Coming up on DTNS, can Q-Commerce conquer India and then the world? Also, what the heck is Q-Commerce plus examples of NFTs that are useful and how one of the best security policies of the year just came from the U.S. government? This is the Daily Tech News for Thursday, January 27th, 2022 in Los Angeles. I'm Tom Merritt. And from Studio Redwood. I'm Sarah Lane. I'm Austin Texas. I'm Justin Robert Young. I draw on the top tech stories from Cleveland. I'm Len Peralta. And I'm Roger Chang. The show's producer. We were just talking about Cleveland and how it rules and rocks both on good day internet so you can get that longer version of this show at patreon.com slash DTNS. Big thanks to our top patrons today. They include Chris Allen, Mark Gibson, and Reid Fishler. Let's start with a few tech things you should know. Meta's Messenger, formerly Facebook Messenger, started rolling out end encryption options to users back in 2016 and it's now available to all Messenger users. You can toggle it on for any message or group chat or call, although it isn't on by default. You have to turn it on yourself. For new conversations, you can toggle on secret conversations that shows up as a lock icon so you know that it's secret. Or in an ongoing conversation, you can use vanish mode by swiping up on an existing chat, which will cause messages to disappear when the window is closed as well. You can also now use GIFs, stickers, reactions, and verified badges in encrypted conversations. There are a lot of tech acquisitions waiting on approval out there. Warner Media and Discovery, and Media and Tech, Microsoft and Activision Blizzard. Some look like they may not happen. We just talked about Nvidia and ARM, just might not ever close. So let's turn the tables and talk about two tech acquisitions that just got the big old thumbs up. China's notoriously fussy state administration for market regulation has conditionally approved AMD's acquisition of chip specialist Xilinx. The conditions involved avoiding tie-ins and discriminating against customers. So that deal is now expected to close this quarter. And Metta got the European Union to approve its acquisition of CRM maker customer. That's customer with a K. Metta had to agree to not limit it. Anybody's access to the customer API for 10 years. Then Europe said, that's fine. Go for it. If you're hoping someday to do some serious gaming on a Chromebook, here's an important story to note. Wednesday, nine to five Google spotted a feature flag in the code for Chromium Garrett to enable support for RGB keyboards on supported devices. It includes per key color programming and custom RGB color selection. These devices are associated with the feature flag, including two Intel 12th Gen Alder Lake laptops and a detachable keyboard. Next stop, formal Steam support and RTX based Chromebooks. Right, perhaps maybe. Speaking of gaming coming to places people would like it to come to, if they use those things, compatible 2021 LG TVs can now download the GeForce Now app from the LG content store. That follows a beta period that had begun last November. So now everybody gets it. The app allows access directly from the TV to NVIDIA streaming service of games that you already own from Steam and Epic. You won't need to have an NVIDIA shield to play them if you don't have one already. But if you do have an NVIDIA shield, got good news for you too. You can now take advantage of the 4k upscaling that the shield does for video streams on GeForce Now games. That is also available to GeForce Now users on certain 10 series or newer NVIDIA GPUs on a PC. The Adobe led coalition for content provenance and authenticity or C2PA for short. Has finalized version 1.0 of a digital content standard. The standard when implemented can identify when and where an image or a video was created and document changes that were made to that piece of media. Microsoft, ARM, Intel TruePic and the BBC are all part of the coalition. All right, let's talk a little more about my local food truck that I'm always worried is going to drop their square dongle into a big pot of refried beans. Is there any hope for that, Justin? Yes, they might now drop their entire iPhone into a refried beans if this is correct. And this is a Bloomberg sources say report that, quote, in the coming months, small businesses will be able to use iPhones to accept payments without requiring extra hardware like those dongles or those little card reader squares that connect via Bluetooth. Apple bought a contactless payment company called Moby Wave in 2019 that would make this possible. The company previously worked with Samsung on a similar project with Samsung phones able to accept payments from contactless cards and NFC payments, including Apple Pay, Samsung Pay and Google Pay. Yes, you could tap a Samsung phone with an iPhone and pay the merchant with the Samsung phone. What a wonderful world we live in. The report does not reveal if Moby Wave's tech will be a brand that is part of Apple Pay's service, though it does potentially mean we might see it show up in iOS 15.4 soon. A reminder that iOS 15.3 was just released Thursday. So we don't know whether it'll be part of Apple Pay, but we know it'll kind of point that way. Now, this would this would be, OK, I go up to my favorite food truck, staying away from the refried beans. I tap my phone to their phone and that's that's and the payment is OK, because they would still need the dongle for cards for credit cards for chip for chip payments, but anything NFC for chip cards that don't have contact that don't have any contactless. Right. Yeah, exactly. So if you were and fewer have, I mean, if it if it has a chip, many of them have contactless, although it's not exactly a universal standard. Yeah, I think of all the technologies that through the pandemic, I think leaped ahead about five years in the one year that we had the intense lockdown. Obviously video communication was one of them was Zoom. I think contactless payment was as well, not only in situations like this, but also in a lot of a lot of restaurant situations or bar situations where you're doing a lot of mobile ordering and running all of the via a drop down menu on your phone. This is another part of it, although iPhones are not exactly cheap, I would imagine that the real worth of something like this is it being a standard and older iPhones being able to use be used as total just, you know, registers effectively iPads as well. Yeah, I hadn't thought about that aspect of it. As Apple does try to emphasize service revenue, I wouldn't be shocked to see them try to implement Apple Pay and through Moby Wave and Apple Pay merchant payments platform off iOS, right? Certainly so. Yeah, I say and also the ability just this isn't just a merchant thing in the way that we've we've often thought about it, digital currencies and we're not even talking about right, but you're getting money, the $5 from your friend, you know, Venmo transactions are all over the place right now to make it something where you could do it via Apple cash from phone to phone might be something that you do. Well, while we are talking about e-commerce, let's stop and talk about Q commerce tech in Asia and the business times both have reports out on Q commerce taken off in India, especially in India, we've touched on this emerging trend before. But now it's got the snappy new nickname. So it's worth looking at again, Q stands for quick. Generally, Q commerce is the idea that you can get something delivered in less than 30 minutes. That's what we've talked about before. We just didn't call it Q commerce. Most of these companies are trying to promise 10 15 minute delivery occasionally might see five minutes but usually around 10 or 15 business times used grab and food panda as an example in their article. Tech in Asia highlights Zepto Dunzo Blinkett and Instamart in India. In the United States, it's Dordache go puff Joker getter bike with B Y K gorillas and fridge no more. In all those cases, it's the old story of offering an astounding service that consumers love. Oh, I'm out of pasta sauce. This apple get me pasta sauce in 10 minutes crisis averted. Then the company pours money in it to make it actually work while they also try to learn how to make it more efficient and hope that the logistics technology that speeds up the fulfillment and maps things out and cues up orders improves enough. And the customer base grows enough that those two lines cross and they can reach profitability at some point. Now these companies rely on something called a contribution profit. This is key to not misunderstanding what the actual problems with these business models might be to convince investors to stay with them. They report contribution profit because contribution profit if I'm going to oversimplify and I am means the amount of money you make per order when you ignore your fixed costs. So you'll hear about these companies losing money on every order but that usually includes the entire cost of the operation.  So the more customers you get the more your rent doesn't go up. So more customers does mean you can make more money. If you have positive contribution profit then theoretically, you just need to get enough customers to outweigh your fixed costs and then you would become profitable. In fact, GoPuff told Tech in Asia it is contribution profit positive. So they just need enough customers. They've figured out how to make money. They just need to have enough customers to pay off their fixed costs. The other aspects of QCommerce is free delivery. You can't keep that going. Not all QCommerce companies forgo the fees but the ones that do run their own stores, dark stores where they stock their own items rather than having to get them from existing convenience stores or restaurants. And most analysts think that the margins are thin enough that even dark stores are eventually going to have to charge delivery fees at which point you start driving away customers. One executive told Tech in Asia it thinks a dark store would have to make about a thousand deliveries a day per location to break even. Resisting the siren song of all this is Flipkart. Flipkart's CEO told The Economic Times he thought 30 to 45 minute deliveries were a more sustainable model. And with the QCommerce craze, he sounds really slow. 30 to 45. What are you? Domino's in the 80s? Come on. It depends on where you live, of course. And these sorts of models are just going to scale in urban areas way better than in, for example, somewhere that I live. It's like, I can't drive anywhere in 10 minutes. How would I expect them to get it to me in 10 minutes? It's just not going to happen. Or, you know, there are very few things that I really want that are that close by. So you kind of have to take that into consideration. But yeah, the idea of contribution profit is interesting because, like you said, Tom, you have these fixed costs as a company. The company goes, okay, we know how much how much churn we're going