Hey everyone, welcome to Higan Iruthil. So this is going to be the tier list for March and we're starting off with The bottom tier which is going to be tier C. Let us look for ASSA. Okay, so ASSA Actually in this game, there are a lot of you know, there are a lot of R's and SR's that are very useful, but again if you develop them And you have better Characters coming then you won't really use them in the late game You're definitely going to be switching to the better characters that you have So again, this tier list is going to be dependent on their max potential So so far for ASSA, ASSA is going to be very useful in the initial stages But again falls off because there are a lot of better healers and buffers in this game So next up, we're going to have Where is MoMell? MoMell is here. So MoMell Again similar She's not going to be she is Not going to be much effective in her max potential Can increase damage sharing in the battle Not really, you know In terms of potential, she has the lowest potential So I don't think She's going to be used very often in most of the content in the game. So next up we have Sela Sela here is a A duetrix, okay, so provides physical shield again Um Her potential is not leaving C. She doesn't even go as far as C Towards max potential. She's very good with recharge and assist But as far as it, you know as her kit goes that is it. So Sela is going to remain at tier C Next up is going to be I have to find her here Find her here Caudier Where's Caudier? Here she is Okay, um early game though. She has a good potential, but late game. She's going to fall off Um, uh, especially for max potential. So again good to start. Um A duetrix Good healing effect can use wind breath. So Again, be just be careful not to over level her up if you intend to use her at the start But in terms of max potential, she really falls off and she's going to be stuck at tier C Okay, next up is going to be Ume This girl is so cute But again, that is that is the only advantage that she has so very good at interrupting knocking up and Again, cuteness can only you know take you so far in this game. So but she is she She can be at tier B early, but again falls off max potential Going to be tier C. So I'm sorry She doesn't really cut it. Next up is Mireya Mireya is here. So again same Max potential is not really That good. Again, I wouldn't want you guys to invest much in her, but She can be tier B in you know in early game, but again Not really really really worth investment long term So burst damage though is very very good But that is the only thing that I see that is going to make her good So we're off to tier B. Most of you guys were asking me about Uferia a while ago. She's good. So again, as I've said Early game if you don't have anything to bring for hoplite Then she's going to be good. She's pyro um Yeah, she's pyro. Sorry and uh very very nice very sustainable, you know For tank characters can restore hp when in low hp. She's very self-sufficient. I tell you very good defense Um, very good for early, but max potential will she'll she'll be stuck with tier b Okay, moving next is going to be folet Folet is kind of similar to To uferia Has a very high early game, you know Value but really drops off. She's going to be max potential tier b Um large aoe damage a lot of you know, there are a lot of casters better casters out there So again, very good attack and defense For both of those but again max potentials it's going to bring her down So might as well look for other casters that can take you to the end game Before you invest in her if you don't if you have if you have if you don't Then folet is going to be uh it for you guys. So Next up is going to be isa Okay for isa Can Is real nice in pulling in that's her that is one of her, you know skills that I think has very good potential Especially if you are looking for placement of enemies Um very good very good attack very good at control But um, she's going to be tier b Her max potential and early game is going to be tier b I don't see her moving from there because again, there are a lot better casters Ahead for tier s and tier a so moving on we have uh black here So black has very good early game potential Um, but will be dropping off to tier b as you max potential him. So again be Be very careful in investing much in him can do encroaching coals though and uh suitable for dps characters um Again, no Probably invest up to level 50 not go beyond level 50 if you have other better characters and invest in them Instead of black, but he is at here's a tier b. Okay.  I like the way she looks Actually, she is she's a very flexible assassin can attack up front can attack up far Can deal aoe damage Very good at controlling attack But again, um, her potential doesn't really go up or down She she's some kind of lack something She's just there, but isn't really applicable to go You know to the higher tiers I like how she plays but again, it's not really assassin like so Um, I'll leave it at that. So she is at tier b guys and next up is going to be cloar Um, nice early game. I tell you I've been using her to you know, uh before especially cbt max potential again Very good. Very good burst. Um aoe or excellent, you know damage for aoe But again, that is as far as her kit takes you so Again, if you're on a budget if you don't have any casters, but I doubt it. You're gonna be having good casters Um, don't invest too much in her if you're using her in the early game Also next up is going to be Hathor Okay, so hathor here So Early game not that much Can be good max potential with tier b. So high damage against single target. So if you encounter bosses But that's about it. Um Nothing really impressive with her kit. So she's actually stuck stuck at tier b Next up one of the heroes that I have been using since cbt. I just recently replaced her with Uh With gilden I'm sorry arman, but you have to go gilden is more formidable as a tank. So garden pyro Good at both sharing and dealing damage um Doesn't really take a lot of damage as gilden. That is why I had to replace her But very decent early game not that much. So max potential is going to be max tier b Um, sorry arman, but you have to go I need to replace you next up. We're moving to tier a so at tier a one of one of I think The most unique characters that we have has a summon Has high aoe damage for, you know, his ultimate But again the cost is too high that The bear drops too late sometimes So grants buffs periodically increases self m damage so again Early game Not too much you have to build him Um, you invest in siacom if you want his max potential to be To be, you know up there or probably good before best So that's it. So siacom a caster again one of the best casters that we have But we have more guys. So next up We have live so recently gotten live um, a do it tricks has a lot of support spells um encroaching cold Very good support a little bit of I think I saw healing there in in her kit So max pot early game can be very good at here a max potential Um stock at tier a so again supports For me supports are valued if they have a balance of healing and you know everything So at this point hopes before I forget Um I think I have her here. So we're done with live. We're gonna go to the next speaking of support So we have screamer here screamer and search that came out recently So that is why they're new to the tier list So for screamer Heal multiple allies against silence enemies applies attack speed bonus Again, um, very good as it both, you know, half and half support and healer role Can be very good, you know can have a very good max potential at a so Again this she is very underrated guys. So try to use her. She is s r if I can recall better So No, again very good for both support and healing. I cannot say much more about her kit. So next up One of the best value s rs that we have as well. It's going to be roko. So definitely one Very good healer to start But she'll be dropping off a bit from tier s to tier a When she's max potential because there are better healers on top for tier s. So that is the only drop off But again, you can really um Easily get copies of her kit. She is s r and I cannot complain with her on my team Okay, next is is going to be mo test ju Mo test ju so ranger animal So very good Very good damage. So sub dps has pet ad and healing so provides wind breath as well So so far very good in burst and attack damage Again doesn't drop off in tier a even from early game and to max potential Next off is going to be rita So for rita Early game she's going to be struggling a bit, but once you max potential her Uh, definitely worth investment a ranger pyro attack buff high burst damage against single target So while fan is going to be excelling in AOE she rita is going to be excelling in single target damage Very good attack burst and assist as well So good at max potential at tier a Next up is going to be basal So basal here um early game is going to struggle a bit and but max potential He's going to be a tier a strong crowd control ability. Um, I nearly got him with one of my, you know, re-rolls But uh, I opted for others. You know what I mean? So I opted for waifus Suitable gar a suitable really for um control AOE and as a tank so again um going to struggle early game, but Max potential is going to be good Okay, one of my favorites here We have here fan. I've been using fans in CBT. I really like how she is played um clearing content Clearing the back line. I really appreciate her AOE and early game in max potential. She doesn't drop off She's very consistent. That is what I like about her small AOE damage can assist team as well Um, although she's not ideal for single target. She is very useful in most Stages so very good at burst and range damage Okay, so next I think this is I'm not sure if she's the no, she's not the last in tier a So this is our free unit Which is media. So early game. She's gonna excel Very good at single target damage preferably bosses But drops off to tier a as max potential So excel excels in both single and AOE target Again, again, what could you look for in a free unit? Plus I got a copy of her So excellent very excellent in the main story as well Okay, so if you're asking if media is good, then that is your answer. Next is Nuno Nuno is um can reduce energy cost shield plus healing um again Better healer probably than than roco some might argue not But again, um early game. She's gonna be very useful at tier a and max potential is also tier a so Again, not a bad investment for an adieu. It's fricks Okay, so we have another one we have here. I think here is the last one For um tier a so for here I'm gonna be struggling early game max potential is going to be tier a Physical shield for whole team can protect ranger in assassin.  So also a good investment at tier a And we have four left for the top Slot here. So we have first our top healer Which is going to be Caesar Um, not healer top garden probably so both gildan and her so Again provides aoe healing for a garden shares damage Probably your you know your ideal Gargant so to say so early game is going to be a but um if you invest in her max potential She's definitely going to be tier s So really really nice tank with a lot of defense. So going to our new addition to the game recently with her banner um, sorry not her That's a pair gildan with uh, Caesar for a bit. So gildan umbra very very high defense She's really a tank She's really a tank guys. Um Really really hard. Um defense Again very good at control both Caesar and gildan Superb tanks. Um, I couldn't ask for more. So early game a late max potential would be s tier So either you have uh Caesar or gildan you can't go wrong. So I don't think you'll need two two shields or two gardens. You just need One so choose the best for you. Uh, it depends on you on which one you're going to be using and uh Before we go to eluya We have here sirslet. So for sirslet here, um, I used her in the first CBT. So deals a lot of critical damage again the damage that she deals Is actually kind of similar to eluya, but she deals it more in a wide area wider area If I can remember Super AOE tons of damage and dps. I can't say more If you did a pyro dps then definitely go with sirslet go for you know for her banner pull for her If you haven't pulled for eluya in the previous banner and again speaking of eluya my dear I love this character. Um Again debuff high burst damage Single target best dps for single target for bosses Her burst damage is really really high That you have to um, what they call this you can really take advantage of it Make sure that she does. Uh, she does more attacks that But again, her only weakness is survivability if you can Make sure that she survives um Being in the front or being in the middle. I don't think you'll have a problem Actually, I tend to forget that she's assassin, but she can do she can be good at up front actually I don't I don't have a problem with her. But again She you have to make sure that she survives Otherwise she can't deal that ton of damage. So again in terms of damage wise, I think she's the top in terms of dps um Aside from sirslet. So that is it guys that is your tier list for He got a root hill for the month of march So comment down in the comment section. What do you think of this tier list? um And hopefully when we add, you know other other characters, I'll be updating this tier list As well. So that is it guys. Um, again, stay safe Take care. This is the warden and I'm out of here


