases fully expanded nozzle p e is equal to p a. So, there are no issues within the nozzle itself if p e is less than p a which means that it is under expanded. So, there would be expansion waves as you can see here which originate from the lip of the nozzle these are the expansion waves through which the flow will further expand and become equal to the ambient pressure. Now, if p e is greater than p a that means it has it has a actually expanded more than what it should be then we have an over expanded nozzle in which case the pressure gets finally, equalized through what are known as oblique shocks because now the pressure has to eventually become equal to the ambient pressure and that happens through what are known as oblique shocks. So, you may have oblique shocks originating from the lip of the nozzle and the pressure gets finally, equalized there if p e is much less than p a then we have an occurrence of a normal shock or which could occur within the nozzle itself in the divergent section and the pressure gets across in a normal shock we know there is an increase in static pressure. So, across the normal shock the exit pressure finally, becomes equal to that of the ambient pressure, but that is through a normal shock which obviously, means there are going to be losses across such a nozzle geometry. So, these are different operating conditions of supersonic nozzle where the depending upon the exit pressure in relation to the ambient pressure the nozzle may operate under different conditions. So, let me now quickly summarize what we have discussed in this lecture. We started our lecture today with discussion on subsonic nozzle conversion nozzle and we have seen that there are certain problems with subsonic nozzle in the sense that there is a limitation to the maximum Mach number which a subsonic nozzle can deliver and that is sonic Mach number that occurs right at the throat. So, we have seen how we can as we change the back pressure how the flow behaves through a subsonic nozzle we also derived an equation for analyzing this. We then took up the convergent divergent nozzle we have discussed in detail about how the flow behavior can be analyzed right from the inlet to the exit as the back pressure keeps changing. And then we have also derived equations for calculating the pressure ratio across the nozzle required for getting a desired supersonic Mach number at the exit of the nozzle what will the mass flow rate corresponding to choked flow and so on. And towards the end we have discussed about different operating conditions of supersonic nozzle where depending upon the exit pressure in relation to the ambient pressure the nozzle may undergo either over expansion or under expansion or if the exit pressure is much lower than the ambient one might also have a normal shock within the divergent section of the nozzle. So, these are some of the topics that we have discussed in today's lecture and in the next lecture that we going to discuss we will basically be having a tutorial wherein we will solve some problems on intakes as well as nozzles. So, we are we are already discussed about intakes today's lecture we conclude our discussion on nozzles and so in the next class we will take up some simple problems on intakes and nozzles and we will solve them in the class I will also have a few exercise problems for you which you can solve based on our discussion during the last few lectures as well as our discussion during the tutorial. So, we will take up some of these topics for discussion in the next class.


Next up we have our final presentation of the scaling and performance session titled, I believe it's pronounced carry scalable BFT consensus with pipeline tree based dissemination and aggregation by Ray Neheiser. My name is Ray Neheiser. So it was a slightly different pronunciation but even people in my own country get it wrong. So that's about I'm going to present to you our joint work curry scalable BFT consensus with pipeline tree based dissemination and aggregation, which was one of these SOP papers as in many of the tags today. So there is a lot of interest for permission blockchains, and there is also a decent interest for large number of consensus participants, and there's just like, relatively famous example are DM that stated in the white paper, or also quarter. Now, most of these systems rely on BFT consensus and most commonly on some kind of PBV derivative, or, or hot stuff. PBFT works relatively straightforward, where there's a leader that sends the message a proposal to everyone, everyone then votes on that that goes for several steps. And then there's a agreement on a given value or a set of values. If the leader fails, the leaders just switch to a different process. And after F plus one steps there, obviously is going to be a correct leader, and the system will be able to achieve that. And as such, BFT is a good example, or the derivatives are a good example, because they offer high resilience, low latency, and optimal reconfiguration as such an F plus one steps they will be able to reconfigure correctly. One of the problems of BFT, BFT derivatives are that they have a high message complexity due to the credit quadratic message complexity. Hot stuff is one of the process that tries to solve that a little bit. So instead of having all the members broadcast the messages, the, there's a center process that disseminates and aggregates the messages. So it has twice the number of communication steps per phase, and relatively similar to be BFT if the leader fails, the leaders just switched. And again after F plus one steps, we have a correctly robust system and consensus can be achieved. So it has the same high resilience is able to drop a little bit of the message complexity and still achieve optimal reconfiguration, but like it said, it now has twice the latency actually. And