through just making this whole thing sustainable. But if we have 10 cans of pasta sauce that are ready to go out instead of one doesn't change those fixed costs, we have the opportunity to make that much more money off of the people who want the pasta sauce, you know, in a very short amount of time. So yeah, I wonder, for me, it's like, okay, when I used to live within walking distance to several grocery stores, how much would I take advantage of this? Because I not only have the benefit of being in a more dense urban area, but I also am closer to those areas. Even if I drove the cost of gas, I'm probably saving over delivery fees. If and when those those become an issue. Do they not go up? Do they really not go up? Because this is a logistics business. And if your consumer base expands, then not only do you need more product to serve them, which is something that does go up, but you probably need new locations and more drivers and all these things that they are counting as fixed. At the end of the day, and I'm glad you brought up India where this is growing, because in the grand tradition of South Asia, this Q commerce craze is the graveyard of empires for venture capital. It has always been an insustainable holy grail for these companies. For whatever reason, they always try to reinvent it. And they think that now that we are further along with mobile data, it'll work better. Now that we pay for more things on our phones, it'll work better. Now that we're used to delivery, it'll work better. If Amazon could not make it fully work in with Prime now, which is they still exist on some level, but hasn't expanded like you would expect, then nobody's going to do it because nobody is better at logistics than Amazon. None of these companies. Yeah, getting back to that contribution profit point, your fixed cost doesn't go up per dark store, right? Certainly pasta, the number of cans of pasta sauce is a variable cost. So that one counts, right? But the but the the store rent wouldn't count, right? But sure, you have to increase the customers for that store. If you increase customers by opening up another store, well, you just had to do your fixed costs. So, you know, that that may sound like, Oh, well, you know, but you just need more customers. Like, Yeah, but that's a hard thing. A thousand people from one store and to deliver in 10 to 15 minutes means you have a compressed area to serve in. So it has to be dense, like Sarah was saying. Otherwise, you won't have a thousand people within five minutes of the of the dark store location. That's only going to work in certain highly dense urban situations. I'm not saying it can't end. And I know we're going long on this, but even then you are talking about customers that have more opportunity because they're walking more to just pick up the one or two things that they need. This is not a situation where they only have one moment a week or six moments a week for which they're crossing by their their local grocery store. These consumers have a lot of options to do it. And so I don't know. It has to be an affluent area, right? It has to be a tech forward area.  And that's the world that we live in. Well, we'll find out tomorrow, but it will be safe way that pioneers this and maybe that's it. Maybe maybe a lot of these companies are just they just want to make sure that they are there so they can get swept up by a Kroger or a Publix or, you know, any of these other major change. That's a lot of that. A lot of them just have an exit plan. You're not wrong there. Yeah. That's they sell the logistics learnings that they had in the end. That could be the exit for a lot of them. Well, speaking of the future of technology, several folks have asked us to highlight uses of NFTs non fungible tokens that aren't, you know, trading pictures of apes or maybe Beatles member of Delia couple of things we've talked about recently on the show. Not that those aren't important, but we found a few examples of where NFTs might be going and we can kick those around today to kind of just the idea of, you know, of expansion. What what can NFTs really be used for that could be helpful to you? Well, this one Lamborghini partnering with Sotheby's and NFT pro to auction off five pieces of digital art might be on your wheelhouse. It might not. You kind of got to be a Lamborghini person, but let's say you are. Each NFT has a physical companion space key that includes carbon fiber that has been to the International Space Station and back. Each space key has a QR code linked to the digital art associated with the NFT that was made by Swiss artist Fabian Offner. OK, so that's got a physical thing. It's not just digital. I get it. So there's something you can you can hold in your hand with that one. Yeah, it's definitely if this is if if this is something you like Lamborghinis, you like spaced, you might really like this. It's something that is a little bit of bragging rights, I would say. The NFT here is effectively a digital version of the piece of paper you would get that. Yeah, the certificate. Exactly. Yes. Second example of something kind of interesting. Warner Music Group is opening the location in the virtual worlds. You could call it the metaverse called the sandbox, where it will host what it calls a combination of musical theme park and concert venue. It'll also sell nearby plots of real estate to fans starting in March. The sandbox uses NFTs to handle sales of that digital property so players can not only own their own space be like this is my part of the grass. This is where I hang out, but also monetize and game resources in this particular metaverse. So in the sandbox, I could own a location so I can log in really close to Marshmallow playing in Fortnite. Totally. Warner artist in sandbox. I feel like this is me buying the cool VIP pass at Coachella, where you get to have a certain area where nobody else can go because you've sort of paid a premium. This is your area, your plot of land. And if you're into that kind of musical experience or just live experience in general, which many other platforms have experimented with, with varying degrees of success, but sometimes very successful, could be cool. Yeah, I would think of it like local theaters will sell you like the entire slate that they are like that they're going to put on be they dramatic performances or musical performances or anything like that. So it's like that, but for digital only things you are getting for every event. Yeah, that's a good comparison. Yeah, all right. The third option here in the new NFT world, this actually might have some legs, especially if you're in the market for a new home. TechCrunch reports on a startup called Propi, P-R-O-P-Y, that used an NFT in connection with the sale of an apartment in Ukraine successfully and is now bringing that platform to the U.S., limited at first, but definitely coming to the U.S. The idea is to put the legal paperwork on the blockchain, reducing the cost and simplifying the purchasing process for everybody. Brokers, Asians, title companies, buyers and sellers could all benefit from an automated paperless closing, such as this, although Propi is marketed towards owners and brokers for now. This is using the smart contacts aspect of blockchains. U.S. states, Vermont and Arizona recently passed legislation affirming they are legally admissible. This is not an illegal thing happening. This can this can be done. So Propi will start by auctioning two properties in Florida on February 8th, so just two for now, but we'll see how it goes. It works as such. The record of the purchases goes onto the blockchain, provides access to the legal documents that prove ownership, you know, because it's in the blockchain, and buyers save a little bit this way, also makes the purchasing process process quicker, which if you're ever about a home, which I have not, but I know people who have, it is not a quick process. Now if the buyer is successful, gets the house, let's say, they get a Florida-based investment property owning a U.S.-based entity that owns the property, the ownership rights of which are associated with an NFT. It's not a fractional ownership. This is not some like, oh, I don't really own it. I only own a digital version of this. It becomes a DeFi asset that can be borrowed against like any other property. So it's a little end around. The company owns the property, and so you're buying the company, and therefore because you own the company, you own the property. But in the end, you don't have to have this huge pile of documents that you have to have normally when you buy a property. I like it. That's pretty cool. Well, I mean, it certainly is a way that you can get more crypto into the world of investment of real estate buying, which is its own. I don't know if in the world of NFT criticism, easier and more frictionless ways that crypto money can be poured into investment real estate is going to win a lot of fans. But certainly you can see the idea of NFTs being a digital collectible for whatever reason is something that I think as a standard, very much has legs, despite the fact that obviously there is backlash to the kind of current moment it is having. Yeah, I feel like the end around there in Florida where you're buying the company is probably because Florida isn't recognizing deeds on the on the blockchain. But in Vermont and Arizona, I'm guessing you might not even need to do that company owning the property thing. You might be able to just do it all on the blockchain. And man, if that if that means like one less day of like here are the 13 docusigns that you have to do in your email today. I'm in. I'm in for it. All right, folks, join in the conversation in our Discord. We don't require you to have an NFT. Just a Patreon account, patreon.com slash DTNS. Get in there and talk about your favorite NFTs. The United States Office of Management and Budget sent a memo to federal agencies calling for new security strategies, including moving to a zero trust model. That's pretty security forward. Agencies have two months to present their plan for transitioning to this new level of security and they have to get their plans in execution by 2024. Zero trust if you don't follow security news means you don't assume just because you're inside your own network that every user or service is trustworthy.  