وَأَقُولُ فِي القُرْآنِ مَا جَاءَتْ بِيهِ أَيَاتُهُ فَهُوَ الْكَارِيمُ الْمُنْزَالُوْ وَأَقُولُ قالَ اللَّهُ جَلَّ جَلَالُوْهُ وَالْمُصْطَافَ الْهَاديِ وَلَا أَتْ أَوَّالُوْ الحمد لله رب العالمين له الحمد الحسن والثناء الجميل واشد الله إلا الله وحده لا شريك له يقول الحقا وهو يهدي السبيل واشدوا أن سيدنا ونبينا محمد صلى الله عليه وعلى آله وأصحابه والتابعين لهم بحسان إلى يوم الديل أما بعد إن شاء الله إتعالى أنا سأتحدث عن وفعلت تفسير كلمة التوحيد وما سأفعل إن شاء الله إتعالى لتفكير من ثلاثة توحيد أريد أن أتحدث عن فضله لا إله إلا الله فضله ومعنى هو its meaning وأهمية له and its importance لذا ثلاثة أشياء إن شاء الله إتعالى هو ما سأتفكير في this session بإذن الله الكريم وعندما you do finish this session I hope that you understand the virtue that this word لا إله إلا الله محمد الرسول الله it holds and the meaning that is in it and how important it is some of you might think to yourselves are you ready know لا إله إلا الله I'm a Muslim and so what I want to say to you is it's a reminder and the reminder benefits a benefits the believer as Allah سبحانه وتعالى said in the Quran وذكر فإن الذكرى تنفع المؤمنين remind for very little reminder benefits the believer so even if you know it will be a reminder for you and insha'Allah تعالى that will be إذن الله الكريم benefit you my beloved brothers and sisters who are listening توحيد is أول واجب it's the first obligation on every one of us and it's not only the first obligation rather it's the last obligation the Prophet صلى الله عليه وسلم he sent معادي من جبل to Yemen where did he send معادي he sent معادي to Yemen and the Prophet said to Muad إنك ستأتي قومن من أهل الكتاب معادي you're going to meet you're going to come into contact with the people of the scripture they are a people who have a scripture they have a book they have a religion the Prophet said فليكن أول ما تدعوهم let the first thing you call them to be what شهادة الله إلا الله let the first thing that you call them to and the first thing that you command them to come with let it be لا إله إلا الله so the messenger said إنك ستأتي قومن من أهل الكتاب you're going to come to a people of the scripture the أهل الكتاب إذا يهود النصارة فليكن لر it be أولا the first thing تدعوهم that you call them to be what شهادة الله إلا الله let that be the first thing that you call them that you call them to and every prophet every messenger who came this is what he called his nation and his people to الله سبحانه وتعالى he tells us in the Quran إذ جاءتهم الرسل من بين ايديهم ومن خلفهم اللى تعبدوا إلا الله prophets before and after those who came all of them they called their people to and they started their message with by say what اللى تعبدوا إلا الله don't worship anyone other than الله عز وجل لا إله إلا الله every prophet said to his nation and his people يا قوم عبد الله ما لكم من إله إلا worship Allah alone you have no other Lord deserving of worship other than Allah عز وجل let him be the first one that you worship so every prophet did that and نبي الله محمد when he came to the people of Makkah and he started his message the first thing that he called them to was what لا إله إلا الله the Salah after 10 years of his prophecy 10 years the Salah was made obligatory 3 years in Makkah was when the Salah was made obligatory the prophet was in Makkah for 13 years 13 13 years 10 years of that was only Tawheed and then the Salah came which is the second pillar of Islam in the last 3 years of Makkah and then the prophet still didn't stop calling to Tawheed because the Salah is the manifestation of لا إله إلا الله the Salah is your action and your proof of لا إله إلا الله is that you stand up in front of Allah and that you pray 5 times a day you put your face on the floor with complete love and complete humiliation for him and humility so the prophet SAW 13 years in Makkah and 10 years in Medina he did not stop one day calling to Tawheed so it's the first obligation that we need to come with and it's the last the prophet SAW he said لا إله إلا الله الإمام المسلم narrated this hadith from two companions the first companion is and the second one is and the second one is the prophet SAW لا إله إلا الله the one from amongst you who is on his deathbed he is going to departure from this world and he is no longer going to live remind him to say the word اما تسأل لا إله إلا الله remind him it's آخر واجب it's the last obligation it was the first and it was what it is the last that's the status and the position and he said من قال لا إله إلا الله anyone who says لا إله إلا الله بزار narrated this بسنده على شرط إمام المسلم بسند صحيح على شرط المسلم بزار narrated this with a chain of narration which is صحيح rather it's the condition of an Imam Muslim that the prophet SAW من قال لا إله إلا الله anyone who says لا إله إلا الله when he's on his deathbed he's about to leave the world دخل الجنة he will enter Jannah يوم من الدهري one day وإن أصابه ما أصابه the prophet said anyone who says لا إله إلا الله when he's on his deathbed he will one day enter Jannah even if it happens to him whatever happens to him meaning if he even ends up going to the hellfire for a period of time he will still go to Jannah one day لا إله إلا الله will take you to Jannah one day لا إله إلا الله it has great virtues the prophet SAW said أفضلوا الدعاء يوم عرفة the best supplication is the supplication of the day of Arafa that's the best supplication وأفضلوا ما قلتوا أنا يوم من قبل لا إله إلا الله the prophet SAW he said the best thing me and all of the previous prophets the best thing that we said the best is لا إله إلا الله أفضلوا سيغة المبالغة على وزن أفعل the best it's a supplative in the Arabic language the greatest the best thing that I and all the prophets that came before me said was لا إله إلا الله وحده لا شريك له الامام ترميدي narrated in a different wedding but the wedding that I just narrated is narrated by Malik in his muata الامام Malik narrated in his muata رحمه الله تعالى the prophet SAW was one day asked أمن الحسنات لا إله إلا الله is لا إله إلا الله from the hasanat righteous deeds is it from it the prophet SAW he responded and he said he أفضلوا الحسنات it's not just from the good things it's the greatest righteous deed that a person can come with which is what لا إله إلا الله the messenger SAW he told us in a hadith that نبي الله نوح نبي الله نوح he called his nation for 950 years دعوة for 900 and what 50 years when we look at the Quran and when we look at the sunnah we don't know anything of the دعوة of نبي الله نوح except that he called Tawheed brothers pay attention here this is a very important point so allah said and we sent nooh to his country so they couldn't pass him 1050 ten years نوح was sent inвиres for 950 years from the sisr the legislation and the rules and regulations we don't find mention for his Nabil except that he called his people to what نوح التوهيد came and got that يجب أن يكون هناك أخرى مجموعة التي قلتها ولا شكة دواء لكن القرآن قلتها و السنة قلتها أن نحن مفتوح على أن تأكد أن الناس يفهم و يفهم و يفهم الواد لا إله إلا الله و نبي الله نحن نحن 950 سنوات و يقوم بكتبه ليس كثير من الناس يقوم بكتبه كما قال الله وما أمان معه إلا قليل فالكون who believed in Noah were very literally number فالشخص who believed in Noah were a group who could go on a arc including animals as well that's all that followed him There doesn't mean that the Da'wah of Nabilah in Noah was wrong That doesn't mean that he didn't do what was told he did exactly what he was told to do and he followed the commandments of Allah but the religion is not about how many followers that you have وكيف الناس يوضعونه ؟ فهي يعني أن يفعل ما الله يتعب with كذلك النبي الله النوح أنه صعب بالتوحيد الله يلاللله ونهي سنحظه كيف فعله على محبه الإيمان مسلم يرأي في الصحيح أن النبي الله النوح يجعله بإسطة انه يقوم بأمركم بالا إله إلا الله أمركم بالا إله إلا الله وقوم بإسطة I command you بلا إله إلا الله سُكتُهِ السُن On his deathbed نُوحِز just before his about to die إِسَتُهِ سَنْ أَامُرُكَ بِلا إلا الله فَإِنَّ الْأَرَاضِينَ فَإِنَّ الْسَمَوَاتِ السَّبَةِ والأراضِينَ السَّبَة لو وُضِعت في كِفَّةٍ ووُضِعت لا إله إلا الله في كِفَّةٍ رجحت بهِنَّ لا إله إلا الله نبي الله نُوحُ سَد if the seven heavens were placed on one scale and the seven earth was placed on one scale sorry sorry the seven heavens and the seven earths were both placed on one side of the scale and لا إله إلا الله was placed on the second side of the scale لا إله إلا الله والآويت رجحت بهِنَّ لا إله إلا الله فَإِنَّ الْأَرَاضِينَ فَإِنَّ السَّمَوَاتِ السَّبَةِ we are talking about the seven heavens we are talking about the seven earths لا إله إلا الله والآويت all of that brothers if you look at the Quran today you read from Surah al-Fatiha and then you read Surah al-Baqarah and then like that the Quran starts with which Surah Surah al-Fatiha right that's why it's called the opening the Quran starts from Fatiha the first command that you will come to is يا أيها الناس سعبود ربكم الذي خلقكم والذين من قبلكم لعلكم تتقون the first order is عبد الله واشب الله لا إله إلا الله عبد الله بن عباسن he said wherever you find the word عبد ربكم من القرآن it means اي وحيد الله singu Allah لا إله إلا الله عبد الله بن عباسن again if you read the Quran from Surah al-Fatiha you open the Quran and you start the Quran the first prohibition the first نهي that you're going to come to is فلا تجعلوا لله أنداد وانتم تعلمون do not associate partners with Allah when you know that shirk so the first thing that was commanded if you look at the opening of the Quran is what التوحيد لا إله إلا الله and the first prohibition is what الشرك الله referred to توحيد لا إله إلا الله referred to it as كلمة الطيبة الله said ألم ترى كيف ضرب الله مثلا كلمة طيبة كشجرة طيبة أصلها ثابت وفرعها في السماء الله said كلمة طيبة يبن جرير الطبري رحمه الله يسأل كلمة الطيبة إن اس آية مينز لا إله إلا الله الربيع ابن آنسل يسأل ألم ترى كيف ضرب الله مثلا كلمة طيبة كشجرة طيبة أصلها ثابت وفرعها في السماء كلمة الطيبة الربيع ابن آنسل يسأل مينز لا إله إلا الله الله referred to كلمة التوحيد لا إله إلا الله as كلمة الطيبة الله also referred to it as كلمة التقوى وألزمهم كلمة التقوى وكانوا أحق بها وأهلها وألزمهم كلمة التقوى كلمة التقوى هي what is it mean إمينز لا إله إلا الله ابن جرير الطبري سدت إن استفسير وألزمهم كلمة التقوى what is it mean إمينز لا إله إلا الله وإذن كلمة التقوى what is it mean brothers in the Arabic language التقوى comes from the word الوقاية what does وقاية mean وقاية means to prevent yourself to shield yourself from something when you come with كلمة التوحيد you come with الوقاية من النار you shield yourself from