one of the problems of these solutions that they're actually inherently non scalable. And it's because one or more processes have to send receive and process all and messages and that leads basically to a bottleneck in terms of both bandwidth and CPU. And there are a bunch of alternative in the literature that tried to solve that, and that are on the on the basis of these algorithms either committee based solutions or solutions that are based on dissemination and aggregation trees. And committee based solutions are relatively straightforward way instead of having all the processes agree on the value we see each round, select a subset of processes, and that subset of process will do it in the name of the others, and then propagate the result. The problem is that there's still a decent chance that in one of these rounds, a majority of incorrect processes on there. So that can cause certain problems like in some cases low resilience, or in many cases also cause non deterministic safety. And committee based solutions avoid this, and such that they're similar to hot stuff where they create just a different communication architecture, where certain processes will relay the messages, and that way, we are able to dispute both the communication load, and the processing load, while maintaining the same resilience as BBD and hot stuff and the overall same guarantees. The problem is that these approaches are relatively hard to configure. On top of that, they have a problem of high latency like hot stuff already has twice the number of communication steps per phase. Now a tree has based on the depth for six, eight, 10 times more, and which leads to problems in terms of throughput as well. And in terms of reconfiguration just doing the same approach of trying a different leader won't do it because depending on the number of internal nodes and how the faults are distributed in the system, we might never find a correct tree this way and actually there's even a factorial number of different trees where only a small percentage is correct. So it's a really hard problem to solve. And in terms of the latency, while the messages propagate through the system, the majority of the time the majority of the processes are just idle waiting for the next message or waiting for the answers to process, which basically is a big problem because the the actual resource utilization is very low, so the throughput is much lower than it actually could be. And that's actually what we tried to solve with Calorie because Calorie is a tree based approach so we also use dissemination and aggregation trees, but we tried to solve several of those problems. And that's the following main challenges where we have optimal reconfiguration for low F number of failures, we compensate the extra latency through a pipeline lighting scheme, and we still offer high resilience. Let's first check out how we do the reconfiguration. Now, let's assume we have a generic tree like here with a fan out of five. And as long as our number of failures is smaller than the fan out. So how we will be able to reconfigure a tree such that we construct a robust tree in optimal steps. So, as we have the fan out here, we have to construct more bins than we have failures. The bin contains then the number of internal notes, so that in this case we have six internal notes. So we about build F plus one bins of six or more notes, and then relatively straightforward. If we then replace each bin, each number each internal notes with a pin, eventually we will pick the bin without any faulty notes which has to be there since there are more bins than faulty notes, and we'll be able to build a robust tree in optimal steps. For latency, we do a similar approach as hot stuff does for their problems but we extended further. So, as the leader sends the first message out, the leader already knows the hash of the previous block so the leader can also construct the second block, and the third block, and in the meanwhile pipeline several blocks optimistically through the system. The problem is how many messages can we actually pipeline. And so we have to look into how to how we configure this actually, because if we choose to small values we will underutilize the resources and have a lower throughput than necessary. So we need large values that will lead to congestion and the latency for the client will be much higher than necessary. So we need a performance model to configure curry properly. So, there's basically a total time that each round takes and the time is more or less dominated by the hop latency, so time, the propagation takes, and the computation at each step. And of the total time, there's a small time, we call the idle time so this basically the total time minus the time the process at the root needs takes to send the messages, and then minus the time it needs to process the messages. And when then if we have the total time at the idle time and the process time, we can then calculate the pipelining stretch which is the number of additional blocks, we're going to process in the system. And if you want to hear more of these details we have them in the paper that's going to be published and SSP. And if you want to have it beforehand you can send me a message on slack and I can give you a preprint. And we evaluated this on grid 5000 with up to 20 physical machines and did a executed the number of different experiments. So I quickly describe a small subset which are the most significant ones. And this particular experiment was executed with three different sizes of validator sets, namely 100 200 and 400 in a setting of 100 millisecond front trip time, and 100 MB links so that's, for example, inner Europe or inner US setting. And curry is presented with the two blue lines one one with and one without pipelining and hot stuff presented in the orange and red line with the yeah. So