So let's let's just always be securing everything. Corporations have been moving to this model as attackers get better at infiltrating networks and you want to still catch the malicious actors even after they get in. So among the strategies with zero trust are multifactor authentication so that you can log in multiple times, not just once into the network. Access controls, no matter where you're logging in from. VPN not being considered enough, not relying on VPN for security. Everything that attempts to access data in a zero trust model, user, device, application, transaction needs to be verified. I found a great post from Dr. Sharon Goldberg, she's CEO of Bastion Zero reviewing this memo. People familiar with zero trust won't be surprised that the memo deals with network segmentation, role based access control, stronger authentication. But Dr. Goldberg pointed out that it includes creating public vulnerability disclosure programs. The U.S. is going to do some bug bounties. It implements encrypted DNS, requires encrypted DNS on government websites, puts a stop to requiring rotating passwords or special character requirements that end up inconveniencing users more than thwarting attackers and have literally been showed to cause people to use weaker passwords. That's out. Passwordless login is encouraged. They also deprecate VPN saying, users should log into applications rather than networks and again from the Office of Management and Budget, enterprise applications should be able to be used over the public Internet. In other words, authenticate people for real and securely, don't rely on VPN as a crutch, secure the application itself. Here are a few points Dr. Goldberg emphasized. Credentials don't live a long time, meaning attackers won't be able to steal a token and last forever in the network. The memo describes something similar to just-in-time access control, which gives an authenticated user access to a resource only while she needs it, and then revokes the access. You don't just leave people logged in. A lot of this relies on good multi-factor authentication, and the memo tells agencies to discontinue SMS or voice calls as second factors. You might say, oh, thank goodness. But it also dismisses one-time code protocols like Authy or Google Authenticator. Users should use cards or USB keys like a UB key. Those are harder to fish. You could still fish a Google Authenticator code really hard to fish a USB key. It also needs to consider the device being used when logging someone in. So if you're logging in from a device that's never been authorized on the network, you won't get to log in. Your laptop or your phone needs to have a security certificate pushed to it, or you can't use it even if you've got multiple factors. This is not only state-of-the-art, folks. This is the U.S. government in consultation with security professionals putting forward a cutting edge, like bleeding edge security protocol, which certainly by 2024 won't be as bleeding edge as it is now. But this, I don't know. To me, I was shocked. This is definitely the right thing to do. At the speed of the federal government, this is Sonic the Hedgehog. This is insanely, blazingly forward. And the fact that they're probably going a little bit more where the puck is headed than where the puck is in terms of the general consensus of security, as you rightly pointed out, this would be something that would be forward for a private company. The fact that these are standards for the federal government is, I think, encouraging. And also, it's smart in that they are not applying standards that are already understood to be kind of theater, like rotating your passwords or stuff like that. You know, I don't know. I don't really have a ton of commentary other than good on you, right? This is why you don't get good news in the newspaper because you can't make fun. You can't have Schaudenfreude about how bad the government is on this one. No matter what your political stripe is. And also, to be fair, this is necessary.  We also saw the story last week about the IRS stepping up their security. That's because it was hilariously weak and led to a lot of very, very costly and harmful phishing and identity theft. This is just good. And it's not just good. It's necessary. And some of these, some of these are things you can only do because you're the government. Because because you're a, you know, you're not serving the kind of client base that, say, a bank is, right? You can have stricter requirements and say, well, if you want to be an employee, this is what you got to do. Amos is pointing out in our Twitch chat right now that sometimes classified computers have USB ports disabled. So, right, USB keys might not work on those, but you can still set up card keys and second factor that uses NFC in those situations. And I'm sure that's considered in the memo. I didn't see that in particular though. All right. Let's check out the mail bag. Okay. We got a few emails in response to the question from yesterday's show about Android apps on Windows. What are they good for? Kevin wrote in and said, one reason why running Android apps on Windows might be useful for streaming, video streaming services. As far as I know, says Kevin, apps are the only method to download episodes on streaming services for offline viewing. Many streaming services lack apps made for Windows. I want to emphasize that might is in that statement. Chrome OS has this ability and some streaming apps are still unavailable or have bugs that aren't present on Android. Crossing my fingers that Android apps on Windows will make offline streaming on a bigger device or without the need for a second device a reality. At this point, I'm only cautiously optimistic though. Andrew M. wrote in, had a similar point about downloads adding, quote, my wife currently spends way too much time trying to edit Instagram videos on her phone because she doesn't want to deal with the transfer complications in the phone app and the phone app the main experience with features missing from the browser site or so she tells me. Oh, Andrew M. Okay, you don't use Instagram. And finally, Andrew B added, what about Android apps on your portable Windows tablet? Microsoft can make an iPad or even a phone competitor and say, hey, we know the Windows App Store isn't the greatest, but you get all the best Android apps there too. Well, I'd let this back off of having Microsoft make a phone competitor after Windows phone for a minute. But they already make tablets with keyboards, right? That's the surface. So I'm with Andrew B on that kind of emphasizing like, hey, you now can get all your favorite Android apps, maybe not all your Android apps, but the best ones on a Windows tablet on a Windows surface. Yeah, that's compelling. Good stuff. Good things. Thank you, Kevin. Thank you both Andrews for writing in. Indeed. Feedback at dailytechnewshow.com is where to send emails. You know, we often say, hey, high of mind. Yet you have ideas about the story that we talked about. Please do send them to us. And you did. So keep them coming. Makes us all smarter in the process. We also have a brand new bosses. One, two, three, four of them, in fact, to thank Michael Kamachi, Aaron Spinelli, Mike Weber, Jason Harris are all our new bosses who just started backing us on Patreon. Thank you, Michael. Thank you, Aaron. Thank you, Mike. And thank you, Jason. But that's great. That's great. Because we always lose people at the beginning of the year when everybody has to reshuffle their finances and we totally understand. So it's good that there's other folks coming in to pick them up and getting a chance to maybe get some cool new loyalty merch if they stick around. Speaking of our loyalty merch, that was designed by Len Peralta, who's with us today illustrating the show. Len, what have you drawn for us? Well, you know, I missed the discussion about the ape NFTs. And I haven't really done anything with NFTs on the show for a while. So I decided to kind of, on that note, create a mascot, an NFT mascot for the show. And I'm going to show, I'm premiering it here. This is DDNS. DDNS, D-T-N-S, get it? DDNS. Yes, maybe related to KK Slider. This is the tech savvy Wheaton Terrier. They have apes. We have Wheaton Terriers. And this is the official mascot, the official NFT mascot of D-T-N-S. It's DDNS. The other cool thing is the only place you can get this NFT is at OpenSea. And I just, I put a link in the Twitch chat. If you're interested in taking a look for it. It's DDNS, the tech savvy Wheaton Terrier is up there for 0.25 Ethereum. So check it out. Check it out.  Yeah, with different attributes. Possibly. Tech-Sided, tech-savvy terrier. I'm holding a smartphone that says that Ethereum has dropped to $29.36. Yes, it's $29.36. If so, I am poorer than ever. Yes. I've lost lots on that. So check it out. Good stuff, Len. Also, thanks to Justin Robert Young for being with us today. Justin, anything new to tell the folks out at home? Oh boy. Every once in a while, the news, it just falls from the sky, like so much rain. A new Supreme Court justice is on the way. If you want to know the entire roadmap of what's going to happen, when it's going to happen, and a few guesses and predictions, including answers to all your wild questions and theories, like whether or not Kamala Harris, the sitting Vice President, will be on the bench, answered and explained on the upcoming episode of Politics, Politics, Politics, that comes out tomorrow. Well, thanks for being with us, Len and Justin. We are live Monday through Friday at 4.30 p.m. Eastern. That's 2130 UTC. We'd love to have you join us live if you can. Find out more at dailytechnewshow.com slash live. And we'll be back tomorrow doing it all again with Rob DeMillo. Talk to you soon. This show is part of the Frog Pants Network. Get more at frogpants.com.


We are talking about three-dimensional flows in axial flow compressors. In the last class, we had a look at various aspects of physics of the three-dimensional flow in axial flow compressors and its various ramifications of the understanding of how axial flow compressor works and how it impacts on the performance of axial flow compressor. In today's class, we will try to capture much of the three-dimensional flow in mathematical form. These mathematical forms are very useful in the sense that eventually they would be used for various computational analysis purpose, which aids the design process and in the process of this coupling between design and analysis, the design time is substantially cut down. We do not have to go through a very costly experimental analysis to finalize the design. So, the design time has indeed been cut down by years with the help of these analytical tools with the help of CFD and in today's class, we will try to capture some of the mathematical form of the physics of the flow that we have done in the last class. So, let us take a look at some of these issues that we are about to capture in mathematical form. So, today's class is about three-dimensional flow analysis in axial flow compressors. Now, as we have seen, many of the blade theories are indeed actually based on two-dimensional understanding and those two-dimensional understanding actually ignore the effect of three-dimensionality of the flow while the fluid is passing through the blade passage. Now, the picture below we have seen in the last lecture and it gives us a fairly detailed idea about the three-dimensional nature of the flow. There are so many things going on inside the blades, especially inside the rotating row of blades that it is really not a right thing to do to ignore some of these