the hellfire لا إله إلا الله what does it shield you from it protects you and it shields you from the hellfire الله سبحانه و تعالى He also referred to لا إله إلا الله as what دعوة الحق الله سبحانه و تعالى دعوة الحق له له دعوة الحق دعوة الحق إنسآية what does it mean دعوة الحق means لا إله إلا الله الله also referred to it as حق لا إله حق الله referred to it as الله تعالى يسيز ولا يملك الذين يدعون من دونه الشفاعة إلا من شهد له إلا من شهد بالحق إلا من شهداء except the one who testifies with what بالحق with truth حق هي means it means لا إله إلا الله it means لا إله إلا الله so كلمة الطيبة means لا إله إلا الله وألزمهم كلمة تقوى و كانوا حق بها و أهلها means لا إله إلا الله له دعوة الحق it means لا إله إلا الله عبدالله من عباس قتاديت من الدعامة السدوسيا and others said it and also له دعوة الحق sorry the ayah الله تعالى يسيز إلا من شهداء بالحق وهم يعلمون it means لا إله إلا الله لا إله إلا الله my beloved brothers and sisters it is a term because it has that station because it has that position and because it's something that we need to say regularly and we need to say continuously on our it has to be on our tongue all the time it's from those letters that every person can pronounce لا إله إلا الله ponder over it they are not from the حروف of the Arabic language which are hard to be pronounced the حرف of God it's hard to pronounce it the حرف خق it's hard for some people to pronounce it وما إلا ذلك لا إله إلا الله are from the حروف which is simple for anyone to say and it's easy also number 2 لا إله إلا الله if you لا إله إلا الله محمد الرسول الله if you ponder over it you will realize that it's مهملا it doesn't have no dots لا إله إلا الله لا إله إلا الله محمد الرسول الله it doesn't have any any dots there's no dots and the scholars they said the reason why it doesn't have dots is the way that the dots were stripped from it you need to strip شرك from yourself and you need to strip those dots from your heart in associating partners with Allah then the شرك what does it do إذا أذنب عبدي ذنب النكت تتفيق قلبه نكتة تسودة when the person commits a sin and goes against Allah's command what happens to his heart a black dot is placed so the person what does he do he strips the same way that the dots were stripped from لا إله إلا الله محمد الرسول الله you strip from your heart associating partners with Allah لا إله إلا الله محمد الرسول الله is seven words how many words seven words لا إله إلا الله محمد الرسول الله counted seven words and the scholars they said these seven words are going to save you from the seven doors of the Hellfire الله سبحانه وتعالى he said about جهنم he said لها سبعة أبواب لكل باب منهم جزء مقصوم جهنم has family doors الله mentions that he has seven doors وإن جهنم لما وعدهم أجمعين لها سبعة لها سبعة أبواب لكل باب منهم جزء مقصوم those seven words they will protect you from the Hellfire they will what they will protect you from the Hellfire but the type of protection that they can protect you from the Hellfire is in two ways the first type of protection is بالكلية meaning you will not enter the Hellfire at all and it will take you to جنة and you will not fall into the Hellfire and the second protection it will do for you is it will protect you from everlasting in the Hellfire a group of people even though they have come with لا إله إلا الله but because they have committed other crimes they will end up in the Hellfire but لا إله إلا الله still has so much power that it can still take you out of the Hellfire so even if you لا إله إلا الله that you came with was weak it will still protect you from and it will still save you from staying in the Hellfire forever so لا إله إلا الله has that position brothers and it has that position now that we've understood the virtue of لا إله إلا الله and there's so much other things that can be said about this word I wanna insha'Allah تعالى wanna go into its meaning and I wanna conclude with that insha'Allah تعالى what is the meaning of لا إله إلا الله محمد الرسول الله brothers the word لا لا at the beginning in Arabic it's called نفي نفي is what it's a negation you're negating and in the Arabic language grammatically in نحو the scholars of grammar they mention لا النافية the law of negation what did we just say right now is you're negating you are refusing the لا النافية in the Arabic language are two types this is very important that you understand this لا النافية that come in the Arabic language في كلام العرب نوعان it's how many types? it's two types the first one and I'm going to break it down and you will understand once I finish explaining why I mention this the first type is اللي تعمل عمال ليس the first one is called so how many types of لا did we say they were in the Arabic اللي تعمل عمال ليس there are two types the first one is called اللي تعمل عمال ليس the first لا it does and it comes with the same things that ليس does this لا it resembles and it plays the role of ليس اللي تعمل عمال ليس what did ليس used to do in the Arabic grammar what does ليس do so first of all what does it enter it's me right مبتدأ أنا what does it do and what does it do ترفع it does نصب of the what so the Arabs they say ترفع الإسم وتنصب الخبر so in the Arabic language the person will say ليس راجلون قائمًا صح ليس راجلون look at the last letter راجلون قائمًا that's what ليس does right this لا it does the same thing you say the same thing لا راجلون قائمًا it does the same thing as ليس but this type of negation this type of negation the first type اللي تعمل عمال ليس it does the same thing as ليس the scholars they say تنفل وحدة وتحتمل العموم it doesn't negate everything it doesn't negate everything for example what did I just say ليس راجلون قائمًا لا رجلون قائمًا قائمًا no man is standing right this لا it only negated one man standing so that means two men are standing or three or four or five so the لا that comes as ليس it's negation is not strong does that make sense it only negates one but it doesn't negate all that's why the scholars they say تنفل وحدة وتحتمل العموم and there's a possibility they can negate everything the second type is this making sense to everybody the second type of negation is تعمل عمال إِنَّا this one does the it resembles إِنَّا إِنَّا is the opposite of ليسا ليسا is from أخوات كانا right إِنَّا what does it do إِنَّا does the opposite of what ليسا does which was what إِنَّا what does it do it does تنصب الإسما and what does it do وترفع القبارة are we all together so what do you say you say إِنَّا الرجولا إِنَّا رجولا قائم إِنَّا رجولا قائم إِنَّا رجولا قائم very early a man is standing right what do you say إِنَّا رجولا قائم لكن it does the same job as the إِنَّا so what does it become لا رجولا لا رجولا قائم لا رجولا قائم this type of لا that does the same thing as إِنَّا this one it's called نفجينسين meaning when we say لا رجولا قائم it means there's not one or two or three or four or five or six or ten or a thousand or a million are standing so the second type of negation is what عموم and it's نصون في العموم meaning it shows that it's an ultimate negation and that's the one that is in كلمة التوحيد لا إله لله does that make sense brothers the لا in كلمة التوحيد is the second type which is that when you say لا إله you're negating fully does that make sense you're not saying there's two or three any whatsoever لا إله إلا الله لكن the scholars they mentioned that the condition for the لا to be إنة or to resemble إنة and not ليس they mentioned seven conditions and he mentioned only two conditions he says one of the conditions I want to focus on here I don't want to go too much into the other conditions because they don't concern us now I only want to mention one pay attention please pay attention I know I don't want to go too technical and that wasn't my game but I really want to show you how important it is to understand this because لا إله لله is Arabic and if you feel you understand what is being said here when you next time say لا إله لله لا إله لله لا إله لله and you do your ذكر you feel it in your heart لا هيا brothers we just said right now you know what it's the second type and this is you're negating any إله other than Allah are we all together you're negating that but the scholars they said when do we say it's the first type of negation and the second type how do we is that an easy question do you all understand that question how many types of negation of لا did we mention 2 the first one we said is and the second one we said is we said that right when do we put it in the first category and when do we put it in the second category the scholars they said it's placed in the second category the strong negation when it meets seven conditions and the great great grammar he didn't mention seven he only mentioned two he actually mentioned one but within that one two comes under it I'm not going to mention all of them I'm only going to mention one condition because that's what I want to focus on one of the conditions is the اسم and the خبر both of them have to be نكرة they have to be indefinite does that make sense the اسم that لا is using the noun that لا is using and the خبر both of them have to be indefinite listen to what I just said right now لا رجل لا رجل here is it a man you know or is it indefinite a man huh indefinite لا رجل if I said are رجل now it becomes definite it's the man are we all together brothers here is لا رجل لا رجل لا so what do you learn from that you learn from here is that the رجل is indefinite and قائم of course is indefinite that's no problem this is let's go to كلمة التوحيد because we said كلمة التوحيد is a second time right لا إله إله is it indefinite إله إله is it indefinite إله إله is it indefinite is it indefinite is it indefinite or indefinite is it indefinite سيبوي he said الله is أعرف المعارف الله كان بينكرة الله is there is no one we know more better than Allah so the اسم has to be نكرة and the خبر has to be نكرة and كلمة التوحيد the خبر is actually معارف المعارف which is Allah so how did we say that it is the second type how do we put it in the second type this is where the scholars then said the خبر is not Allah the خبر is not the خبر here is حق the word حق is the خبر and then the scholars said why did you choose the word حق for why did you bring the خبر as حق because they said Allah said in the Quran ذلك بأن الله هو الحق وأنما يدعون من دونه هو الباطل are we all together and some said they bought a jar أنا مجرور and they said بحق وما إله ذلك لكن حق one word is good so what do we say now let's go back to the meaning لا إله لا what does it mean that there is no إله there is deserving حق إلا الله except Allah there is a خبر right to make it a نكرة and the reason why we chose حق is because it's found in the it's found in the Quran Allah used that ذلك بأن الله هو الحق الله is حق right so we use the word حق and the reason why we say it's a نكرة is because حق can be used for other than Allah so since it can be used for other than Allah it's not definite anymore it makes sense brothers لا إله means there is nothing that we worship the word worship in the English language I only use it to just make it close to you to understand but it's not a correct translation for the word عبادة عبادة is bigger than worship عبادة what does it mean and then we're going to conclude عبادة brothers when you look at it you have to look at it from two angles how many angles do you have to look at it from two angles the first angle that you need to look at it is how would you do the عبادة and how do you do something the scholars they mention if you're doing something for Allah you need to do it with complete love and you need to do it with complete what humility and humiliation and humbleness for example we take our face we put it into the floor who are we doing this for Allah we've put it ourselves low صح so we humbled ourselves but when you're doing it are you in love with Allah are you in love with Allah of course you're doing it for love you may be forced by someone who say to you prostrate to me and out of fear you may prostrate to him but are you doing it with love so he can never get