we configured the pipeline in search of Corey according to the previously presented theoretical model, resulting in a stretch between four and six. And so we can see on the x axis the throughput and a number of processes and the wire throughput. And we can already see that there's a pretty big difference between Corey and the start rate based approach where Corey actually has an throughput advantage of up to 26 times the throughput of hot stuff. And that is even that is due to these inherent scalability issues that I mentioned earlier with the large validator sets. And that also shows that the non pipeline version of curry above 200 processes already performs better than hot stuff and at 400 and already has doubled the performance, even though the high latency should be a relatively large problem. In the second experiment, we did a different setup where we had 200 milliseconds round with latency and 25 megabyte links, which is a setting, which is a geographic blockchain setting, which can also be found like in the algorithm paper for example. And for this experiment we vary the block size between 32 K and one MB, and then check the maximum throughput we can achieve. So we have on the x axis the throughput and the y axis the latency for this. Now hot stuff is relatively straightforward. But basically when we increase the block size, the latency also increased because the system starts bottle necking and the throughput increases as well until it reaches the maximum the system is able to handle. Now encourage results a little a little bit different. So first of all, if we have very large block sizes and the performance, we can't pipeline as well because we can just pipeline 0.1 blocks. So that's why we have at the top part of the graph, a little reduction in throughput. Similarly, because we only had 20 available server physical machines at very low block sizes, we are computing so many blocks in the system, such that it was up to 25 concurrent blocks that the performance degraded a little bit and we had actually a lower throughput than we actually could and a slightly higher latency because of the concession. The key takeaway of this graph is that there is a, the increase of latency is actually much higher than the increase, increase of light is much higher in hot stuff than the increase of latency in a calorie. So that in certain scenarios, even though we have to treat with the twice the number of communications that in this example, Calry still performs better than hot stuff in terms of latency in a number of the scenarios. We did a small test where we evaluate the impact of failures on the system. So we measured this in the same setting as the previous experiment with 200 millisecond round trip latency and 25 megabit links and configure the system in a way such that the current leader fails after 40 seconds and consecutively after being elected the next two leaders fail in the same manner. At this contribute a low number of failures, we see that Cori not only configures in a small time period as hot stuff, but it's also able to rescale up the pipelining to attain a similar throughput values before. So concluding Calry is able to easily scale to hundreds of processes in comparison to the state of the art. We outperform previous work by a factor of up to 28. In one of these scenarios, we have no resilient straight ups and achieve optimal requirement for a small value of F, which is arguably the most common case. There's much more experiments in the actual paper. And we also have any prototype available on GitHub if anyone is interested. Thanks everyone for listening and I'll be happy to answer any questions.


okay it's my garden all right this you've seen before flamingo seahorse and gecko the other gecko my solar lamps all right solar lamps okay I got green beans Italian Roma green beans there's my seago palm Thai basil hot peppers in that pot sweet Carmen sweet red peppers in here here's the egg plant Japanese egg plant okay is one is one eggplant all right that I have to pick let's see I don't know if there's enough light there's the other eggplant okay and this of course is the other side you know peppers are coming out okay Thai basil is very aromatic better than the Italian basil and that's of course the cayenne peppers they're not out yet but they will grow Italian green beans I already have them on here let's see the insects are biting me it is one it is one almost ready to pick with the others let me go to the other side very hot and muggy today we've been having a heatwave okay peppermint is growing garlic chives more garlic chives shamrock tomatoes I put strawberries in here but there's my barbecue smoker okay more bamboo chains people blow in fireworks people blowing fireworks the old stumpy table remember that so I got two kinds of tomatoes I got cherry tomatoes in here okay and I got the large tomatoes in this pot in here and the reason why I have everything in pots in five gallon buckets with potting soil is because the dirt the soil in this town is horrible it's loaded with rocks and very thick sticky clay like soil it's very bad for gardening only good for pine trees that's it good for pine trees but not good for gardens believe me okay that's it and I'll show you when everything is out next time