three-dimensionalities. So, we will today try to capture some of these things in mathematical form so that much of it is actually included in the design and analysis process. So, we will keep this picture in mind which we have done in the last class and try to move forward to see what all things in some summary form, in a overall form is captured in mathematical formation. Now, we see that one of the things that is normally ignored or assumed to be not present is the radial component of the flow and we had a quick look at a simple three-dimensional radial equilibrium. What it actually means is that the radial motion of the fluid particles inside the blade is sort of assumed to be or pretended to be not present at all. Now, we see what are the reasons why radial flow would almost invariably be present in axial flow compressor. Now, the first reason is a centrifugal action of the rotational motion which is passed on to the fluid and this centrifugal action would invariably try to impart certain amount of radial flow to the fluid as it is passing through the blade specially the rotating blade. Then the convergence of the annulus flow track, we will you know discuss a lot of things about the flow track little later in this lecture series, but the flow track in the modern compressors is quite often converging type and specially in this highly loaded modern aircraft engine compressors and this kind of annulus flow track geometry introduces the radiality anyway. Then of course, we have the twist and the taper and various three-dimensional blade shapes the solid body of the blade often has highly three-dimensional shape. These days they are in fact becoming more and more three-dimensional and as a result of which a certain radial component of the fluid is invariably introduced into the fluid motion as it passes through the blades and then of course, we have the tip clearance effects. Now, the tip clearance effects we have studied in the last lectures and we know that there is a substantial cross flow through the open tip of the rotor and this introduces three-dimensionality of the flow and definitely introduces a certain amount of radial component to the fluid flow. Then if we look at the fact that you know the first picture that we looked at even today that a passage vortex is formed inside the blades. Now, this formation of passage vortex creates radial flow a strong component of radial flow in the main flow itself which is passing through the blade passage. So, as a result that is another contribution from the various things that are happening to the introduction of radial flow. Then through the blades quite often we assume in our theories that the temperature then the enthalpy and the entropy gradients are you know 0. Now, that is an assumption in a real blade quite often we will find that there is a certain gradient in the rear stages of a multi-stage axial flow compressor. We would find a temperature gradient from root to tip or even from blade to blade. There would be enthalpy gradient we assume that the enthalpy is uniform along the length of the blade from hub to tip and we had also assumed that the work done is constant from hub to tip in the earlier simple theories. And then of course, there is a general assumption in various theories that we have propounded that the entropy gradient in the radial direction is absent that means there is no gradient. Now, these are assumptions in reality some kind of gradient would invariably appear as the flow goes through the various stages and those will have to be taken into account when you are analyzing the fluid flow. Now, taking them into account means bringing in certain amount of thermodynamics and those thermodynamic issues would invariably be present in the real flow as I mentioned specially in the later stages of an axial flow compressor where the temperature is higher the flow has become more three-dimensional and as a result temperature enthalpy and entropy gradient start appearing in the fluid flow passing through the blade passage. Then we have the blade solid body thickness which is a blockage. Now, this includes the camber and the stagger you know more the camber higher the thickness higher the stagger this blockage to the main flow is likely to increase. You see the flow is basically an axial flow and the moment you have blade there it solid blade it obviously has a blockage and this blockage will change with these essentially with these three parameters the thickness of the blade the camber and the stagger. Now, you see we have already noticed that the thickness the camber and stagger all three of them actually vary from root to the tip of a blade. Now, if they are varying from root to the tip of the blade it stands to reason that the blockage effect would also vary from root to the tip of the blade and this variation would also then introduce another aspect of radial flow or three-dimensionality into the flow and then of course, we have the involved boundary layers. Now, these boundary layers are developed because of the flow essentially being in a adverse pressure gradient in a compressor and these boundary layers over the casing and the hub internal surfaces actually create a certain amount of blockage. These blockage is a fluid mechanic blockage and this blockage often has a tendency to deflect the main flow in wards from the casing and from the hub and this inward deflection of course, introduces a three-dimensionality it introduces radial flow in addition to the fact that it has a tendency this blockage has a tendency to reduce the main flow rate that means the actual flow rate that you would see would be less than what was assumed initially probably during the design. So, these are some of the effects of actual realistic flow on the formation of radial and three-dimensional flow features inside actual flow compressor bleeding. Now, we have created a radial equilibrium theory earlier a simpler version. Now, this is based on the premise or assumption that the radial gradient of the forces which are experienced by the fluid and we had taken a fluid element earlier of an appropriate shape and size and that fluid element experiences radial gradients and those things contribute to the radial movement of the flow and if they are to be checked that means the radial movement of the flow are not to be allowed it becomes incumbent that those forces must be balanced by the static forces exerted by the pressure gradient which also created inside the flow. So, that at any instant of time the fluid system or the fluid particle or the fluid element is in radial balance of forces that is in radial equilibrium it is this balance of forces between the dynamic and the static forces that we would move forward take forward today to create a more comprehensive radial equilibrium theory much different from much more complex and much more involved than the simple radial equilibrium theory that we had created in the last class. So, this balance of forces is one of the issues that axial compressor torumational designers quite often need to do during the process of design and analysis. Now, let us try to lay down a few simple conditions mathematical and geometrical conditions that are going to help us in formulating the mathematical theory of three dimensional flow. We assume that we have motion of a particle with respect to two coordinate systems and this particle p is moving in an arbitrary path within the two coordinate systems.  So, we have two origins and two coordinate systems and the small x y z coordinate system is a moving coordinate system. In fact, with respect to axial flow compressor it would be a rotating coordinate system which means it is fixed on the rotor body. So, it is a it is a body fixed coordinate system which rotates with the rotor whereas, we have capital X Y Z which is a fixed coordinate system and a static coordinate system and the stated analysis could be done with respect to that coordinate system. But the rotor needs to be analyzed with respect to the rotating or body fixed coordinate system. So, we do have two coordinate systems to deal with in this theoretical formulation and we need to keep that in mind. The moving coordinate system is at a distance capital R from the origin of the fixed coordinate system and the particle p is at a distance rho dashed a rho prime from the moving coordinate system origin and is at a distance small r from the fixed coordinate system origin. So, we have three distances over here. One is this coordinate system is at a distance capital R from the fixed coordinate system and then the particle p itself is at a distance rho dashed from the moving coordinate system origin and is at a distance small r from the origin of the fixed coordinate system. So, this is how we have put together particle that is moving in an arbitrary path. Now if we move forward the two reference systems have relative motion which is represented by r bar r dash r bar and that is it is the motion of the position vector r with respect to fixed origin o omega is the rotation of the particle with respect to the moving axis system x y z and v x y z is the translational motion of the particle with respect to the moving axis system small x y z. Hence the velocity of the particle p with respect to the fixed axis system capital x y z based on this figure would be v x y z equal to d r bar d t of x y z capital x y z. So, this is the basic definition or description of the fluid particle that we are tracking in a motion involving two coordinate systems. Now, velocity of the particle p with respect to small x y z that is the moving x y z is v small x y z and that would be d rho dashed d t as per the diagram that we had given. Now the vectorially the motion of particle p is summation of the motion of the moving coordinate system with respect to the fixed coordinate system and the particle p with respect to the moving system. So, vectorially r bar would be equal to capital r bar which is the distance of the moving coordinate system to the fixed coordinate system and rho bar which is the distance of the particle with respect to the moving coordinate system. So, from which we can say that d r bar d t x y z that is capital x y z would be equal to d r d capital r bar d t plus d rho dashed bar d t and these are of course, the velocities of the prospective coordinate systems. So, we can write that down that the velocity of p with respect to the fixed system would then be capital x y z that would be equal to r dot plus v x y z that is small x y z plus omega that is the angular velocity into rho dashed. So, that gives us the vectorial summation of the velocity field that we have in front of us for the tracking of the fluid particle through the two coordinate systems. Now, if we define the accelerations the acceleration of p with respect to fixed coordinate system that is capital x y z is given as a capital x y z equal to d v capital x y z d t with respect to capital x y z and the acceleration of p with respect to the rotating or moving