those two the only one who can get those two is Allah ولي ذلك امر القيم says it is وعبادة وعبادة الرحمن غاية حبه وخضوع قاصده هما قطماني وعبادة الرحمن غاية حبه وخضوع قاصده هما قطماني وخطوة الأحض إلن وخطوة التترحين for whom for Allah that's how you do the عبادة here the second thing is what is a عبادة what can I say this is a عبادة the scholars said عبادة is اسم جامع لكل ما يحبه الله ويرضاه بناء الأقوال والأعمال الظاهرة والباطلة عبادة is speech إيمان ده is actions. so إيمان ده can be what? speech. it can also be what? actions. these actions are external and what? internal. and also the scholars they believe the speech is external and internal. for speech has two comes out from it external and internal and action. two come out of it which is what? external and? how do we know that Allah loves this action? how do we know that this action is إيمان ده? Allah has to love it and Allah has to be pleased with it. its speech and its actions. Allah loves it and he's what? how do we know Allah loves it and Allah is pleased with it? the سكولس here they say only through the Prophet. none of us here has met Allah. none of us have. the only way that we know Allah loves this and that this is pleasing to him سبحانه وتعالى is through the Prophet. الطرق كلها مسدودة. all of the roads are blocked. all of the roads are closed. the only road that is open to Allah is the road that نبي الله سلى الله عليه وسلم. so عبادة is built on what Allah loves and what he's pleased with. it could be speech and it could be once it meets that definition I gave you you are not allowed to divert it for anyone other than Allah. that's حق الله. it's the right Allah has of his creation. Allah said in the Quran وقضى الله ربك ألا تعبدو إلا إياه وبالوالدين إحسانا إما يبلغان عندك الكبر أحدهما أو قلاهما فلا تقول لهما أف ولا تنهرهما وقول لهما قولا كريمة وقفض لهما جلاحة ذلي من الرحمة وقل رب رحبهما كما رب ياني الصغيرة. إنه ندأ أيها الله تبارك وتعالى يسين وعبدو الله ولا تشيخو بيشة وعبدو الله. so you have to learn the word عبادة. and what it what it means in order to understand لا إله إلا الله. there is many money many many more things that can be said. there's many other things that I had in mind to cover which were the conditions of لا إله إلا الله. the conditions and the prerequisites that are needed for a person to come with but the time is short and I don't like to lengthen a topic I want everyone to understand if I go for longer you lose concentration. I think that is enough إن شاء الله تعالى for today. anything which I have said that was wrong or incorrect is from me a Shaytan and Allah and his messenger are free from it. سبحانك اللهم بحمدك أشدو الله إله إلا الله أستغفروا كواتوب إليه.


I don't know guys.  They're right away. We'll change the chat a few maybe. At the Hunters mark on them. I'm out this one. I'm gonna wallock Pit by the way, yeah? Uh, doesn't matter. Clean the Luster off already. Cool. I'll go me again. You can fear, you can fear. I got the chat mark, I got the chat mark, I got the chat mark. I don't know why you cannot fear. Yeah, going back on me. I can try and fear off it, but there's a shadow fury, so... You just go through everything. Okay, okay, okay. You can try to fear. Yeah, I'm going for it. The chat mark as well. I got the chat mark, I got the chat mark. No, I can't, I can't, I can't. Flowing me. Flowing me again. I'm sitting this, okay? Just run. I'll line the fear if possible. Yeah, I lined it, I lined it. I'm going to attempt to hit him, maybe, again. Let's go slow. I'm going to try and lock here. I'll try and lock here. I'm going to get feared here. Going to get feared here. I'm trying to line, I'll line now, I'll line now. I only have Trinket, but nothing else, really. Yeah, I have Trinket as well. I got so much of him now. I don't have any defences, by the way. Nothing.  I'm trying, I've got it now. Let's go at least. I can feel it now. Maybe I fair shaman here? No, no, no, I can't. You can trap up my own shaman here. Hold on. I can. Got the bomb juice. Yep, got it, got it, got it. Let's check, check, we'll look. Can I get this? I'll take some of your shaman. Nope. I'll see you soon. Miss yes or minus yes? Let's hit this. Let's hit this. I'll clone the lifeloom, resisted it. Stun me if you can feel it here. Melding it. Off myself or off myself? But take the damage here, maybe. Sends more luck. Spell to your dots. Let's get the shaman, let's get the shaman. He'll be fine. We'll take what we need to spell through. Through Hunter's Fire. Chink it's now. I'm shaman here. You're grounded. I'll get sheared. Slain me. I'm not shrinking. Got your fear. I can't see it. Gonna get finned soon. Shaman is oomsome. I'm cutting clone shaman. Now press grounding. Press ground. Watch this stun, okay, stun's coming. I can fear off if he dispels it. He will hide him next time. Iron Jesus is with us for once. Yeah, fear off. Yeah, he stunned me there. He can't fear me yet though. Call me, he wants to fear me. Really badly. Nice, nice. He's trink it, trink it. Nice, I'm gonna fish him. Good. Spelling pet. Pet's clean, pet's clean. He'll shoot. Spell them still though.  I don't have to deal again. I clone that. Yeah, I check. I check, I check. I do, I check. That works. Spelling pet. Shot. Clone healer here. Going for fear. I do it, I do it. Yeah. I recall. I think that the grounding is on the range of the wall. It's here, it's poor. There's a sensible one here. All the old, if you start up here. I'm just petting it. Rapid fire. Got the freedom. That's on you now. Let's have a PK. Lightning. No slow, no slow. I'll clone it. I'm starting to trink it. Yeah, I'm kind of worried here then. There you are. Showed you. Ones DK. This one's. Clone power. Nice, nice, nice. I bash on the. I'll clone the. Strangle me, watch out. I'm going to hit you in a sec. I'll do it now. I'll clone the gargoyle now. One more pet. Let's get it for the DK soon. Now. All my pet, by the way. Yeah, I shoot it. Where it charges me, oh. Sacks off. I'll clone DK. Trink it here. Lost myself. Lost myself. I'll clone the power. Nevermind. Nice. I'll do it. I'll do it. What are you putting? I'll put the reset on the wire. I'll put the DK here. It's going to be a glitch. If you get freedom I'll have. I don't mind. Miss-kick. I'll put the sound. I'll put the sound. I'll put the sound. I'll put the sound. Just spelling warrior? I'm just going to. I'll get a warrior now. Just go over here. It's going to chip out. Just going to chip out. Feaning warrior. I'll clone a strinkit, I think. I'll just.   They've sent so much damage into me. All right. Oh, they're bugging it. Can I get combo?  Don't go over, please. If you get found there, you did. Combo. Very nice. Is that enough? You tired? You got a lot of trash, boss. Yes, yes. Yep, no. This guy broke. He might blink CS, yeah, he did it, but you have PS. Can't get your sheep.  I'm going to hit me here, deep meat. Try and stop sheep. That's it. I don't know. I don't know. I have to trinket. I think I'm going to preside those shields.  Oh, nice, dude. I'm going to preside these shields. Half sheep, half sheep.  Down straight. PS. Flonk, Flonk, Flonk. There we go. There we go. I'm out, Poly. I'm going to give it to him. Diros. I'm going to give him a red kick. A red kick. That's all you need to do. Just flip the blinds.  I mean this really is it. He has one poly. We lose the game, basically, if you don't death drive. Good job, but you know... Look at that, he's got tees. Right, I'm mounting up now, hoping Shaman can pounce lock, so he doesn't disturb me.  I've got Shama for you by the way, I can't right now, I've got Snakes here for the howl. No, Clay. I'll finish. Double. Yes, I'm trying. It's okay, I've got Shama. I'll just touch something off this. Trying to line knock. Okay. Two of you in one. Gotta go way now. Stun me now, I'm gonna get knocked. Maybe not. I'll check now. I'll check, I'll check now. I cannot. It's okay, I think. He does these spells, he spells. I sense the druids, the clones, and they're off. Resisted my Cyclones. I can't live. It's lost there as well. Getting it cloned off as well, just chill this chill. I got the heroes knocked with Shaman. I'll rush you off this. If he does go, please. Yeah, yeah, they're going me. No, no, no, no, no, not yet, not yet. I'll touch Shaman here. I'll touch Shaman here. Yep, I'll rush you as well on top of it. I've got Shama as well, can you see her? Yeah, yeah, going, going, going. Good, good, good. Can you dispel it, of course? Do you turn the sphere, do you turn the sphere? Maybe he doesn't dispel that one. It's not the clone. Cloned the lock here. Missed yes or me, watch out. Stay down. No chinking for them anywhere. I have done for them. I kicked them. Healing you. I pounced the lock. I got a new shield. Let's go to this. Missed yes, got you now. Just live now, we win. I clone Shaman here. Reset, please dispel the lock. Yeah, I'm getting. Got it. Can't really push that right now because I drew clones. Careful. I can fill off as well. I'll wait, I'll wait, I'll wait. You can stop. Watch out, watch out. I'm not doing anything. Hex me, coming to you. I'm getting a restart. I hit the lock, cancel it now, cancel the lock. Oh my god. He bites, yeah. That's a nice Bruno. Did you have a silence? I should have maybe called. Look at the double. That's pretty good, honestly. Pretty nice I guess.  I think kill. I don't think we really have the mana. I mean we have the brick in innovate. We just go for the priest to be fair. Say what you want me to push. Let's get a warrior early. Maybe you can emcee the warrior. Palad did you say you cut it? No no, let's get the warrior emcee off. Yeah, okay. Let's go Bruno. Go little cat, you can do it. Get her emcee. Okay. Should we get it? He's going to dispell it. I'll try again. I'm just burning here. I've got the freedom off. I'm worried full. Do I emcee on you? Yeah, topping you. Still do I emcee on you? Am I on the spot or? No, you just have it. Hodge me, setting this okay? Don't worry now. Kick palad, come palad now. Got it. Still do I emcee on you? Emcee warrior. I'll come palad again. I'll come palad again. I'll kick the penance. I still have Ross of Valor if you want to go ham. I'm going to fiender.  I'll tap him as well. I'll tap him as well. Come palad, come palad. This guy, he's dead. I don't know man.  Did he like get like two back to back dodgers and a mortal or what? I don't know. He wasn't up for so long. No, he just got the shame again. He's too far now. Keep going now. I'll go again now. I'll go wallock. I'm slowing this guy. Go wallock, wallock, wallock. I got the chemist. I can maybe fear off the core. Got it, got it, got it. I'm going to have to smack as well. Trinket it all, all of them trinket it. Fill me now, fill me now. I didn't get line. I want to go down bro, don't worry. I saw the shame, I'm going down. I'm with you. I hope my pet follows me. Be a good pet, be a good pet. Can you explore me please? Yeah I don't, sorry. You will do my pet, you will do my pet. I lost the shuriky.  I'm coming, I'm coming, you're okay. I just trapped him here actually. Ported.  Shuriky in five, yeah. Lost is ended. I'm spreading. Maybe you're worth innovating. Do it later, I'm drinking. Ooh, we're going to have a bump either. We're not jumping. We're going to have tires now. You can stop the shuriky area. It's going to peek from one side. Just get or trap him Homer. I'm drinking here. Got your roots on me. I can't get you there. Nice. So get it. Watch out now. I'm not going to go there Homer. Watch out. Can you come through? He's spilling droid. Got any shadow on him? Watch out, do you have me? Yeah, yeah. Ooh, nice clone. I love it. He's done getting fit. Oh, sorry. I didn't have anything to stop it. Maybe you can innovate me here. I've got a frostbite over there. Cloned here a bit. I really care about that too much. Watch Shaman, you can fear him here. Yeah, okay. Yeah, yeah, I have to get the fear. Melting the fear. Get the ground up please. I'll clone the warlock here. Fear me for, carefully. You've got a grenade, it should be fine. Rossi bro. I jump, don't you? I can stop the re in here however. Okay, I'm pushing up to the lock then. Not anymore, not anymore, not anymore. Okay. Cloning on me. I'm going to refill it so I should be alright here. Okay. Which is running. I'm medallocated. It's a weird thing this morning, so I'll do that. I swear. I don't think he's around. We really need to resebrate him. You cannot say that man. I know. I'll get your dog. Go shame him. Get the warlock here. What's up with the warlock? Get the pet off this.  