K-7 returns. Number one adventurer, K-7, form a United States secret agent who operated in 22 countries on land on sea and in the air, brings you a story of today. We take you to secret agent K-7's headquarters. This is K-7 speaking. Send in agent M for assignment. That's one K-7. Special agent M reporting for duty. Agent M, somewhere in Paris, there is a stationary agent who must be found. We know that this man is not an ordinary spy, but that is about all we do know of him. Information is brought to him, and when the time comes, he passes it on. Several operatives have worked on the case, but all have failed. These records contain the known facts. You won't find much to help you. Keep me informed. Agent M spent the following days casting a bot for a lead. In the meantime, Yvonne was inactive. She visited the Paris fashion center replenishing her wardrobe. It was early evening, 10 days after agent M started his investigation, when Yvonne waited for him outside a small sidewalk café. Near her stood a blind man. M is late. It isn't like him. Good evening, Monsieur de Blandman. Thank you, Monsieur. I wonder if I have a coin for him. Yes, here's one. Here you are, Monsieur. Thank you, mademoiselle. You're an American. Well, how did you know that? Your voice. It isn't often I hear my own language here. The tourists don't often come to this neighborhood. Oh, and you're an American too. Yes, mademoiselle. But why are you here in Paris? I've been here since the war. I enlisted in the Canadian forces. After the war, I stayed.  The war? Yes, mademoiselle. Oh, I'm sorry. Oh, no, no.  I'm happy. Often the urge to go home strong, but since I can't, I'm content to stay here and serve. What do you mean? I still serve my countrymen, mademoiselle. Don't ask me how. I can't tell you. But I still serve. What's your name? I am known to everyone here as Monsieur de Blandman. Yvonne. Oh, my friend has come for me. Good night, Monsieur de Blandman. Good night. I didn't see you come up in. Let's sit at this little table here. Oh, I suppose we might as well. Did anything happen today? Nothing, Yvonne. K7 told me that several operatives had failed on this case. It looks as if I am going to fail too. I can't find a lead. You're tired, M. Let's call the waiter an order. You'll feel better after a good dinner. If I could only find a starting point. I've never failed on an assignment before, Yvonne. If this one flaws me, I think I'd resign. M, you've done some wonderful work. You mustn't be so easily discouraged. That blind man out there has the right idea. M, I was just talking to him. He's an American. He served in the Canadian forces. There must be some answer. And he's been in Paris ever since.  He still serves his country? So he said, but he wouldn't tell me how. I don't understand what he would. What's the matter, M? Yvonne, listen. That's code. The blind man's tapping out a message with his cane. Is the car at the curb? Yes. And now that the message has been tapped out, it's pulling away. Yvonne, stay here. I'm going to try and follow that car. And the car disappeared before Agent M could find a cab. However, M was convinced they'd made a beginning. He and Yvonne took turns sitting at the sidewalk table near the blind man. Four days later, while Yvonne was on duty, the same car stopped at the curb. A man stepped out. Has the mail arrived? Yes, Monsieur. Tap it out. Don't try to step into your car. Who are you? What do you mean by pointing a gun at me? I want you to answer some questions. And what if I refuse? Like this. Now you'll do as I say. Get in the car. Get in, I said. Don't. Within a few hours, Agent M realized that something had happened to Yvonne. He immediately took Monsieur the blind man into custody and questioned him. My assistant has disappeared. You must have heard something. I have no information for you. You mean you refuse to tell me what you know? I must refuse. Perhaps you prefer a military trial. The firing squad is the penalty a spy pays in this country. If I must die for my country, I'm ready. I gave my eyes during the Great War. If now I must sacrifice my life, but you're not serving your country, you're serving the state that's trying to overthrow world peace. You're serving the war makers. What do you mean? I serve America. They told me. Monsieur the blind man, I think I understand this whole plot now. You've been tricked. You're not working with American agents. You're working for an aggressor state. You've been tricked. Used by spies you cannot see. There's a ring of truth in your voice. If I was sure you spoke the truth. What is your name? Your real name? Mario Tejans. Mr. Tejans, listen to me. I am willing to go with you to the prefect of police or to the secret service, if you prefer. Have my credentials examined. You cannot see me. But in that way, you can convince yourself that I am who I claim to be. You're willing to go to the police? Right now, my assistant, Mr. Rel, has been seized by enemy agents.  You've got to help me. Enemy agents? I wondered why they spoke my language with an accent. I will help you. I thought I served America. If I've been mistaken, I... I tricked you because you were blind. Did you hear Mr. Rel seized? Yes. She was arresting the man who was listening to my message. He knocked the gun out of her hand and he took her away in his car. Have you any idea where she might have been taken? No, no, I... I'm afraid I can't tell you that. I don't know. Wait. Tomorrow, he'll return. What do you mean? Your assistant interrupted as I was tapping out my message. Tomorrow, the man who seized her will come again because he must have the information. I only hope tomorrow won't be too late. The next afternoon, the spy who seized Yvonne approached Mr. the blind man on foot. When he thought no one was listening, he again asked the question which identified him. Has the man arrived? Yes. Tap it out. Quickly. Wait. Are you all right? Of course. What about the girl? She's being held prisoner in my rooms.  He will know what to do with her. Here. The address is written on this slip of paper.  That will be a pleasure. But the girl is safe. Of course she's safe. What is it to you? Oh, nothing. Nothing at all. Then tap out the message. I can't stand here all day. What up your hands? Who are you? Special Agent M. You're under arrest.  Did you find out where Ivan is, Mr. Titans? Yes. She's at the address on this piece of paper. Good. That is a trap. Yes.  I found that you're lied. Agent M, I've just been told that not only is your assistant at that address, but tonight the head of this firing comes there. He also can be arrested. You'll never arrest me. Oh! What has happened? He tried to get away, Mr. LeBlainman. I had to kill him. Now we'll go and get Ivan. This is a reward. A grateful republic is sending him back to his homeland. Ivan and I will report to you and... Mr. LeBlainman was a stationary agent. This type of spy is the most numerous of all and appears in many guises to cloak their illicit activities. Stories of other types of agents and spies will be told in the future. Listen for my next story. This is K7 Speaking.