coordinate system that is small x y z and that is a small x y z equal to d v small x y z d t with respect to the small x y z coordinate system. These are the two accelerations which we will be contending with because we have seen before the acceleration is what contributes to the creation of dynamic forces that is mass into acceleration. So, we need to write down what the acceleration terms are going to be for this three dimensional fluid flow. So, let us move forward then we can write down that the total acceleration of p with respect to the fixed coordinate system capital x y z would be a capital x y z and that is d v x y z d t with respect to the capital x y z and that would then be equal to d v small x y z d t plus r double dot this is the acceleration term the earlier one r dot was the velocity term of the position vector r and then d of omega rho dash d t. Now, this is of course due to the rotational component of the coordinate system small x y z itself with respect to capital x y z. So, this is the acceleration term that we can write down with respect to the coordinate systems that we have defined earlier. Now, the acceleration with respect to the body fitted rotating coordinate system small x y z now this is a summation of its translation and rotating motion at the moment we are assuming that it has translational motion and rotating motions and this we can write down in terms of d v small x y z d t and that would be equal to d v small x y z d t plus omega into v small x y z. Now, you see the rotating component is the second term over here now if we write that down over here we see here d omega rho dash d t x y z would be can be split up in two terms that is omega into d rho dash d t and d rho d t into omega dashed. Now, in the first term d rho dash d t which is a differential of the position vector rho dashed can be written down in terms of d rho dash d t is equal to d rho dash d t into small that is of the small x y z plus omega into rho dashed. So, rotation in x y z can now be captured in the form of these equations with respect to the position vectors that we have defined before. Now, acceleration of the particle p with respect to the fixed origin O may be written down now we have seen that we need to write down the acceleration terms and these may be written in terms of a x y z that will be equal to a small x y z plus r double dot plus twice of omega into v small x y z plus omega into omega into rho dashed dot plus rho dashed rho dot plus omega dot omega lot into rho dashed dot. Now, if we assume now this is the full the first this is the full equation that we get of the acceleration term with respect to the fixed coordinate system. Now, if we assume that the angular velocity omega is constant and it does not change then the rho omega dot term would of course, immediately go and as a result of which we get a little simpler version of the acceleration term and that is a capital x y z and that would be equal to a small x y z plus twice omega v small x y z plus omega into omega rho dashed. So, this is the terminology that we finally, get for acceleration assuming that the flow is a constant angular velocity which is very fair because most of the time the actual flow compressors are rotating with constant angular velocity except when they are in transition during acceleration or deceleration of the machine. Now, if we look at for a compressor blade passage the flow velocities that we are looking at are v small x y z and now this is the relative velocity you remember we had two velocities that we had defined one was a relative velocity and another is the absolute velocity. Now, we can relate those two known velocities with respect to what we are doing right now today. So, v small x y z is the relative velocity and v capital x y z is the absolute velocity C. We have seen earlier that sometimes the relative velocity is the larger component that is typically at the inlet to a rotor sometimes the absolute velocity is the larger component and that could be true at the exit of the rotor.  Now, this can be written in terms of v plus omega r that we had written earlier r being the radius at which the fluid particle is rotating with respect to the rotating coordinate system and this earlier we had written down as u. So, v plus u then becomes the vectorial summation which gives us C and this is what we had done earlier very quickly in our two dimensional flow theories. So, we come back to what we had done in two dimensional flow theories in the sense they were nothing particularly wrong with them except that they were two dimensional in their nature. Now, if we differentiate this situation what we get is acceleration terms and now we see that a capital x y z would be equal to d v capital x y z d t and then d omega rho dashed d t with respect to capital x y z. Now, the first term then is the translational motion and the second term is due to the rotational motion. So, both the terms would need to be taken into account for finding the total acceleration and then the final acceleration then is a capital x y z is equal to a small x y z and then twice of omega v x y z plus omega into omega rho dash. Now, this is what we had done earlier if you remember in the last slide. So, we get back. So, this equation with constant angular velocity is what we again get back here using the concepts that we had used earlier in our two dimensional flow theories. So, we get the same acceleration term combination of acceleration with respect to rotating motion and combination of the two and the translational motion. Now, the third term is often sometime referred to as Coriolis force or Coriolis acceleration and we have done that before also and this is what typically comes out of a full mathematical formulation that we are attempting in this class today. Now, if we consider that equilibrium of forces along arbitrary flow direction S, we get between any two actual stations separated by a small distance delta S where a i is constant a i being the area at that particular station. So, if we take two stations of an actual flow compressor longitudinally the during which we assume that a i is constant a i being the area annulus area at that particular station and we assume that is constant and in this longitudinal flow field which is a small distance delta S and in this we try to track what is happening in the flow field in this small distance delta S that we have defined here. Now, over this distance what we see here is the pressure force that is working this is of course, the static pressure force delta P into a i which is constant now over this flow field and then we have a i into rho rho now is density please understand we have always used rho as density and that is why used rho dashed earlier as a position vector. So, this rho is density and delta S which is the distance. So, a into this is the volume and rho is the density. So, that is the mass and this is acceleration. So, mass into acceleration is the force that is the dynamic force that is being created and this is the actual force that is being created by delta P that is the pressure differential or pressure change over this distance small distance delta S. If we resolve this from this what we get is 1 by rho delta P by delta S equal to acceleration A x y z. So, this is now the pressure gradient along the distance delta S. Now, we can write down that the acceleration equation from the last slide now can be written down in terms of this acceleration term can now be replaced by 1 by rho delta P and then we get d v d t plus omega square r position vector rho dashed is now replaced by r which we are familiar with r being the radial distance of a particle from the axis of rotation of the moving body that is the axial flow compressor axis and twice omega v which we had called sometimes in some books is referred to as Coriolis force. So, this is what the equation we get now. So, acceleration term has now been replaced by pressure terminology or pressure term pressure gradient along the distance S or delta S. So, with this we can now write down that as the flow in compressor blade is a diffusing flow we need to think that d v d t is likely to be negative that means the flow through the blade passage is actually decelerating flow. So, d v d t is likely to be negative in nature and as a result of which the equation can be slightly recast as minus 1 by rho into delta P equal to d v d t minus omega square r plus 2 cross omega cross v. So, that is your vectorial representation of the Coriolis force. So, we get a compressor blade now position signifying that d v d t is most likely to be negative in nature. Now, this gives us a situation that we now need to look at representing the flow in a manner that gives us a generalized flow path of the particle while the position of the particle is being tracked. It has its rotational motion captured in the form of omega and then we have the three coordinate system which we are familiar with the radial coordinate system as r, the axial coordinate system as a and the tangential or the peripheral coordinate system as w which we call the whirl component. Now, this is what we have been doing earlier in our two dimensional flow theories where we are the radial component, we are the axial component and we are the whirl component and we call the three velocities for example, v a, v r and v w. Now, v r had been neglected earlier in all two dimensional flow theories, but we are going to bring that back here and v w remains the whirl component or the peripheral component and we would now go back to those terminologies which we had used earlier and are somewhat familiar to us from the earlier theorizing that we have done. So, as we can see there is nothing particularly different about the notation that we had used earlier and the notation that we have introduced in today's lecture, you can find very easily the parallels between the two and the equality between the two sets of notations. So, you may have to really just sit down and look at these notations and find that these things actually mean one and the same thing. So, with this we look at the new axis notation system. Now, the assumptions made here are that the fluid is frictionless, the rotor is rigid and rotates with constant angular velocity and assumption we made just a little while earlier. The flow is steady relative to the rotor, we assume that the flow is not experiencing any unsteadiness, we will formalize it in our mathematical formulation and the radial variation of density is neglected. Now, this is something which is an assumption in many flows that may not actually be true, but radial variation of density to begin with for design purposes and for design analysis look that assumption is reasonable and a valid assumption and may be proceeded with. Now, this leaves still enough scope for formation of vorticity, the entropy gradients and stagnation enthalpy gradients in the flow field from hub to the tip of a typical compressor blade. So, these gradients and the