Do you see them now? I'm good.  He missed it, missed it.  How does he not shoot at you? Anyone there though? Yeah, you did, but we're all practically all stacked. Like he could have gotten free people then. Somehow he got one person and they were in debt. Okay. Alright. I don't see shame in no. Any full senders? Let's go shame him. Let's go shame him. When he pushes one more time, I'm opening. That's not my pet. You're seeing it actually. There's no shield so. I'm first for it. Purging. He drew it. Yeah. Spell. He's pretty good. Nice. Send, send, send. Both nocks gone. He turns. I'm going to him. Heming their starfall. All fine. Going under. More more pets. Shaman jumped down actually. Don't let the pet die. Yeah, it should be fine. Maybe you can read. I just want to wait for the last. That's not too much. I can go out and innovate though. I'll be there in a minute. Wait for the hour. Man is not too bad.  Huh? I have to go now. Sure we can. Want to scatter, scatter Shaman into MC? Can we do that? Yeah sure if we can. They don't stop it.  I'll incline mid. I'll iterate here. Recline wait. Yeah you can do it. We should go. Let's scatter the booby and go then. Touch the nock. I'll clone the booby now. Got it. Do I feed him now? I can clear off. I can reclone the booby. Got it. Just go through. Keep going, we have to keep going. Kill, kill, kill now. It's about as early as Mastery. Nice. I'll clone and put a shrink here. I'll play this as well. I think with full gear. The strat is going to work way better as well. The barrel has full gear. It seems legit.


Hello and welcome to lecture number 21 of this lecture series on turbo machinery aerodynamics. We have been discussing about turbines and in particular axial flow turbines in the last few lectures. And we have had a chance to discuss about quite a few things about axial turbines. We started off with the very basics of turbines in general which is basically to do with the thermodynamics of turbines. And after having a very detailed discussion on the thermodynamics of flow through turbines. We have also discussed about the types of turbines. And we have seen that there are basically three types of turbines possible. One is the axial flow turbine, the radial flow and the mixed flow turbines. And we have been talking about the axial flow turbines in the last couple of lectures. And in the last class we have discussed about the fact that there are basically two configurations of axial turbines which are possible. One is the impulse turbine and the other is the reaction turbine. And when I discussed about these two different types of turbines, I happen to mention that the reason why there are these distinct classes of turbines is the fact that the way stagnation or enthalpy drop takes place in a turbine is different in these two different types of turbines. Now, in a turbine stage, we know that turbine stage basically consists of a stator or a nozzle followed by a rotor. There is certain amount of pressure drop taking place in the nozzle and there could be certain amount of pressure drop taking place in the rotor as well. But there are certain types of turbines where the entire pressure drop or the enthalpy drop takes place only in the nozzle and the flow simply undergoes a turn as it passes through the rotor. So, these types of turbines are called impulse turbines. And there are also types of turbines where the pressure drop or enthalpy drop is split or shared by both the nozzle as well as the rotor. And these are known as reaction turbines. So, these are the two different or distinct types of turbines which we had talked about. In today's class, when we begin with, we will basically be talking about a parameter which can be used as a parameter to distinguish between these two types of turbines. So, that is one of the main things that we are going to discuss about. We will start the lecture with discussion on what is known as degree of reaction. After that, we will be talking about the losses encountered in turbine, what are the different forms of losses. And subsequently, we will also be talking about the efficiency or different forms of efficiency in a turbine. Now, when we talk about losses, there are well we have already had a very detailed discussion on well 2D as well as 3D losses in the context of axial compressors. It is the exact same concept which can be also used in a turbine. Therefore, I will not really go into the details of the different types of losses and how it can be estimated and so on because we have already talked about that in the case of compressors. We can simply extend that to turbines. And so, I would rather not repeat the same thing here. But I will of course, go through the essentials of losses in a turbine and also how it can be estimated in a very generic sense and without going into too much of details because they have already been covered in compressors. And then we will talk about efficiency and what are the different types of efficiencies in fact, in turbines you can have different forms of efficiency. There are at least 4 or more different types of efficiencies that can be defined for a turbine. But we will restrict our discussion to 2 forms of efficiencies which are more commonly used. One is known as the total to static efficiency and the other is known as the total to total efficiency. There are also static to static and there are other types of efficiency which are not really used commonly and so we will not discuss those in a great detail. So, let us start our discussion with degree of reaction and what we mean by degree of reaction and how it can be used in a turbine. Now, degree of reaction as you have seen in the case of compressors is a concept which is used to kind of understand how much amount of work sharing is done by the rotor as a comparison of the entire work done in a stage. And so in the context of a turbine here the flow basically undergoes acceleration as you already know by now that it is an accelerating flow in a turbine and acceleration takes place both in the nozzle as well as in the rotor. And therefore, as a consequence of that there is an enthalpy drop taking place both in rotor well in the nozzle as well as the rotor. Degree of reaction gives us some idea about well it is basically an indicator of the amount of enthalpy drop that is taking place in the rotor or in the rotor as a as compared to the enthalpy drop taking place across the entire stage. So, that is the basic significance of degree of reaction. So, but before we go into details of degree of reaction let us take a look at the typical velocity triangle which I had discussed in detail in the last class. Let me quickly recap what this velocity triangle means. This is a typical stage of an axial turbine which consists of a nozzle and a rotor. So, flow enters the nozzle at an absolute velocity of C 1 which is at an angle of alpha 1 leaves the nozzle at velocity of C 2 which is the absolute velocity and making an angle of alpha 2 with the axial direction V 2 is the relative velocity which makes an angle of beta 2 with the axial direction. And then flow from this enters into the rotor and leaves the rotor with the relative velocity of V 3 making an angle of beta 3 with the axial direction and C 3 which is the absolute velocity makes an angle of alpha 3 with the axial direction. The blade speed in both at the inlet as well as the exit of the rotor is assumed to be the same and equal to u. So, this is a very typical or a generic velocity triangle applicable to any axial flow turbine. And so our definition of degree of reaction is with reference to since it is with reference to a very generic axial turbine it can be used in the case of impulse turbines as well as for reaction turbines. And what we will see very soon is that impulse turbine is a special case of a 0 degree of reaction turbine that is when the degree of reaction is 0 then that turbine refers is basically an impulse turbine. So, as I had mentioned earlier degree of reaction is defined as static enthalpy drop in the rotor divided by stagnation enthalpy drop in the stage. So, if you look at the rotor these are stage it is between station 2 and 3. So, static enthalpy drop is h 2 minus h 3 divided by h 0 1 minus h 0 3 that is for the stage well of course, we can always say that h 0 1 is also equal to h 0 2 because in the stator there is no enthalpy change stagnation enthalpy change. Now, so if you look at a coordinate system which is fixed on the rotor or in the relative frame of reference the apparent stagnation enthalpy is basically a constant. And so we have h 2 minus h 3 is equal to b 3 square by 2 minus v 2 square by 2. So, if the axial velocity is assumed to be the same upstream and downstream of the rotor then this can be reduced to h 2 minus h 3 which is stagnation or static enthalpy drop in the rotor is one half of v w 3 square minus v w 2 square which is half of v w 3 minus v w 2 multiplied by v w 3 plus v w 2. We also know that the stagnation enthalpy change across a stage which is given by h 0 1 minus h 0 3 is basically a function of the blade speed and the change in the tangential component of the absolute velocity that is u times delta c w is basically the stagnation enthalpy drop. Therefore, h 0 1 minus h 0 3 is also equal to u times c w 2 minus c w 3. So, let us simplify the degree of reaction here. So, degree of reaction would become v w 3 minus v w 2 multiplied by v w 3 plus v w 2 divided by 2 u into c w 2 minus c w 3. Now, if you go back to the velocity triangle let us go back to the velocity triangle here if you look at the components or the difference between c w 3 and c w 2 that is basically equal to the difference between v w 2 and v w 3 that is in their tangential direction. Therefore, v w 3 minus v w 2 is basically c w 3 minus c w 2 and so, this degree of reaction will basically reduce to minus v w 3 plus v w 2 divided by 2 u. Now, from the velocity triangle you can also see that v w 3 which is the tangential component of relative velocity at the exit of the rotor is c a times tan beta 3. Similarly, v w 2 is c a tan alpha 2 minus u. So, degree of reaction basically reduces to half of 1 minus c a by u tan alpha 2 plus tan beta 3. So, this is one form of defining the degree of reaction that you can relate degree of reaction. We have seen this definition even for compressors and we have also seen that degree of reaction is a function of a few parameters. One of them of course, it is the ratio of axial velocity to the blade speed c a by u besides that there are the angles alpha 2 and beta 3 in this case. So, it is a function of the angles as well as the axial velocity and the blade speed. So, we can also simplify this in the sense that if you look at 0 degree of reaction and also look at 50 percent degree of reaction turbine, we will see what are these special cases of axial turbines where we can look at an impulse turbine and a 50 percent degree of reaction turbine. So, degree of reaction starting from the fundamentals it is basically ratio of static enthalpy drop in the rotor divided by stagnation enthalpy drop in the stage which we can simplify as we have seen and relate degree of reaction to the flow coefficient which is c a by u and the angles in this case it is the absolute angle at the inlet of the rotor and the relative angle or the blade angle at the exit of the rotor. So, it is tan alpha 2 plus tan beta 3. So, let us look