Hi you guys, welcome back to another post for January. All month long I am showing you all the fun and cool things that you can do with denim, whether it be upcycled or recycled or even brand new. Today I'm gonna be showing you how to take a thrifted denim jacket or vest and turn it into this really cute quilted and denim combo. The quilted portion that I used for my version was actually a pillow sham. So don't feel like you need to find an entire quilt to make this. You just need a very little bit for the pieces here. So without further ado, let me show you how to put this little thing together. Okay, our first step is gonna be to cut apart our jacket because we're gonna end up using the pieces we cut away as our pattern pieces for the quilted fabric. So I cut off the lower bodice. Like I left on the yoke and I left on this little flap for the pocket. I'm not gonna do another pocket, I don't think. But I thought it'd be a cute detail if this still flapped down. So I cut around that and you can see I just cut just along the stitching line that they have there. And then for like the button band area I did cut it away but I left myself a little bit of seam allowance so that whenever I go to attach the quilted portion I have a little bit of room to work with there. So I left a little seam allowance here. I couldn't do it here because of the flap but I also wouldn't have been able to do it really if I wasn't keeping the flap because of the flat-filled seam. So don't worry about it up here. There's another tricky way. If there's a flat-filled seam here there's another tricky way for you to get the quilted fabric attached. So once you get both of your bodices the fronts removed, you're gonna do the same thing to the back picture the middle piece here. I ended up using that for another portion of the code I'll tell you about in a second but just cut the back off below the yoke again again leaving myself a bit of a seam allowance. This one's a little bit larger.  So you can see I did that here. They would have been right sides together so it went something like this. And again I gave myself a little bit of wiggle room all the way around just to ensure I'd have some seam allowance if I needed it.  Same thing for the other side and then here is the back as you can see it's all one piece cut from these two with the center still attached. I shouldn't have cut that off before I started the video but I was getting cutting happy. Okay, so we've got our back piece we've got our two front pieces and then we've got our like the frame of our jacket. Next, and this is what I used the center of the back for I had to cut these strips because this is a sleeveless, this is the best, a sleeveless coat, it's the best. I cut the sleeves off a long time ago this became a different recycle project. Either way I need to finish my seam allowances here. If you are going to keep the sleeves and you wanna use those out of the quilted fabric too by all means cut off your sleeves cut up like the underarm portion of the sleeve and then use that as your pattern piece for your sleeve because I'm keeping mine the best I need to finish off the raw edge here so that whenever these two things get lined up like this I will have this part finished with the same denim that came from the jacket so it'll look like that nice and pretty. Okay, so how do you reassemble this? So again, we're gonna finish this with bias tape, right? We're gonna use this as bias tape we're gonna finish off this arm side so that will be nice and finished. Once that is done you are going to turn the jacket like so. And again, this is the top yoke, right? This is the back yoke, this is the front yoke. So this goes here like this. So we need to fit this back into its original form. So the best way to do that is if you have something that had a flat felt seam or anything similar you should have this kind of little seam allowance here. They finished this one with some bias binding themselves. So I'm gonna use that as the part where I sew it onto. And again, remember, this is all finished. So yeah, like that. And it's a little bit thick. So I was using wonder clips, that's what those are called for that to hold that in place. And I'll just take my zipper foot on my sewing machine and stitch very, very closely to this line as best I can. It might be a little bit tricky to get into the corner, but once I do that, I'm gonna turn. So then these raw edges get matched up as well. So right sides together, I've got my little seam allowance from the jacket. And this can get pinned in pretty easily.  Kind of like stitching in the ditch. Once you get that done, this is what your jacket should look like. Okay, so you're gonna do that for the left and the right side, okay?  So it's just gonna go right sides together, right sides together, matching your centers and matching the arm size. And you're just gonna sew this all the way down following this little seam here. So now at this point, you have one of these numbers where you have your front and your back.  And then you will have like basically your vest is all put back together again. I just need to figure out the hem. Here's the original waistband. So I could definitely sew that back on. That would be really, really cute. Just so it looks like this is fully in set. I think that's probably the best plan. Okay, here I'm just showing you how I was able to finish off the center front of the waistband. I turned the waistband up and then turned the raw edges to the wrong side and then just stitched along the hem where the quilted part and the waistband come together. And then you turn that back right side out and it makes a really clean finish. All right, and there you have it. It really couldn't be more simple than that. Here is a peak C at the inside, really nothing fancy. I didn't end up running my raw edges through the serger so that helped a little bit. But I think she's really so, so, so cute. If you wanted to take this a step further and add some pockets, you could absolutely do kind of like a kangaroo pocket that would be really cute or a patch pocket or anything like that. But mine's a vest. So I don't imagine I'm gonna be wearing it when it's super, super cold outside anyway. So I'm gonna skip the pocket part. But I just adore how she turned out and I love maybe more than anything that I was able to get this done with a sham, with a pillowcase. You just never know how much fabric you're really gonna get when you start pulling those things apart. This was one sham and one denim jacket. So all in less than $10 on this cutie, cutie little project. Let me know if you give this a go. If you have any questions about anything, let me know that as well. You can leave your thoughts and comments and questions all in the comment section below. But that is gonna do it for me today. I will be back with another fun project featuring denim really soon. See you guys then. Bye.