formation of the passage vortex and the tip vortex and the trailing edge vortex all these things would indeed bring in the three dimensionality which actually impacts the real flow and we are trying to see how much of these things can be captured a prior a in a mathematical formulation. So, that it can aid the design and analysis process of axial flow compressor. So, these are the assumption that we have to live with in our mathematical formulation. The other things we are going to bring in are the definition of the unit vectors which we have written down here or in terms of d i r i being the unit vector in the radial direction and then d i w which is the one in the world component or the world direction. So, the overall v is v r into unit vector i r v w into unit vector i w and v a into unit vector i a those impart the directionality with which the flow is preceding in or the flow has three components in radial world component and the axial component. The other thing we are going to do is look at the fact that capital D D T is a total operator. Now, from your basic mathematics you know that the total operator can be split up in two terms. One is the operator with respect to the space coordinate where s is the length in any direction. So, the same term can be written down in terms of total operator d d s and that plus d s d t. Now, d s d t of course, is the unsteady terminology t being the time. Now, as a result of which d s d t is an unsteady terminology if the flow is assumed to be steady and at the moment we are assuming the flow to be steady then d s d t is equal to 0. Hence, that term would be neglected and as a result we would be left with only the total operator with respect to the space or the distance s and the with respect to time it is considered to be 0. So, the equation for the flow inside a compressor we would now like to recast using r theta z coordinate system because simply because it is a more appropriate for a rotating coordinate system also because of the fact that there is a variation of parameter in the circumferential direction and from blade to blade and this blade to blade circumferential variation is quite often an important variation. We know that the two surfaces of the blades are indeed actually dissimilar one is a suction surface one is a pressure surface. So, theta variation from suction to pressure surface is quite often an important variation it sometimes is quite a lot in a highly loaded and we shall we know that that variation also changes from up to the tip of the blade. So, variation from one blade surface to the other in the passage is an important variation it everything varies the pressure varies the velocity varies the temperature varies the enthalpy varies from one surface to the other in one passage. So, that can be tracked by variation of theta that is the angular circumferential variation from one surface to the other the other is of course, from root to tip and the third is in the z direction that is actual coordinate actual distance.  Now, these coordinate systems and the flow velocities in the relative frame which we always have considered as v capital V its components are being shown again as v a v r and v w as we have done before in 2 d flow theories where we have used v a and v w we did not use v r as at that time we assume that v r does not exist. So, we see here that the acceleration term can be split up in 3 components. Now, the equation may be resolved in its 3 components using the r theta z coordinate system that we have brought in now.  Now, that is in the radial direction. So, the left hand term is the pressure gradient and the right hand term is the dynamic acceleration terminology of the terms. The second equation is in the circumferential direction theta coordinate and that is 1 by rho del p del theta 1 by rho 1 by r del p del theta.  In the axial direction it is 1 by rho del p del z equal to v d v a d s and that is in the axial direction. So, again the left hand term is the pressure gradient and the right hand term is the acceleration term which gives rise to the dynamic or the kinematic forces. So, these are the 3 components of the equation that we had written down in the earlier slide and 3 components are in the radial, circumferential and in axial directions. We can now denote these components in a very simple vector diagram in which all the velocity components are shown here. We see the velocity velocity vector v r has now appeared.  We are looking at a particular plane on which we have the fluid particle and this fluid particle is experiencing a rotating motion omega. It is at a distance r from the center of rotation and it is at a angular distance theta from the reference axis. So, at this position it has 3 velocity components v a that is the axial velocity v r that is the radial velocity and v w that is the peripheral velocity. A combination of all the 3 is of course, the overall relative velocity with respect to this coordinate system which right in the beginning in today's lecture we have seen itself may be moving with respect to a fixed coordinate system, but let us look at this moving coordinate system analysis right now. Now, we see that a combination of v r which is the radial component and v a the axial component also gives a velocity which can be now described as v m and this v m is a velocity which is a resultant of v r and v a and is on a particular plane this plane is a radial and axial plane a combination of radial and axial plane in this plane which is perpendicular to the plane we are looking at which is the radial and peripheral plane and v m is on that radial axial plane and this v m is referred to as meridional velocity. We will come to this definition of meridial velocity. So, the velocity triangle for this flow gives us that the C w would be equal to v w plus omega r what we see now is that the velocity triangles which we are all familiar with actually gave us C w that is equal to the axial velocity equal to v w plus omega r omega being the angular velocity and in the earlier coordinate system that we have just seen we get a v w which is the peripheral component relative peripheral component with respect to the rotating coordinate system. So, we come back to our C w which is vectorially has to be equal to v w plus omega r in this coordinate system you remember this whole thing is rotating the particle is rotating with respect to this with angular velocity omega. So, this entire coordinate system is rotating with angular velocity omega now the equation a and b from the two slides earlier we had three components from the slide 21. Let us go back very quickly what we see is we have two components of the full equation in two directions the radial and the peripheral if we bring forth them we have the radial component can be recast as 1 by minus 1 by rho d p d r equal to v into d v r d s minus C w square r by r and this we write as equation d and the second equation is now 1 by rho r into del p del theta equal to v by r into d r C w d s. So, what we have done is we have replace the v w's now with C w because that is the absolute velocity component that the flow is actually having with respect to the fixed coordinate system.  We can now define a meridional velocity to begin with let us define a meridional direction and this meridional direction is d m into unit vector i m equal to d r into unit vector i r plus d a into unit vector i a and this is what I was talking about just a little while earlier that this meridional flow is in a plane that is composed of radial and axial plane. So, in this plane we can have a meridional direction defined and this meridional direction of a flow or a particular flow path of flow particle taking a particular path would have would create an angle phi with respect to the axial direction. So, this phi is the angle with which the meridional flow is proceeding in the meridional direction which is not the same as axial direction.  Now, c w of course, we are familiar with is the world component of the absolute velocity r being the distance of the fluid particle with respect to the axial coordinate system. As a result of which we get a formation again on the left hand side we have the pressure gradient on the right hand side we have the acceleration terms due to the dynamics of the flow. This gives us the fact that in the meridional direction if we complete the definition of meridional direction tan phi is v r by v z or v a and v is v of meridional direction v m into sin phi and phi is defined here and as a result of which we can write down that the force balance equation only in the radial direction can be recast or rewritten as 1 by rho del p del rho is equal to c w square by r minus v m square d sin phi d m equal to minus v m sin phi d v m d m. Now, this is the full equation in the radial direction now by our definition v d d s the total operator is equal to v m d d m this is mathematically approved and as a result of which we can replace with respect to the meridional velocity and using the meridional direction in this equation. So, if we look at the flow as we are what we are describing is that we have the meridional plane over here now and this is the direction of the fluid particle or fluid path given as phi v r is the radial flow component v a is the axial flow component and v m here is the meridional flow component in a fluid path and this is what we are talking about and v w of course, remains the peripheral component or the world component that we have talked about which means this total v would be the full component of all the three components put together omega of course, is the rotational angular velocity that the entire flow is experiencing with the rotating blade. So, given this model given this model we can now write down that d sin phi d m would then be equal to cos phi d phi d m and d psi d m will be equal to minus 1 by R m. Now, minus 1 by R m is indeed the radius of curvature of the meridional flow and this radius of curvature of the meridional flow is due to the fact that the meridional path may not be a linear it may not be a curved path and if it is a curved path the radius of curvature of that path in the meridional direction would create a certain centrifugal action and hence the meridional radius of curvature of the meridional flow is being brought into the picture. Now, this negative sign is somewhat arbitrary, but the axial flow compressor the flow track inside generally moves towards lesser value of phi as it moves actually forward that is the R m becomes higher and higher which means the flow tends to become later on flatter and flatter. So, it moves from high R m to low R m as it moves forward through the blade passage. Hence, the full radial equilibrium that we are looking at now is 1 by rho del p del R equal to C w square by R plus cos phi into V m square by R m minus V r d V m d m and this is the full radial equilibrium equation which you may say is a circumferentially averaged from blade to blade flow properties inside a term