at some special cases of the degree of reaction. Now, if you look at a symmetrical velocity triangle configuration where alpha 2 is equal to minus beta 3, what we will see is that we get the degree of reaction as 0.5. So, this is known as a 50 percent degree of reaction turbine, we have seen this in the previous lecture as well. Another special case is when V w 3 is equal to minus V w 2 then we get degree of reaction as 0 which is basically an impulse turbine. So, if we were to look at an impulse turbine little more carefully and compare that with the 50 percent stage. For a given stator outlet angle that is alpha 2 the impulse turbine stage requires a much higher axial velocity than the 50 percent reaction stage. In the impulse turbine it is generally seen that all the flow velocities are higher and therefore, it is generally also seen that the efficiency of an impulse turbine is usually lower than that of a 50 percent reaction stage for 2 turbines which are generating the same power. That is of course, a general observation that because of velocity components are higher the losses are likely to be higher and therefore, efficiency is usually slightly lower than that of a 50 percent reaction turbine stage. So, let us look at these 2 special cases. This is the impulse turbine stage we can see that the V w 3 or V w 2 will be equal to minus V w 3. If that is so then degree of reaction becomes 0 and such a turbine is an impulse turbine stage. So, we have V w 3 and V w 2 which are opposing each other and equal in magnitude. That is when we have degree of reaction as 0 and what is the physical implication of this in degree of reaction 0 it means that there is nothing much happening in the rotor as far as enthalpy drop is concerned. The rotor simply deflects the flow and there is no change in the enthalpy in the rotor and that is why degree of reaction is 0 because if there is no change in enthalpy in the rotor the numerator is 0 degree of reaction is 0. Now, if you look at a 50 percent reaction turbine stage then we have the angle it is a symmetrical velocity triangle and therefore, alpha 2 will be equal to beta 3. So, if those angles are equal in magnitude then you get velocity triangles which are symmetrical you can see that this is the velocity triangles are basically mirror images what you have at the inlet is mirrored at the exit. So, that is why you have a symmetrical or a mirror image velocity triangle if the reaction turbine is a 50 percent reaction stage and what it means is that the enthalpy drop is shared equally between the rotor and the stator and that is what a 50 percent reaction stage basically means. So, what we have defined in the last few minutes is this very important concept of degree of reaction where which basically tells us the amount of enthalpy drop which is shared between the rotor and the stator and how we can you know use that as a parameter to distinguish between these two types of turbines impulse turbine where you have degree of reaction as 0 which means that there is no enthalpy drop taking place in the rotor and we have seen that such a velocity triangle we have the tangential component of relative velocity V w 3 is equal to minus V w 2 they are equal in magnitude, but they are opposite in direction and that is why in the velocity triangle you can see that they will oppose each other when you take up their components. 50 percent reaction stage velocity triangles are symmetrical and you have alpha 2 is equal to minus beta 3. So, these angles are same making the velocity triangles symmetrical or mirror images across the rotor. So, now that we have discussed about degree of reaction let us move on to a very important aspect of performance of turbines that is the efficiency. I think I mentioned in the beginning of the lecture that efficiency in the case of turbine unlike in compressors we have in turbines defined in different ways basically depending upon the application for which the turbine is being used.  So, here the application is such that you would not want the turbine exhaust to have any very high levels of kinetic energy because that is getting wasted. So, you would like to use up as much kinetic energy as possible from the turbine itself without having to waste kinetic energy. So, here we would like to expand it to the minimum possible enthalpy static enthalpy and therefore, any kinetic energy that is there at the exit is considered a waste. So, in such turbines we usually define efficiency in the form of what is known as total to static enthalpy and the other form of enthalpy that we are going to define is known as total to total enthalpy which is what is of interest to aero engineers because in a gas turbine engine which is used in an aircraft for example, the there is enough kinetic energy available at the turbine exhaust which can be again expanded or further expanded through a nozzle to generate thrust and you would not want the turbine exhaust to get or turbine to exhaust itself to the minimum possible kinetic energy because you would also like to expand the flow further in a nozzle to generate thrust. So, in such applications you one would prefer to define efficiency based on total to total or stagnation enthalpy. So, these are the two commonly used forms of efficiencies as I mentioned there are also other forms of efficiencies which are not very commonly used like static to static and so on. We will restrict our discussion to these two types of efficiencies total to static and total to total efficiencies. Now, so some general comments which I had meant let me just list them down here. So, the aerodynamic losses in a turbine as we have seen differ with stage configuration or the degree of reaction and so improved efficiency is associated with a higher amount or level of reaction which implies less work per stage and therefore, higher number of stages for a given overall pressure ratio. So, the reason why we need to understand efficiency or the sources of losses is that it firstly helps us in making a choice between different configurations either impulse or a reaction, but the other advantage is that it will also tell us how one can control these different forms of losses. So, based on our understanding we can define two types of efficiencies total to static efficiency and the total to total efficiency and which efficiency definition to use will basically be determined by the application for which the turbine is being used. So, in let us say the land based power plant as I mentioned the turbine output is basically in the form of shaft power that is the turbine is connected to a generator which generates work out electricity and therefore, exhaust kinetic energy is basically considered as a loss. Therefore, in such a case the ideal turbine process would be isentropic such that there is no exhaust kinetic energy that is the exhaust itself is static and there is no kinetic energy associated with that exhaust and that is where we would define what is known as total to static efficiency. In aero engines the turbine exhaust is required to have certain amount of energy which will further be expanded in a nozzle to generate thrust. So, there you would not want to expand the turbine to such a level that it is static at the exit and then with very little kinetic energy, but you would like that some more kinetic energy left which can be expanded further in a nozzle. So, there we would normally define the total to total efficiency in such applications. So, let us take a look at a general turbine process or expansion through a turbine and then we will come up with the efficiency definitions. So, this is an expansion process in a turbine stage well where station one is the nozzle entry, two is nozzle exit and three is the rotor exit. So, two is also the rotor inlet. So, the flow initially has pressure at the inlet stagnation pressure at p 0 1 and static pressure at the entry is p 1.  So, we have flotted this on a temperature entropy scale. Now, if this entire process were to be isentropic then the expansion takes place along these dotted lines. So, p 0 1 all the way up to the exit which is 3 s if it were if you are considering a static condition at the exit and. So, the actual turbine process of course, is defined by this solid line the bolt line here between static pressure p 1 static pressure p 2 at the nozzle exit or rotor entry and p 3 at the rotor exit. The corresponding stagnation pressure at the rotor exit is p 0 3 which is basically what you have the temperature at station 3 plus the dynamic head c 3 square by 2 c p will give us the stagnation temperature there. Now, the corresponding conditions in the isentropic case would be t 0 3 subscript s or at the rotor exit which is the stagnation. And so, when we are defining efficiency in two different ways that we are going to discuss about. Let us first take up the total to static efficiency. Now, in this case we are talking about an ideal turbine work with no exhaust kinetic energy which means that we have expanded all the way up to the station which is given by this particular state. So, from 0 1 all the way up to the station and which means there is no more kinetic energy at the exit of the turbine. So, we have the ideal turbine work in this case would be c p times t 0 1 minus t 3 s. So, the total to static efficiency in this case is defined as the it is denoted by symbol eta t s which is total to static t 0 1 minus t 0 3 divided by t 0 1 minus t 3 s that is t 0 1 minus the temperature corresponding to this t 0 3 divided by t 0 1 minus t 3 s. So, that is the total to static efficiency. The denominator we are going to simplify because this is an isentropic temperature here. So, this can be expressed in terms of the corresponding pressure ratios. And so, we have t 0 1 minus t 0 3 at the numerator divided by t 0 1 into 1 minus p 3 by p 0 1 raise to gamma minus 1 by gamma this follows from the isentropic relation. So, this is basically 1 minus t 0 1 by t 0 3 divided by 1 minus p 3 by p 0 1 raise to gamma minus 1 by gamma. So, this is the basic definition of total to static efficiency. Now, if you look at applications typical application being turbojet engines where the exhaust kinetic energy is not really a loss it can be converted to thrust using a nozzle. So, in such cases the ideal turbine work is not equal to the static conditions at the exit, but this stagnation conditions. So, the ideal work in such cases would be C p times t 0 1 minus t 0 3 s. And therefore, we define total to total efficiency which is eta t t that is t 0 1 minus t 0 3 divided by t 0 1 minus t 0 3 s. And again the denominator we will express in terms of pressure ratios because that is isentropic. We have 1 minus t 0 3 by t 0 1 divided by 1 minus p 0 3 by p 0 1 raise to gamma minus 1 by gamma. So, we have defined two forms of efficiencies the total to static efficiency and the total to total efficiency. We can also now relate these two types of efficiencies and see how these efficiencies can be compared for the same type of or for the same configuration. If you were to compare these two different forms of efficiency of course, with certain assumptions we can still compare total to static efficiency and total to total efficiency. And we will also see how using these efficiencies we can calculate work done by a given turbine. So, if you are to make an approximation that t 0 3 s minus t 3 s is approximately equal to t 0 3 s minus t 3 is equal to c 3 square by 2 C p which is let me go back to the diagram here. So, what we are saying is the difference between t 0 3 s minus t 3 s and this and the t 3 s is c 3 square by 2 C p. So, which means that effectively t 0 3 s and t 3 they are not much different as you can see from this t s diagram itself. So, it is a very much a valid assumption that we can make. And so, if this were to be the case if you make this assumption then we can relate total to total efficiency as equal to eta t s divided by 1 minus c 3 square multiplied by 2 C p t 0 1 