Now, the Chairman, House Committee on Science, Technology and Innovation, Benny La, has charged the energy sector on the need to explore the vast opportunity and renewable energy to better the lots of Nigerians. Unable La gave the charge during the 2022 budget defense session of the Energy Commission and six other research centers under it. Emanuel Ehidjian's report is also presented from our studios. The Chairman of the Committee, Emanuel Ben-Elah, said there will be two opportunities in the renewable energy sector will boost energy generation in the country, as well as further develop skills and improve minds and livelihood of Nigerians. He charged the Energy Commission to explore the renewable energy sector as an area to improve energy efficiency. Nigeria can no longer afford to shelf its expertise that can empower and be beneficial to our teeny-hute, unemployed populace. The Director-General of the Energy Commission, Benjamin Professor Ehidjian, while presenting a total sum of 9.7 billionaires as the budget for the agency for the 2022 fiscal year, said the Commission is looking at alternative sources to improve energy supply for the country. We will also post the annual Science and Technology Expo held by the Federal Ministry of Science and Technology, which we protect. We will have the National Energy Summit next year at a forum where we have a stakeholder to discuss issues. Members of the Committee have objected to the lamping of the 2022 budget of the agency together with the six research centers stating that it will affect the performance of the centers. The centers seems to have been lumped together with the agency's headquarters. This has not been the practice. Usually every center you have your super-energy refresh center, you have legal, there are many defense centers. The lamping together of the budgets for all the centers, but I'm sure I think it is very disingenuous. If as a parliament we allow it to stand, it smacks the service to the country, Nigeria. And we have the powers to actually make this proposal, this deal become an act. Members advised the Commission to engage more in environmental friendly projects that will impact on the country to encourage other African countries to tap in. The Committee will meet the National Food Science and Technology in its next sitting. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


First, I will introduce about the background. China is a very big country with extremely different climate and geographic conditions. For example, the elevation range from below zero to over 8,000 meters. It's also a country with different climates, including tropical regions and cold regions, and the humid area and the dry area. And also it's a country with different kinds of ecosystems, basically covering all kinds of ecosystems on the earth, including forests, grassland, wetland, cropland, and able system, and so on. So it's a very huge country and very diverse natural situation. So considering this situation, the central government issued a kind of strategy called the main function area strategy. So the total land was divided into four kinds of types. One is optimized development area. Yeah, that's those areas like Beijing and Shanghai and Guangzhou, those areas, the megacities. And then we have the key development area, including such area as Wuhan and Chengdu and so on, these cities. So the optimized development area and the key development area are both urban area. And then we have another one is the agricultural production area. And also we have the ecological function conservation area, we call the FQS area. So the FQS area contains about 85% of the entire land in China. So as mentioned, the ecological function conservation area is the major area that is related to the ecological protection. The main purpose of this area is to provide the ecosystem services and products. And it's the area related to national ecological security. So the government takes some kind of policy to protect the importance of ecosystems, including the negatively industry lists, including the dominant ecosystem services. That means, for example, if one place is an ecological function conservation area with the water conservation and retention, then the industry, for example, the mining industry or the commercial forest logging is not noted in this area. And the FQS area is also having a high proportion of protected areas, we call it the ecological landings. So based on the performance of the ecological protection, the central government transferred a lot of money to those areas. And the total amount of a transfer increased over the years. For example, in 2010, the total transfer is 24.9 billion yuan. And to nowadays, last year, 2006, the total amount is 62.7 billion yuan. So basically, one county will get 0.1 billion yuan. But there are some changes in those areas. First, the current policies are mainly negatively restricting policies, also restricting policies for the industry development. And then the second one is the large amount of poor people living in this area. And the new inflation amount of financial transfer from the central government cannot solve the problem of poverty. The third one is the ecological protection in Africa needs a larger financial importance from the local government, local level. So facing these kind of challenges, we need to find another policy for the development of the economy in those areas. So this idea is the value equalization of the ecological products. What do we want to do in the future about this policy? We have some concerns. So first one is we should consider this idea that related to the new five development concepts. These five development concepts are just issued by the central government, including innovation and cooperation, green, open, and sharing. So firstly, it is innovation because the realization of the value of ecological products is a new theme. We might have a lot of tests and some may be