Alright, so I hope that you guys are excited as I am because CASPA for 2021-2022 will be opening up in a few short weeks this April-April 29th. So what that means is that you all have to get preparing and there are some things that you all need to be thinking about just in case they happen. And one such thing is what happens if you're weight-listed? What should you be doing? So that's what we're going to be answering in today's video.  It's Adana. Welcome to my channel. So I had a question posed by one of you which again, I love you guys' questions so continue to leave me comments in the comment section below, subscribe, like my videos, do all of that great good stuff because it helps my YouTube algorithm, helps my channel get out to other people who are looking for more information on other variations of the healthcare field and the PA profession is the best profession in the nation right now. So it's something that you all should absolutely be thinking about. So this question was from Edgar Weyland, I hope I said that right and it's not Weyland but either way Edgar asked, hey you might have answered this in another video. What steps should a student take if they are weight-listed? Okay. And so Edgar this question is kind of similar to if you don't get in the first time type of thing right? Because although you are weight-listed and you're waiting to see if somebody like declines their application or not, then you can't put all of your eggs in that basket. So there are a few simple steps that I think everybody should be thinking about doing or looking into doing as you're applying through CASPA and you're getting offers for interviews and possible wait lists, you should definitely be looking at the next step forward. One such thing that you should be absolutely thinking about is, hey if I do not get in what am I going to do? So if you're weight-listed and nobody gives up their seat what are you going to do? Have you just wasted that time just waiting for this one school to respond to you? Because I did that. I did that one of those years that I did not get in and so again I want to share all of my experiences, my foolish experiences with you guys so that you guys don't make these same mistakes. So what you absolutely should be doing is looking ahead at other schools that you're interested in and then how you can better your application moving forward. Obviously you were great enough to get an interview. You were good enough where they kind of want you, they want you at their program but there are some students that maybe edged you out on how they interviewed or edged you out a little bit on your GPA and so if you can just review your application and look at areas that you can actually improve on those are the steps that you should be doing or taking while in this wait list period. Because those wait listed schools they will let you sit until their whole roster is filled and then if somebody declines then you kind of get added on and that means that you're getting closer and closer to next year when CASPA will close and open up again and so you don't want to be wasting time waiting on schools. Another thing that you should be doing is probably just checking in every once in a while to see how many other interviews the school has and how many seats they're waiting to fill because that's something that you want to know if you're wait listed you're like okay are all the seats filled or is there two seats that are still waiting to be filled? Do you have two or three more interviews for those seats? Those are things and questions that you want to ask because depending on that that gives you a better idea of where you stand in like the wait list area I guess you can say. And it also gives you an idea of kind of like where you are on the list in terms of a first come first serve basis because if you interviewed early on in the cycle but they still have like four or so or three or four more interviews to go, yes there may be students that they pick from those interviews but at the same time like you're high up on the list because you were one of those wait listed first okay. Another thing that I definitely think you should be doing is absolutely positively researching the school researching the program in terms of like hey how much it costs when you need to get your financial aid information in place because if you are accepted you don't want to be scrambling at the last minute to get all of those various different pieces in place because again when you're wait listed you're not given that information early in the application cycle you're given typically an offer for a seat later on in the cycle and that means that it's closer to the time where you now have to go and say hey job that I have or that I've had for a year or two years or three years I'm actually no longer going to be here I'm giving you my one month notice or three week notice or two week notice depending on how much time you have left there that I'm no longer going to be here because I got into PA school, yay I got into PA school right and so at the end of the day those are some of the things that you really have to be thinking about but I definitely feel Edgar that all three of those things are really important because they help you plan for the future and you always hear me say the plans of the diligent right if you haven't subscribed to my channel you probably haven't heard me say the plans of the diligent lead to prosperity but if you have you know for sure that that's one of my favorite phrases so plan diligently for the future plan for any like happenstances like what if I don't get in what if I do get in but it's late and then just make sure that you have all of your ducks in a row so that when you do get that acceptance be it from a waitlisted school or from one of the school other schools that you interview at you're ready and prepared to hit the ground running as a new PAS thank you so much for this question Edgar I really appreciate it again you guys leave your comments in the comment section below for me go ahead and subscribe and like this video it really helps my YouTube algorithm out a lot follow me on Instagram at it down to the PA and on Instagram I get that's the university and check us out at get that's the university dot com because we do have a lot to offer to help you not only get into but through PA school thank you guys so much for watching I will talk to you guys next time