minus t 3 s. So, what you can see here is that if this assumption were to be true and you calculate the total to total efficiency and total to static efficiency for a turbine. We could see that the total to total efficiency is likely to be greater than the total to static efficiency which is also obvious from the t s diagram that I had shown. If you look at the expansion process for the same turbine if you calculate both these efficiencies the total to total efficiency is likely to be higher than the total to static efficiency. Now, so using these definitions one can also calculate or make use of these definitions to calculate the corresponding work done by the turbine depending upon the application itself. So, if you were to use the total to total efficiency then we have the work done or specific work done as in the case where let us say in an application of a gas turbine engine used in an aero aircraft engine like in a turbo jet. Then the work done by the turbine is related to the efficiency which is total to total efficiency multiplied by C p into t 0 1 into 1 minus p 0 3 by p 0 1 raise to gamma minus 1 by gamma. And similarly the work specific work related to the total to static efficiency as eta t s into C p t 0 1 1 minus p 3 divided by p 0 1 raise to gamma minus 1 by gamma. So, using the efficiency definitions and the specific application for which these efficiencies have been defined for we can use these efficiencies to calculate the corresponding work done by the turbine under these are different applications. So, let me give you one example to just indicate the effect of reaction. I think I mentioned when I was talking about impulse and reaction turbines that both these turbines in the last class as well I mentioned that there is a difference in the specific work done and loading that both of these different types of turbines can handle. And also the fact that there is a certain difference in the efficiencies that one would get by using these two different configurations of turbines. So, let us take a look at the influence of loading on the efficiency we will in this case calculate total to static efficiency. So, you have reaction on the x axis the efficiency total to static efficiency on the y axis and three different values of loading. So, one can see that as you increase the loading and keep changing the reaction what happens to the efficiency. So, let us take a look at one of these cases let us say loading factor is equal to 1. So, as you change the reaction on the extreme right we have an impulse turbine which has a reaction of 0. So, as we start from an extreme which is an impulse turbine and we move towards let us say 50 percent reaction case. You can see that there is a steady increase in the efficiency and after that of course, there is a drop in the efficiency. This is for loading factor is equal to 1. Now, if you look at a loading factor greater than 1 that is say loading factor of 2 or 3 then the trends are slightly different. In fact, you get the highest efficiency when the reaction is equal to 0 that is for an impulse turbine stage that is with higher amounts of loading your impulse turbine stage has a better efficiency than any other case of reaction. Because the moment you have any amount of reaction it is no longer an impulse it it basically becomes a reaction turbine and that is also true for higher values of loading between 2 and 3 and so on. And so, this is just to give some idea about what happens as we change the amount of loading with increased levels of loading how does reaction influence the efficiency. This is also linked to a comment I had made earlier I would want you to think about why is it that as you increase the loading an impulse turbine seems to at least perform better in terms of efficiency. And what is the effect of increasing loading on let us say the efficiency of the turbine as you keep changing the level of reaction from impulse which has 0 reaction. Let us say to 50 percent reaction where the reaction is the enthalpy drop is equally shared by the nozzle and the rotor. So, just give it a thought on why there should be a drop in efficiency as you move from impulse towards higher levels of reaction. So, let us move on to the next topic we have for discussion in today's class that is to do with losses in a turbine. I mentioned in the beginning that I will restrict the discussion to just the basics of losses because I have already had a detailed discussion on losses when we are talking about compressors. And so, most of the concepts we had discussed there is applicable for the turbine as well. Of course, the magnitude of losses will be quite different for compressors and turbines, but the concept is still the same. So, I will not repeat the estimation of losses that we had discussed in detail with reference to a compressor because it is also applicable for a turbine. Now, when I had discussed about compressors and losses in a compressor I had mentioned that there are distinct forms of losses there are basically we could classify losses as 4 sets of losses. One is on account of viscous effects are known as the viscous losses. Then there are 3 dimensional effects like triplicate flows and secondary flows. One may have shock losses and also mixing losses. And so, if you were to isolate these losses if because if you have to estimate losses in a turbine and one would like to target let us say different forms of these losses and see if we can minimize these losses. One would need to know let us say what is the contribution of viscous loss, what is the contribution of 3D losses like secondary flows or triplicate flows and so on. But it is not very easy to segregate these different losses. There are empirical correlations for estimating all these different forms of losses. We had discussed some of them in the context of compressors. One could extend the same for turbines as well. Total losses in a turbine obviously is some total of all these different forms of losses whether it is viscous loss or 3D losses which includes secondary flows and triplicate flows, shock losses and the mixing losses. So, let us look at these losses in little more detail, but not too much as I had mentioned. Just some preliminary discussion on these losses. If you look at viscous losses there are again different components of viscous losses. There is one on account of the profile or the nature of the airfoil cross section and that is known as the profile loss. Annual loss loss would refer to growth of boundary layer along the axis and end wall losses on account of boundary layer effects in the corner or junction between the blade surface and the casing or hub. Now, in 3D effects we have secondary flows which is on account of flow through curved blade passages, triplicate flows which is basically the flow leaking from the pressure surface to the suction surface. And what is generally observed is that if you look at the 3D effects the losses are likely to be higher for a turbine primarily because of the fact that the flow turning is much higher in a turbine as compared to a compressor. Secondary flows for example, is directly related to the amount of flow turning and if you compare a compressor with that of a turbine the flow turning in a typical turbine blade is much higher than that of a compressor. Secondary flows are likely to be much higher in the case of turbine. This is also true for the tip leakage flows basically because tip leakage is on account of the difference between the pressure surface and the suction surface and blade loading is usually much higher in a turbine than in a compressor. And therefore, leakage flows are also likely to be higher in a turbine. And what complicates the matter in a turbine is the fact that you also have a higher temperature and it is no longer just pure air you also have a combustion product coming in from the combustion chamber which might complicate the flow behavior in the case of a turbine. Now, let me just give you one example of profile loss I will as I mentioned I will not go into details of estimating all these losses we have done that for the compressor and you could easily extend that to the turbine as well. Now, if you look at let us say the profile loss and look at what happens as you keep changing the incidence. Now, I have these profile loss distribution for two distinct cases the impulse turbine and the reaction turbine. The solid line refers to the impulse turbine and the dotted line is for the reaction turbine. So, one can see that there is a significant difference between what happens in an impulse turbine and reaction turbine the losses as you can see are much higher for an impulse turbine case and that varies significantly with the incidence. So, the sensitivity of impulse blades to incidence is much higher especially a positive incidence you can see that after around 8 or 9 degrees the losses increase substantially. There is a very sharp increase in losses that positive incidence around 8 or 9 degrees. Of course, this is for a very typical case of a turbine blade. On the other hand if you look at a reaction blade it is probably little better adjusted to higher changes in incidence of course with very high incidence exceeding 20 degrees there is of course, a very steep increase in the losses even in a reaction stage. But, if you look at the performance of a typical reaction blade it is not very sensitive to incidence between let us say plus minus 10 degrees. Whereas, an impulse blade is quite sensitive to incidence and especially at positive incidence angles. We also have alpha 2 plotted for both these cases what we can see is that alpha 2 remains more or less well behaved whether it is impulse or reaction turbine even though the incidence is different. The basic reason for this being true is the fact that in both impulse as well as reaction blades the flow is encountering an accelerating flow I mean a favorable pressure gradient. So, even if there is a higher level of incidence of the flow entering the nozzle because it is an accelerating flow the flow is generally well behaved which is unlike in a compressor where the flow encounters an adverse pressure gradient. So, the outflow would be extremely sensitive to the incidence angle as well that is if the incidence varies between a beyond a certain range the outflow angle also correspondingly changes drastically because of the fact that it the flow is encountering an adverse pressure gradient and. So, the chances of flow separation is substantially higher in the case of a compressor which is not true for a turbine where the flow is almost always encountering a favorable pressure gradient. And therefore, that partly explains why the gas outflow angle alpha 2 really does not change much and the insensitivity of outflow angle is larger much larger for a turbine as compared to that of a compressor. Now, if you now we come back to the types of losses in a turbine if you recall when we discussed about losses in a compressor we had classified them into two distinct sets of losses one is to do with 2 D losses and one is to do the 3 D effects like secondary flows and so on. Now, if you look at just the two dimensional losses for which there are lot of empirical correlations available 2 D losses basically are relevant to axial flow turbo machines and we have seen that in a compressor as well that when we were discussing about axial compressors that if you look at 2 D losses they are mainly associated with the blade boundary layers shock boundary layer interaction separated flows and wakes some of these of course are not really that significant for a turbine for example, the separation or blade boundary layers which are fairly well behaved in the case of turbines and separation on the other hand in certain operating conditions one might have a leading edge separation bubble in the rotor. But that is the chances of such occurrences are very rare unlike in the case of compressors where boundary layer behavior is always a concern