success, some may be failure, but it is innovation. Another one is cooperation. We need cooperation from the local government, from the research institute, and the business company, and also from the local farmers. We need cooperation. And the most important thing is green. So that means the way of realization of the value of ecological products should be green will not cause the degradation of ecosystems and ecosystem services. And also it's open to a local level or international level and also sharing. So because we share the ecological products from the nature and also the value realization of ecological products might be achieved by sharing through the ways of internet, WeChat, or Facebook and other ways. And another one is about the main ideas that are already showing in the government's document. First one is the establishing the idea of natural capital in the country. Not only to the government, but also to the local, to the public. They realize the importance of the natural capital. The second one is the ecological products and services are valuable. And when we use the ecological products and services we need to pay, it's not free. And the third one is the nature conservation is the process of increasing natural value and natural capital. It's also protection and development of productivity. Therefore, it should deserve a large amount of economic composition. And the final one is said by President Xi that no sea mountains and no sea water are golden and sailways. So those ideas are presented in the recently government document. And what do we want to do in the future? I think either from the government or from the researchers, we have something to do. First one is the identification of the range and types of ecological products and services. When we see the ecological products, it's not everything is a product. It should be related to the natural existence. And also it will not mean cause the negative impacts on the natural ecosystems and their functions. So that's why we need to identify what's the ecological products. The second one is we need to calculate the ecological assets and the ecosystem services or the ecological products. The third one is formulation of models based on the local and international cases. And the fourth one is the formulation of the mechanism for value realisation of the ecological products and services. I think those are the main tasks that need to be done in the future. And from the government level, the main function strategy proposes to do some demonstration of studies about the realisation of the value of the ecological products. So four provinces, including Qinghai, Guizhou, Jiangxi and Zhejiang, four provinces are chosen as the demonstration of studies. And these three provinces, including Nishui, Fuzhou and Naishan, three provinces already come here. They will give an introduction about their case studies. So I just stopped here and those provinces will give their presentation of these case studies. Okay, any questions? If no, I just give time for these provinces. Okay.


تشرف بالاشتغالي بالعلم ولا تبغي به ما عشت يا دا دا دا لا وياله من شراف عظيمي والجمال ما افتقوا الى البيان والبيان اخراج الشيء من حيز الاشكالي إلى حيز التلاجي تجلي ونقصنا لا يعتمل إلى معنى الواحدة ما يتبغيه وتنزيله وانه مشتقل من نصوط العاول والكوبسي وضوائق ما احتمال أموال أحد أموال ما أموال أخر يولو وضوائق بالذي ويسمع وضوائق بالذي اوضى رحمة الله يذهب into a unit from the unit of صول الفق which is known as مجمل and he speaks about نص and he also speaks about ظاهر and he also speaks about مؤول 4 things 4 things is what he is going to speak about here he is going to speak about مجمل he is going to speak about نص he is also going to speak about ظاهر and he is also going to speak about مؤول and he started with which one he started with مجمل مجمل means something that is ambiguous it is anything that requires clarification it is مفتقار إلى البياني it is anything that requires clarification and it needs to be explained الله says in the Qur'an أقيم الصلاة يستابلش تبرياء how do we do it we don't know it is مجمل it is unclear we need something to clarify what it means what is صلاة what is it the Prophet had to clarify it so that's what the author said what was better for the author to say is that مجمل means محتملة معنى ييني أو أكثر لا مزية لأحده معن غيره this is the best definition which is that مجمل it technically means anything that can take two meanings or more and you can't strengthen one of those over the other it is محتملة معنى ييني it takes two meanings or even more لا مزية لأحده معن غيره which you cannot strengthen one over the other you can't so in summary مجمل has to have three pillars for it to be called مجمل the first one is تطرق الاحتمال إلي ambiguity must enter into it or more like the possibility of it taking more than one has to enter it it has to be something that more than one that's one the second is it has to be two or more meanings احتمال the possibility has to be in two meanings or more number three is you can't strengthen one over the other أنه لا يوجد في أحدها ما يستحق به تقديمه على غيره you cannot strengthen one over the other you can't say this one deserves more over this one if you do then this is not called مجمل then the author he defined what it means which is the opposite of مجمل he says بيان means taking something out from the role of ambiguity into the role of clarification that's what it means حيز means it's in what does شيخ عبد الوحيد say what does شيخ عبد الوحيد say حيز when he defined it دمين you're taking out of the domain of اشكال which is ambiguity إلا حيز التجلي إشكال is the opposite of تجلي تجلي is something that becomes it's just clear to you now that's what it means أبو معالي الجوين as I said to you before he himself criticizes his own definitions and how he explains things here in his book in his own book البران and this is one of the things he criticizes of himself the usage of the word what the usage of the word حيز him using that