machine blade row. Now, this radial equilibrium equation captures the all the components of the dynamics of the flow in terms of all the acceleration terms that come about due to three dimensionality of the flow. Now, this we can see is has more terms than what we had seen in the simple radial equilibrium equation we had done couple of classes earlier which tells us that more of the dynamics or kinematics of the flow have been captured in our mathematical formulation and this tells us that if we now simplify backwards that means if we consider that the flow is actually more or less actual then the last term is actually eliminated. In the very early designs it was a done thing that the flow path was considered linear and the second term is also then neglected or it vanishes and which gives us back the simple radial equilibrium equation which we had formulated earlier in terms of 1 by rho del p del R equal to C w square by R. Now, this was the simple radial equilibrium equation what we need to look at now is a full radial equilibrium equation and we see now that the simple radial equilibrium equation was somewhat inadequate and it becomes necessary to utilize the full radial equilibrium equation in design and analysis of modern actual flow compressors. Now, if we go back and summarize some of the things that we have done we can say that wherever the flow is not experiencing the centrifugal force the radial equilibrium cannot be applied and with this understanding it was at one time assume that radial equilibrium is not applicable between the rotor and the stator where no blades exist. However, experiments have shown that in between the blade rows in the actual gap between the rotor and the stator there could be a radial shift of the meridional path and hence for accurate design analysis the radial equilibrium full radial equilibrium equation should be used in that flow path also between the rotor and the stator. For the computational purposes further steps need to be taken from this mathematical form the radial equilibrium equation is transformed into a form that contains partial derivatives of all parameters with respect to radius and peripheral coordinate theta because all the parameters like pressure and density and enthalpy are likely to vary from root to the tip of the blade and also likely to vary from blade to blade. So, this blade to blade variation and root to tip variation need to be captured I will show you in the next slide how the physical model or mathematical model attempts to capture it in its computational form. The next circumferential average of those parameters is then integrated over the theta from the pressure side of one blade to the suction side of the other blade and then the flow is analyzed at various axial stations with the energy equation continuity equation and the radial equilibrium equation. So, you need all three of them to analyze the flow now this is what I was talking about that you have a model in which you have two blades in between the two blades you need to create these surfaces. These are known as S 1 surfaces which if you vary S 1 from root to the tip of the blade you have the variation of various parameters from root to the tip of the blade. The S 2 surface is from blade to blade that is from pressure surface to suction surface of the other blade. So, if you take the variation of parameters on S 2 surface and then vary them circumferentially in the theta direction from one surface to the other you have the variation of all the parameters in the circumferential direction. After you integrate on the S 2 surface and on the S 1 surface you get integrated parameters of all the parameters. So, this model has been used by the computational people to transform radial equilibrium equation into a computational tool for analyzing the flow through axial flow compressors. It is necessary that the flow properties obtained in this manner at various axial stations be consistent with one another as the flow properties are evaluated from up to the tip at each station. That means that the radial acceleration of the fluid particle is to be accounted for through radial equilibrium equation which is the additional equation you need to use in addition to the energy equation and the continuity equation or continuity condition for analyzing flow through axial flow compressors. Now, this can be achieved by assuming shapes for the meridional streamlines. So, you need to assume the shapes of the meridional streamlines consistent with the continuity condition which expresses the radial acceleration in terms of the streamline slope and the streamline curvature. So, you got to find the meridional path of the meridional streamline along which you can apply the radial equilibrium equation that meridional path can be found by using the continuity condition along the meridional path. This of course, implies that you need may need to iterative method of solution because prima facie to begin with you may not know the meridional path, you may not know the streamlines that create the meridional path. This method in which surfaces are used to build up the flow inside the termationary blade has been widely used and this widely used formulation is being used for last 20-25 years for analyzing flow through axial flow compressor from blade to blade surface and those on the meridional plane and they need to be solved separately to account for all aspects of the three dimensionality of the flow through axial flow compressors. The 3D flow computations has provided huge assistance to the engine designers or the compressor designers more specifically. It has cut down the design time and it has reduced the dependence on costly experimental analysis experimental analysis making the blade testing it in the rig is a very costly business and time consuming business computation has cut it down substantially. The 3D methods have helped understand various flow phenomena such as the secondary flow development choking in the stages as and when they occur effects of involved flows not to speak of problems like stalling and those can be then sorted out in the design itself before the blade is actually fabricated. However, the designers use these solutions quite often in conjunction even today in conjunction with empirical relations specially the losses that occur are very difficult to capture in CFD and hence quite often empirical relations do again come back into picture and experimental data to account for some of the losses and thereby predict the performance of the design axial flow compressor blade which means that there is still a scope for improvement of these methods. So, that the empiricism the empirical formulations are reduced further to the minimum some of it may have to be done in the last stage of the design before the blades are actually fabricated and tested. However, the dependence on the empirical formula can be reduced if the CFD method is taken forward. So, that more and more of the three dimensionality that we have seen right in the first slide is captured in the formulation. So, in today's class we have done lots of attempt to capture lots of three dimensionality in the mathematical form and finally, we have got a full radial equilibrium equation that is substantially different and far more complex involved than the simple radial equilibrium equation that we had done earlier. This allows us to go forward and do an analysis of a modern axial flow compressor and aid in the process of the design of this modern axial flow compressor. So, that brings us to the end of today's lecture of creating a mathematical formulation of flow through three dimensional flow through axial flow compressor. In the next class we will look at an attempt to solve some of the problems of simple 3D flow theories that we have done earlier and we will try to use those theories to solve some of the problems use the free vortex theory and other vortex theories to solve some of the typical problems and show how the numbers actually come up in solution of axial flow compressors.


Hello and welcome back to the craft box. My name is Rinnan today. We are on episode 43 of the Pirate 101 Walkthrough series and Today we're gonna be starting by finding the abandoned church and finding Sabatini If you haven't gone checked out last episode, go do that It was good and you'll understand where we are and what we're doing and If you want more go look at the playlist so you know exactly what's been happening So yeah, this is the church right here. I believe We're nearly done with Koran's as well like no joke It's kind of good finally Okay, let's dock here That docking place like you get the notification to dock back way way later than most other places, which is weird Okay Yeah, so we're basically finding Sabatini so we know we're um um No, what's his face? Captain Blood hideout is Captain Blood's hideout is But yeah, we've got two episodes left after this one.  I don't even know Okay, so your last episode we got Corporal Sanders Which is rich was kind of a surprise like wasn't expecting to get him at all. So yeah Okay Yeah fish ace So yeah after cool ranch which is three more episodes including this one and we head on over to Mooshu which is Which is not too long of a world So that's good. And then we have Marley bone, which is really short and then we have aquila Which is the last big world before the end of the game because Valencia 2 is like five episodes Max my could have probably convinced it down, but you know, whatever So, yeah The reason why I didn't I think I didn't convince Valencia 2 down and my plan in was because it's it's really hard And I don't know if I'm up for the challenge to do all of it like really really quick So, yeah, he's not dead. No Really? Okay, that's fine. You know what? Wow, that was good, okay Okay, these guys are actually really easy. He's dead. He just killed himself. Okay This battle isn't too hard. It's good Do Really There we go done. That was good. Okay, let's get these chests Okay, I Wait, where's my fountain? Let me just get on my ship, and then I'll decide if I'm gonna skip or not. Let's see where's the fountain Forming muti. Okay, that's good. We can we can go there because we're going back to Santa Polio now. So that's good Yeah, yay Nice Perfect. We landed right next to the stage coach. That's amazing. Okay, and We are going over to Santa Polio travel Perfect amazing stage coaches of the beast Load load load, please load. Thank you Okay There's a lot of people here today. Jeez Kinda crazy if you ask me So many people Okay Here we go Over to Isla de Mirtus de los Mirtus. I don't even know. I don't even Spanish Okay Slight leg that's cool. People are fighting that's always bad. No Get out. Okey-dokey Load go go go. Thank you.  