because of adverse pressure gradients. So, mixing of these wakes that come from the rotor blade with the nozzle downstream of the second next stage obviously, creates a certain amount of losses and that is of course something that can be estimated by mixing loss models which are available from which one can estimate to a certain amount of accuracy what is the effect of these wakes shed from the rotor on subsequent stages. So, if you look at 2 D losses in particular we can classify 2 dimensional losses into different forms we have profile loss due to the boundary layer and its effect and whether you have laminar or boundary layer separation which is of course rather rare in the case of turbines one may have wake mixing losses because of the wake from the rotor interacting with the subsequent stages. One may also have shock losses which I will also discuss in little more detail in a later slide and of course the trailing edge loss due to the blade because trailing edge is usually rounded as we have seen in compressors one may have to provide a certain rounding at the trailing edge and there is certain amount of loss associated with that rounding as well. So, the total loss in a turbine like in the case of compressor is obviously, a sum total of all these different components. So, without going into details of how to estimate these losses we can just summarize that the overall losses in a turbine is a sum total of all these different forms of losses one may have profile loss on account of the nature of the blade surface itself one may have shock losses and secondary flow losses which can be quite significant in turbines triplicate loss and of course, end wall losses. So, if you make a comparison of this with a compressor let us say a transonic compressor where also you may have shock losses. The major distinguishing factor between turbine and the compressor in terms of losses would be the 3 D effects which are likely to be much more significant in a turbine like secondary flows and triplicate flows as compared to a compressor where of course, these losses are still present, but if you were to make a one to one comparison the losses in the case of turbine when it comes to secondary flows and triplicate flows are likely to be higher. But of course, there are methods of controlling some of these in a turbine because many of the turbine blades also have cooling mechanisms which again we will discuss in detail in later lectures. So, some of these cooling holes are also sometimes used to minimize let us say the triplicate flows or secondary flows in some way or the other we will discuss that in some of our later lectures. Now, there is another aspect I wanted to have some discussion on that is to do with deviation and I will probably spend a couple of slides on this aspect as well. Now, this is also true with in the case of compressors and that it is a known fact that the flow exiting the rotor does not really leave the blade at the angle for which it has been designed for. But it of course, in the case of turbines it is easier to estimate the outflow angle because the flow is encountering an accelerating flow passage and if the flow is not basically choked or if there are no shocks present at the exit of the rotor then it is at the exit of the nozzle it is relatively easier to estimate the amount of the outflow gas outflow angle from the nozzle. But of course, if there are shocks present that something which I will show you little later then the outflow angle can be quite different from what it has been basically designed for. So, what is basically found from experience is that the actual exit angle at the design pressure issue can be fairly well estimated by cos inverse of d by s as long as the nozzle is not choked. So, let me just explain what I mean by cos inverse of d by s. So, if you look at a typical nozzle exit flow when I had shown a picture of the cascade I had mentioned that this is basically the throat of the nozzle and the flow exits the nozzle at an angle of alpha 2. So, if you look at the pitch at the trailing edge which we have denoted by s and this is the throat and which is denoted by d then one can estimate the outflow angle the gas outflow angle alpha 2 as what is shown here that is cos inverse of d by s. That is if you take an inverse of of course, this is still an approximation, but it is found that it is fairly well the approximation fairly well captures the angle at which the flow exits the nozzle. Now, this is true as long as the nozzle is not choked because once it choked once their nozzle is operating under choked condition then there is a possibility that the outflow is supersonic which means that there is a possibility of the presence of shocks at the exit or the trailing edge of the nozzle presence of shocks can deflect the flow and cause a certain amount of deviation and in such cases of course, one cannot really estimate the angle exiting the nozzle as just cos inverse d by s. So, if you look at a case where there is the flow is not choked it is un choked then there is obviously, there is no the flow is not supersonic at the exit of the nozzle and which means that the flow angle can be basically well estimated by just taking the inverse of d by s. Now, if you look at the other case where there is a possibility of shock in which case it is basically choked flow after the throat because it is if you let me take you back here after the throat we might have an expansion here which might cause the flow to become supersonic. If the back pressure is low enough then you may have it basically acts like a converging diverging nozzle and one may have shocks emanating from downstream of the throat. If there is a trailing edge shock exiting at the flow exiting the nozzle then the presence of these shocks obviously, can deflect the flow to a different angle. So, as you can see here the flow is not really exiting at an angle that it was designed for the presence of these shocks there is a trailing edge shock or a reattachment shock and so on. The presence of these series of shocks can cause the flow to get deflected or deviated at an angle which is quite different from what it has been designed for. So, in such cases as what you see here the angle alpha 2 is not well established or estimated by simply taking a d by cos inverse of d by s. Of course, there are also a empirical correlations in this case to estimate the flow angle because if you know the shock structure of the flow leaving the nozzle from the analysis of the flow through these different shocks one can sort of estimate what is the angle at which the flow is leaving the nozzle. But that requires a much more complicated analysis than simply taking considering just the geometric parameters and estimating the exit flow angle to be a function of these geometric parameters. So, in the presence of supersonic flow where there are shocks present the flow structure is obviously, more complicated and the flow undergoes deviation which is more quite different from what one can otherwise easily estimate. So, I just brought up this aspect of deviation because of the fact that in nozzle flow there is a possibility that the flow exiting the nozzle can be supersonic and therefore, the flow might undergo deviation which is quite different from what it has been primarily designed for which means that this flow entering into the rotor basically has a different angle than what it has been designed for and therefore, one needs to consider take this aspect into account when estimating the flow through the entire stage. So, let me now quickly recap our discussion in today's class we had discussion on three distinct topics. We started off with degree of reaction and I spent some time discussing about degree of reaction its significance and how one can estimate degree of reaction and based on this estimation how one can determine the configuration of the turbine whether it is impulse or reaction and so on. We then spend some time discussing about losses the different types of losses the 2 D losses and the 3 D losses and I mentioned that there are certain aspects of losses which are the contribution of these different sources of losses is different in the case of turbine and a compressor because of the very nature of flow passing through a turbine or a compressor. We also discussed about the efficiencies and the different definitions of efficiency the total to static efficiency and total to total efficiency which is what we discussed in detail today. And of course, towards the end I also discussed about the aspect of deviation which is of significance especially when the flow is unchoked and well especially when the flow is choked and the flow exiting the nozzle is supersonic. We will continue our discussion on axial flow turbines in the next lecture. We will basically be talking about the performance characteristics of an axial flow turbine and how one can match the exit flow from a turbine with a downstream component like a nozzle. So, these are 2 aspects that we will be discussing in the next lecture which will be lecture number 22.


Number SCP-1365 Object Class Safe Special Containment Procedures SCP-1365 has been kept in its containment chamber at Site-73. A mock-up bike rack created for containment purposes has been proven sufficient in neutralizing SCP-1365's teleportation abilities. In order to ensure it does not breach containment, no bike racks or other structures designed for temporary bike storage are to be constructed within a 100 meter radius of SCP-1365's containment chamber. Testing requires the approval of a Level-3 Administrator and is only to be carried out by D-Class. During approved testing, medical staff must be on call in the event that test subjects are advised to encounter with SCP-1365. Description SCP-1365 is a 2007 ████████████ brand bicycle, serial number ██████████ SCP-1365 is unremarkable in appearance, aside from being in excellent condition and bearing a small sticker reading Bike Justice attached to its main body. Whenever a human attempts to mount SCP-1365 and ride it for a distance greater than 20 meters, SCP-1365 enters its active state. Subjects will find themselves unable to control their leg or arms, with both being used to steer and power SCP-1365 without any direction or guidance from the subject. After 10 minutes or 500 meters of travel, whichever is sooner, SCP-1365 will forcibly dislodge the subject, either via crashing into an inert object or simply throwing the subject off. In 90% of cases the force used by SCP-1365 is sufficient to kill or fatally wound the subject upon impact, with the remaining 10% of subjects usually suffering a permanent disability impeding motor functions, such as paralysis. Three to four hours after the death or incapacitation of the subject, SCP-1365 will vanish from its current location and reappear at the nearest location designed for the temporary storage of bikes in public places. Through unknown means, any damage sustained during the previous activation event will be repaired and any evidence of previous use, such as blood stains from a previously killed subject, will be removed. Separating sections of the bike and putting them in different locations results in all separated pieces reforming at the storage location within the allotted time. In all cases, SCP-1365 has never been accompanied by a bike lock or similar anti-death device. While SCP-1365 displays no compulsive or memetic properties encouraging subjects to use it, it is nonetheless frequently activated and left uncontained, likely due to its pristine condition and the lack of anti-death measures normally taken to protect the bike. Addendum After an activation event on the 22nd of July 2020, a note was found attached to the body of D-34242, the deceased's test subject. The note was of the same composition as the bike justice sticker on SCP-1365 and was considerably difficult to remove.  Now is the time to strike. We can beat them if we try. Bike Justice