word حيز is incorrect you know why it's incorrect حيز is من سفات الحسي حيز is from the characteristics which shows something is tangible are you with me brothers and ambiguity is not something that's tangible ambiguity is something which is معنوي so how can you define something with a definition that shows that it's tangible when what you're talking about is معنوي and it is not حسي this is side benefit he himself goes into explaining that that's the author's definition of what the word بيان means so as we said if he himself criticizes it then he gives us we can also criticize it as well the best definition is to say about what it means بيان is مع المبيان is مطبحة دلالته it's anything which is دلاله دلاله means the way it expresses its evidence is clear فلم يتطرق إليه خفاء and no I'll just make up an English word I might be wrong or right it's not the first time I've ever done it plus English is even a standard language which you can't add what you want to it or not English if you feel like it you can just add what you want to it no problem what's holding it down for it not to be added to it so anytime you feel like it you can add any prefix to it it's not a wording if you want and I like doing that a lot it's just called creativity so I can change it don't worry plus I'm the linguist here I'm the one who does linguistics in university you guys who does linguistics in university exactly so if I say something is right okay I think it's the right word هدن is it the right word something is hidden it's not a word well now it is now add it to your dictionary you guys know the woman who wrote is it J.K. Rowling's or J.K. Rowling's the one who wrote Harry Potter is it Rowling is it Rowling or is it Rowling اختلف العلمة anyways you know she added her knowledge into the dictionary do you guys know that right her usages of English language in her Harry Potter was taken from it شرك كفر بوك and it was added to the Oxford dictionary brothers and your muslim brother he has making up words and you guys don't want to add it to your dictionary yeah حفظة is that fair it's not fair yeah okay so what it means is that هو ما تضح الدلالات فلم يتطرق إلي خفاء there's no hiddenness خفاء means something's hidden it's not hidden in any way it's clear I want it to be accurate in the depth تطرق means when something creeps in it enters into it it be hiddenness does not enter into it at any way this is called مبيين it's clear then they define what is known as نص they say this مسألة is نصن في المسألة اما نصن في الدلالة what do they mean by that if you don't know these terminologies you're going to suffer because scholars are going to argue and have debates and discussions and they're going to say نصن في المسألة what do they mean by نص نص means ما لا يحتمر إلا معنى واحدا نص is something that doesn't have any other meaning when Allah said in the Quran تلك عشرة كاملة تلك تلك عشرة كاملة Allah said this is that can 10 completed can you understand anything other than 10 from this I'm asking you guys a question now you can't so the عدد نمبز are نص نمبز are نص 10 is 10 is there anything else you can understand from 10 you can't take right so قل هو الله أحد what is it it's a نص there's no other meaning that you can take from it can you take that 2 or 3 قل هو الله but what about when you say إنا نحن are you with me brothers إنا نحن what is that it's not us نحن we can't take more than one meaning نفسه and also معه غيره or the we of royalty does that make sense that's not نص then but نص is what عدد نمبز are generally نص وقيلة it's also said تقويله تنزيله its interpretation ويجب أن يكون قد يتفهمه. هناك يتكلم أنه يتكلم نص. ثم يتكلم عنه. الأول مفتاح هو ما نحن نخطيه. ما لا يحتم إلا معنى واحدة. هذا هو مفتاح نص. أتكلم هذا المفتاح الثاني الذي يكلم. هذا هو حقيقة ورعاية ما نص يعني. ثم يتكلم عن أين نص يتكلم عنه. أين يتكلم عنه؟ ويقول من منصة العروس. ويقول منص. أسف. منصة العروسي. يقوم بكسر الميم. يقوم بكسر الميم. لأنه يسمو آلة. يسمو آلة. ولا يقول منصة. يقول منصة. ويقول منصة. ويقول منصة. ولكن مفتاح نخطيه هو ما؟ منصة. يخطيه. هنا يقول المصة. مشتق. ومنطه سيقول مشتق. يخطيه ويقول سيقول مشتق. ويجعل عنده يقول منصة نخطيه. نعلم عن المصة المشتق. ماذا تعلم؟ مالذي يعني مشتق؟ شيء يساعد من شيء. أين يساعد منصة مخطيه منح؟ يوجد أaiser من المصة تساعد منه. يوجد منصة مخطيه. يخطيه فما يخطيه نخطيه. أين يقول ذلك. لا أستطيع أن أقول أنكم أعرفون منصة العروس هذا هو المشتق لا يجب أن يعني أنه يموت منه ليس في أي طريق فهي فقط يعني أنه من المشتق تلاق الحروف هذا هو ما يعني بالنسبة ثم أصدر رحم الله تفعيل رحل ما هو رحل محتمل أمريني هل أنت there brothers ظاهر يعني شيء that can take two meanings أحدوم أظهر من الآخر one is more apparent than the other so two things have to be found in the definition of ظاهر in order for it to be ظاهر first one is that it carries there's a possibility of two meanings the second one is the second one is one of the two meanings is stronger than the other are you with me brothers are you there brothers ظاهر what is it brothers something that has two meanings one is stronger to you and the other one is what weaker to you right the part that is stronger is called ظاهر and the part that is weaker is called مؤول the 60% or the 70% is called ظاهر and the 30% or the 40% is called مؤول you only are allowed to take the تأويل when there is what when there is a تأويل to show you the weaker meaning does that make sense if the ظاهر is the راجح is the stronger and it is the correct one are you with me brothers the percentage that is less if you're going to take it there has to be external evidences that pushes it does that make sense so when a person speaks to you you always understand it according to the apparent meaning we take the ظاهر of people's statements are you there are you with me unless there is an evidence that pushes it away from ظاهر to you nowadays we are called literalists right they want to belittle us and say you guys are literalists صح ignore it to say that because everybody takes people's statements from ظاهر unless they feel