Thank you. Okay We're here Lots of people here as well. Wow Okay, she's up this way. I went the wrong way that's not good Okay Here we go. I Have been expecting you you come seeking answers The cards will give them to me and I shall interpret their message Ask your question and the reading can here's our question. Where can we find captain bloodskeet? The first card represents Source of the present and key to the future Here is judgment the card of laws rules and packs The card is reversed deception the trail Mutiny these are the sources of all the obstacles that face you now You must set things right the second card is the present the challenge confronting you here is the drowned Mariner captain blood the pirate who lives beyond death Here is the answer to the question Captain blood has taken the key you seek How can you take it from him the cards show tell us the last card is the future Which reveals the solution to the present challenge? Here is a dark card the race Who is death? Death was the dark master captain blood cheated this is the source of the pirates power This himself will show you the way Dead in your heart want to treat weight How do we call him to rave and be death servant them birds? No Feed them corn.  It's quite cool. Okay. Anyway, let's head over um Head back over To send a boy over there was a life fountain there that I bounded to Yes, it was Let's go back real quick Gonna bad thing is we have to go back there, but that's fine. Okay Okay, who are we talking to you? Hello Help me honor my mother's memory by taking back some bags of corn flour and her secret recipe confront the vial banditos Is there like a way to get this without talking to you possibly if we like go back a bit more There we go Sweet there we go. Okay whoo that was That was a bit of a challenge there Ba-ba-ba-ba-bop. Okay Let's get on over back again. It's a bit of a back-and-forth game here talk to The Ravens why was I turning?  Okay, let's go Let's just waste this fuel because I can okay but Don't even dear trying to battle me. I am way too good for you Okay And back again That was quick Okay The Ravens Here's the Ravens the corn captain beat the birds. Okay That's cool Here we go call death. You must offer something he wants There is a vial killer who has offended dead like Bart is his name He led a group of pilgrims from Santa Boyo to the haunted Skyway Betrayed them and scattered the spirits to the winds Gather the lost spirits in haunted Skyway and take them to the graveyard of the old church Yeah, we'll find you Okay, there we go. Let's head back over to the haunted Skyway again just as well after Mark over there Do Okay, let's go and collect these lost souls Hopefully doesn't mean battling any ships because I don't want to do that Okay Let's see Where are we going for these lost souls? Are they these little things here? Yes, they are. Okay. That's cool That's cool They're not too hard to get Just watching out for bone snakes because they are scary. There's the next one, huh? Is there any over here? I saw some before. Um, maybe there isn't. They haven't respawned yet. Oh, they have yas. Perfect. Okay, that was easy. Up. Nice. And back over to Black Bart. You know what, let's just go like that. I know I was there, but you know. You know. Los. Okay. Let's just hit over and find Black Bart. Or to fit, yeah, find Black Bart. Okay, that was easy peasy. Ba-bum, ba-bum, ba-bum, ba-bum, ba-bum. Enter now. Ten, nine, eight, seven, six, five, four, three, two, one. Okay, that was cool. Let's go in. And the shadows rise. Death be near. You're there. The spirit is mine. I took up and I'm gonna take up. Okay. Next fight, yay. Okay, I can use tombstones. Wow, okay, fine. We'll do that soon when I can be bothered, you know. Okay, done. Ba-bum, ba-bum, ba-bum, ba-bum, ba-bum, ba-bum. Okay. Agility is good. Which means we crit. Ba-bum, ba-bum, ba-bum, ba-bum. Don't call it noise, it's so cool. Okay. That was pretty cool. Okay, that was good. Ba-bum, ba-bum, ba-bum. Let's just do that, cause we can. I'm on it. Okay. Damn it, it didn't work. No. We actually have to go up and use them. That's not even fair. We have to defeat all enemies, I think, anyway. So I might as well just keep going. Ba-bum, ba-bum, ba-bum, ba-bum, ba-bum. Nice. Okay. Let me get her, that's good. Sweet. Okay. We've got one down.  Yeah, we're gonna have to soon. Sooner than later. Um, let's see. Ba-bum, ba-bum. Nice. Double tap. Ba-bum, ba-bum. Perfect. That was really good. Okay, chill out. Chill out, Ten. Double tap.  Chill, Will. Boom. Boom. Boom. Boom. Boom. Boom. Yeah, more spawn. So you need to destroy the gravestones, so more don't spawn. Okay, that's fine. Okay, this is interesting mechanics. I can't remember this battle. Okay, just try and hit me. That's cool. Fine by me. Okay, yep, hit me all you want, guys. That's fine, you know. Ba-bum, ba-bum, ba-bum, ba-bum, ba-bum. Ba-bum, ba-bum, ba-bum, ba-bum. I'm on it. Actually, kinda want you to go for him. Done. Okay, let's just see how this goes. Hopefully no more should spawn, so that's always good. Wow, that was good. Okay. You're good. Nice. These guys are so good. My companions are so good. Musketeers are OP. Confirmed. Okay, Black Bart is nearly dead, which is good. Relentless, really, really. Duck Holiday's gone. He's gone. He's gone. Really? Calm your farm. Jeez. No. Duck Holiday, no. You were so good. At least that was a mega hit. One down, that's good. Ba-bum, ba-bum, ba-bum, ba-bum, ba-bum. Let's just get Black Bart out in there. Okay, that's good. He's dead. Double-tap. Good, perfect. Really? Calm your farm. Really? Stop, really? Stop? Good. No, don't bug. It's fine. You know, okay, this is going to be interesting. I want to just drop.  I did not press crown shove. I do not need it. What are you... getting? Please stop. No, we're getting Black Bart out of your bed. There's going to be me versus those two, I swear. At least he's going to have to come a long way to get me, which is good. So you know, just... really, really? No. This Black Bart guy, he's no joke. The only bad thing for him now is he's going to have to come a long way to get me. And I think I can get him somehow. Somehow. Somehow. Whoa, what's that? Okay. That's weird. I'm trying to get Black Bart out. He's the most dangerous here. Okay. Yeah, come for me. Really? You're dodging. You're dodging, yeah? Okay. They're in line, hopefully, so we can get both of them. Nope, they're diagonal. We can still get both of them. Done. Okay. Perfect. One down. Bart. Bart. Bart. Bart. Perfect. Phew, that was a struggle. Just as well I went to get those gravestones. Literally one companion. Hopefully we don't have to defeat anyone. This seems worth the trouble. But he was, is, rather obsessed with immortality. And so on his deathbed, he challenged me to a friendly game of cards. Yes, I know, I have a gambling problem. I'm getting help, all right? Look, I don't have to answer to you. It really is none of your business. Anyway, there we were playing cards. In the final hand, Blood raised the stakes and debt me his immortal soul. I had him. That's when he cheated. I played my cards, but Blood went to the bathroom and never came back. And he took his cards with him.  I can't collect Blood's soul because I haven't won the game. But I can't win the game because the game can't end. Blood's hand remains unplayed. He hasn't lost yet, you see. Very clever. It was a dreadful loophole, and of course I've had the rules changed. I'm afraid it doesn't apply retroactively. Captain Blood is stuck between life and death, and I can't touch him. He cannot be killed, or even harmed really, until our game is over. Captain Blood's cards must be played by his own hand on the table where my cards are still waiting. No, it's all dreadfully improbable.  Look, I didn't ask you to do this. You called me. If you want to find your precious map, you need the key to Captain Blood's treasure. The only way to get that key is to pry it from his dead fingers. So good luck with that. Call me when you've convinced Blood to put his cards on the table. I'm sure you'll think of something. And how do we find these cards? Who knows where they might be? A member of Blood's crew would know. Sly Winkum was in Blood's crew. Let's see what he can tell us. Wow, that was... that's also one of my favourite parts of the story. That puppet shows off and I love them. They're so good. Okay, let's head over to Sly Winkum. And since it's a wee way away, I will be right back once I'm there. Okie dokie, we're back. About to speak to Sly once again. Let's go. Tell you what, if that hand is still out there, it'll let you finish that game once and for all. Back to Santo Pollo we go. Don Rodrigo will be eager to hear about this. Know what I mean? Okay, we get another surprise here. I know what the surprise is, but I'm not gonna spoil the surprise. Most of you probably know what it is as well, but it's a surprise. So I'm not gonna spoil the surprise until it happens. Okay, let us head down to Stagecoach and see what we can do. Let's head over to Santo Pollo. That's terrible, okay. El Dorro and Captain Blood fought on a cliff, high over Gold Creek. El Dorro cut off the pirate's hand and it fell along with his sword into the lake high above the creek. Why do you ask? What? The greatest evil Santo Pollo has ever known is back. You will not fight alone. El Dorro shall join you for justice. Fear not, my love. I will defend the people of Santo Pollo while you accompany the captain on this quest. This is our surprise, yay. El Dorro, hello. Okay, let's just sort out our convenience. Bonnie Ann, you're out again, sorry. Let's sail in. Let's just get him some earpicks. We're gonna give him relentless. Okay, let's defeat these guys, I think. Yeah, complete in 15 turns, that's right. Agility, cool arms.  Done, okay. Let's check out El Dorro, see how good he actually is. He's pretty good. Okie dokie. Let's just pull them down here, I think, is probably the best idea. Just fully buff up with agility. Done, perfect. El Dorro, jeez, already doing all the earpicks and relentless, that's great. Just what I need. Just, thank you. El Toro's perfect. Perfect. So perfect. Let's get both of them. I want you to go on him and him. Done. Wow, okay, that's good. That's that time, that's unlucky. You got a relentless, so that's good, Tyson. Boom, boom, boom. Perfect. Done. Perfect. Actually, you're dead, so let's just start moving up this way. 11 turns, we can do this, this is easy. That's my favourite earpick of everyone's. Like out of all companions, that's my favourite. Block, no. Block, no. Why you no block? Dammit. Okay, there's agility gone. Or one of them, the main agility. Let's just do it. Done. Perfect. Yay, we did it. Amazing. Let's collect Blood's hand. Here we go. Beware, pirate. Miranda is a terrible place. When blood-cheated livings happened, the place is cursed. Watch yourself. Okay. So next episode, we will go into Miranda and kill or defeat Captain Blood, which is pretty intense. So yeah, two more episodes. So thank you for watching. Remember to leave a like and subscribe. And remember, actually, and remember to press the sweet little bell so you know exactly when the next episode comes. And remember, craft outside the box.