there is an evidence to show that that is not what is meant by it are you there مؤول means تأويل are you there brothers but remember تأويل is used in many different meanings here we are talking about as for ابن جلين الطابري when he says to you وتأويل قولوا تعالى he doesn't mean تأويل here this meaning he means تفسير because what تأويل is the synonym of تفسير as well are you there but here is another meaning when أشعاري comes to you and does تأويل of Allah's characteristics don't accept the word they use to the what تأويل to him why because تأويل means taking the weaker of the two with an evidence and he hasn't got no evidence so what do you call it تحريف that's why ابن تأويل didn't take the usage of the word تأويل in his book have you guys read the debate on his كتاب عقيدة الراسطية it's written عقود الدرية في بعض الملاقب الشيخ الإسلامي ابن تأويل when he debates anyway he used to go to debate he used to always bring his عقيدة الراسطية with him he used to put on his armpit he would go to the debate and open it and say hey this is my عقيدة do you guys have any problems we can have a debate about it so they'll look at it so one of the things they brought against him is why did you use the word تحريف and not تأويل he said because تأويل has a correct meaning in it تأويل means taking the weaker of the two with an evidence but I don't believe you guys are taking you're doing تأويل with an evidence because we believe you can do تأويل when there's an evidence for it what we believe you guys are doing is distortion it's not called تأويل does that make sense and this is as I said brothers we're in a time and an era where we need to really learn that it's the world of terminologies British values what does that mean there's no definition for it we're getting beaten up and bashed up Islamophobia is growing due to what a word with its definition hasn't yet been placed صح what do you mean by British values I don't even get this you keep throwing at me all day you're going against British values you're going against British values what is British values man صح are you with me brothers so you have to say to the person before we go into a discussion and a dialogue regarding an issue let's agree on definitions because I'm going to use the word extremism but I mean something that you don't mean you think extremism is me having a beard right now I don't see that to be extremism does that make sense so don't just talk with them about extremism we condemn extremism and they're next to you they're next to you and they say where come them in extremism as well does that make sense you're both using the same word but he means something different he's defining it different to what you're defining it at don't get caught up with it so first of all you say listen our definition of the word غولو extremism is different are you there for us leniency is extremism صح somebody not praying is extremism they see extremism only be to only be what exaggeration we see negligence is also a form of extremism صح ان ذا because Allah says يا أهل الكتابي لا تغلو في دينكم and Allah is talking about to the nasara who came with negligence and the yahood who came with exaggeration both parties or more the yahood who came with what negligence and the yahood who came with exaggeration both parties were told don't go extreme in your religion so the sister doesn't wear hijab yeah who takes a hijab off and the boy who's who's not praying the salah and everything we say why he's so extreme for are you with me brothers that's how we have to look at it are we with and that's why we're at a time when we need to learn to ask definition of words are you with me we need to say what do you mean by that word okay I don't mean by that and it is the طريقة the أهل البداع caused harm to Muslims and Islam is they came and they said إيمان means تصديق مجرد just mere belief actions are not part of iman why because iman means in the language just belief and a whole concept just came from a definition of a word and they took actions out of iman when it's part of the reality of iman are you with me brothers today define jihad what's jihad مقاتلتي الخفار الحربيين right are you with me brothers pay attention so you're fighting a kathir who say حربي what do these people do are they fighting people of حرب from the definition they're wrong they're fighting women and children on the streets are you with me they're killing Muslims in Muslim lands when did jihad become killing Muslims it's khufar the definition says khufar are you with me brothers so what we need to do is we're at a time where we need to say listen let's define what the word means first of all and that's why I said we need to do a series called تصحيح المفاهيم are you with me brothers what is دعوة today that means go back what is دعوة brother that's what we need to say so we need to say some people so we need to make a series called مفهوم الدعوة مفهوم الجهاد مفهوم الخلافة مفهوم الجهاد and etc we need to do تصحيح المفاهيم series like that where we take شرع terms and we define what it really means in the شريعة are you there brothers are we all in the same point page that's what's needed a series like that where these things are clarified and explained or else there'll come a time when these terms are loosely used and it brings about because each definition brings out احكام يتلتبوا منها rules start coming out from it صح it doesn't just stay at a mere definition brothers it doesn't people start that definition starts to manufest on people's limbs and they start to do actions based on it it's important and this is something I'm telling you brothers ابنو تيميا fought against صح ابنو القي من the beginning of his كتابة علام الموقعين he debate he argues this concept تصحيح المفاهيم of the اصطلاحات somebody's gonna come up to and say to you music is Halal it's a ruling right if you ask him how did this come about he'll say to the previous in what they used to say it's Makruh okay what's Makruh then what's the definition of what Makruh Makruh meant to the self هذه الأمة to be Haram that's the definition are you with me for him it is what ما طالب الشارع تركاه طالبا غير جازيمين that's what he believes it is فح he's defa he's taking a definition of the متأخنين the lake comes and he's forcing it on the متقدمين and then now it comes out from this is no I mean a تحكم then I can't start coming from it so that's what I think we need to we need to do this anyways the so what is the word مؤول I'm a تأويل what's the definition of it ما صرف عن معنى مؤول means anything that is diverted from its apparent meaning إلى معنى المرجوح to a meaning that's weak لدليل دل علي based on the evidence that showed it four points is what my definition holds here the first one is there has to be something diverting it وجود صرف it's something that's تأويل of it ردول and تحويل sorry something is turning away this definition the second thing is it has to be diverting it from its apparent meaning the third one is it is diverting it to a meaning that is weak fourth is there has to be evidence that shows this weak this weak meaning evidence you have to show me an evidence based on it and from this what we learn as well is that the ظاهر is two types first one is ظاهر بنفسي something that's apparent in and within itself and the second one is something that is not apparent in and within itself and guess what's the thing that what is the thing that's not apparent in and within itself some of the scholars they call it ظاهر because they say that the ظهور of it is another meaning but now it became clear to us that this is ظاهر now does that make sense ومن صحابنا نقادي يحمل على الداد ومنهم نقادي يتوقفوا عنه فمن كان على مجهول الطوبة وطاعة ويحمل عليه باحة في حطه وحطنا وقرأه صاحب الشريع على نقادي الصادل من أحد هو قرأه صاحب الشريع وقرأه على الفعال كفعه وما نفعله في وقته في وقته في وقته وعليه ولم يمكن فحكمه وحكمه وما نفعله في مجلسه وما سماه الله وقد رحلت ولم يستون تفعيل رسولهaded و Motiv who mistakes Pour he means and the himself Expanalقر Rob سحاب وقط فني ومن صاحب الشريع ومن التورب Problem for about whatever two points The first one is Ich Tхصاص وهاد الفصل الفبيل العفعان The first one is this chapter is only I mean this unit is only going to be spking about actions nothing to do with speech nothing to do with verb it's just action the second benefit that we take from this chapter is it is only specific to the prophet's actionsoning صلاة الله عليه وسلم


Codesia has been working towards open access since its founding in 1983. The organization's mission is to promote research and scholarship across Africa and the African diaspora and it has developed a wide range of policies and practices to support this goal. These include publishing books, journals and other materials in both English and French making them freely accessible online and providing grants to scholars who are unable to pay for their own publication costs. Additionally, Codesia encourages collaboration between scholars from different countries and disciplines and works to ensure that all voices are heard and represented in the research and scholarly discourse. This article was authored by Francis Nyamjo.


on the ground. Presented by theCUBE, here's your host, John Furrier. Hello everyone, welcome to theCUBE on the ground. I'm John Furrier, the host of theCUBE. We are here at the IBM Open Architecture Computing Summit here in Seattle, the day after DockerCon. I'm here with Stormy Peters, Vice President and Developer Relations at Cloud Foundry. Nice to see you again. Good to see you, John. So Cloud Foundry, I'll say all the rage with part of IBM. This is their event, but Cloud Foundry has a lot of different partners, but it's been really interesting. Blue Mix, based on Cloud Foundry, has been growing like crazy and their community's going nuts over it. How is Cloud Foundry doing vis-a-vis other developers and what's new with Cloud Foundry? Is anything updated? And obviously the success has been great. It gives the update. Yeah, so Cloud Foundry is growing really quickly, as you mentioned, both within each of our provider companies like IBM, Blue Mix, as well as across the industry. And what I think is really exciting is we have like 63 member companies in the Cloud Foundry Foundation. And some of them are providers, but a lot of them are users. So we're seeing this open source ecosystem grow up around people using Cloud Foundry to manage their multi-cloud environments. So I was talking to Sam about Cloud Foundry and it's what's interesting is there's a lot of real developers involved. Seeing your open source guys, people have been around kind of my age and now a younger generation is coming up. How has the Cloud Foundry morphed over the past couple of years? In terms of enabling, because IBM's leveraging it, people have put a little twist on it. That was kind of by design. Is that something that you guys see more and more of kind of people using Cloud Foundry building around it? And how does that affect the ecosystem open source? So what I think is really interesting about Cloud Foundry as an open source software project is it's built on this pair programming model. And that's pretty new to the open source world. Pair programming is not new, but pair programming combined with open sources. So we have what we call a DOJO, which is a center. There's like an IBM DOJO and rally. There's DOJOs at different member companies. And people go there to learn about Cloud Foundry and actually physically go for six weeks and they sit next to someone all day when they're coding. And then when they graduate, they continue to pair like that. So it's two pairs of eyes on every piece of code. A lot of mix within the community. So kind of mentoring, but then they leave and they have that connection back. And they still pair with other people. So you might have an IBM person partnering with a pivotal person or an EMC person. It's a terrific model that really changes how open source software is written. And what's the biggest thing that surprised you at Cloud Foundry? If you look back and say, okay, where it is today, what's the big thing that surprised you? I really like that all the user companies are joining. Like it's really awesome to have a community that users are so excited about it, they're joining. And we're working with other foundations like OpenSec and others to make sure that there's standards and interoperability between the different Cloud environment. So it's a truly multi-Cloud solution. So what are you working on these days? What's your key tasks that you're taking on? I'm focused on our developers. So making sure that we have a strong community of developers working on Cloud Foundry across all of our member companies. And other things in terms of technologies, are there any new things involved in Cloud Foundry we should know about? Yeah, so we're working on different standardizations. So we're working with OpenStack to make, because many of our partners, they might run an OpenStack or AWS or Azure. So we're working very carefully with them to make sure that the whole stack works together from OpenStack all the way up to Cloud Foundry. And we're also working with the OpenContainer initiative to make sure that there's standards for containers so that they interoperate well together, kind of be open source friendly world, working mostly interoperability. And Bosch can now deploy, install and deploy Cloud Foundry across all these environments on its own. So the question we got at DockerCon this week was, what does Cloud Foundry fit into the Docker madness? Because it was basically a Docker parade all week here with DockerCon, great success there. Cloud Foundry is in that world. What does that fit in? Well, I kind of see users move. So it used to be that you added more hardware when you wanted more computing power. And then you started adding more virtual environments, virtual machines when you wanted more computing power. And now kind of people are in the container mode, add more containers when you need more computing power. But you still have to manage those containers. So Docker is super popular. And you see Docker also expanding to help people manage their Docker containers. Cloud Foundry is helping people take those Docker containers and other containers and deploy them, manage them, scale them. It's the entire platform. And for the folks that didn't make DockerCon, what's your big takeaway from DockerCon this year? I think that there's so many, so we did a container report recently with Cloud Foundry. And we found half of all the people we surveyed, they weren't Cloud Foundry users, they were general IT. Half of them were considering using containers, but only a quarter of them had managed to deploy them in production yet. So people are very enthusiastic about it, but they're still looking for an entire solution like Cloud Foundry to manage it. And final question, what's going to be the roadmap for Cloud Foundry the next year? What's the key things that you guys are working on with developers? So with developers, we're actually working on certification. So there's this huge need for companies to hire knowledgeable Cloud Foundry developers. And so we're working on the certification process and training. All of our training so far has been sold out, so there's obviously a huge demand for it. More training. Stormy, thanks so much for stopping by on the ground here, appreciate it. Stormy Peters, VP of Developer Relations at Cloud Foundry. You're watching On the Ground, I'm John Furrier. Thanks for watching.


What's up? How are you guys today? We're gonna take a look at my kitchen fridge pantry Just to give you guys an idea of all the foods I've been eating lately to stay as healthy as possible While recovering from my liver damage now since I have a limited amount of space here I've been a little bit lazy in making certain things just because it's so much more work with the small sink You know no counter space This for instance is the reinforced beef stock that I make so We take the collagen bone broth from Franky's free-range meat I chop up a bunch of extra meat I have lying around to add a lot more protein and be vitamins to it and then I'll just pressure cook this For an hour or two and I'll use that as a base for soups I'll dip my sandwiches into it just adding a lot a lot of nutrition very important part and back here is some of the Garlic and onion potato chips we have on Franky's free-range foods These are what I have as a side dish when I'm having a sandwich and usually I'll have the sandwiches when like I just want something fast easy no prep at all speaking of sandwiches. We have some organic bread from the bakery here Just in the freezer staying as fresh as possible That's really the only thing that I've been having that's in the freezer I don't really have a lot of stuff in the fridge because I usually just bring meat home the same day from Franky's Free-range meat so in the front here is a mayonnaise. I've been using we have some miscellaneous Steaks hot dog sausages that I'll have from time to time some wine that I'll cook with But most of what I've been eating these past few weeks guys has just been the roast beef from Franky's free-range meat Either slice it and put it on the sandwich or I'll slice it and put it in like the beef udon that I've been making and Also some shiitake mushrooms if I feel like sauteing them today, maybe I'll have some more but That's really it the only stuff I've been eating in the fridge is the meat and the mayonnaise and the mushrooms So I'm pretty happy to have discovered this organic udon noodle that I can tolerate that I feel really good eating found these on Amazon bought a few packages of them, so You guys can't have pasta can't tolerate pasta This is made with a different type of wheat and I like it a lot more cooks very fast very easy I've been having this or the roast beef sandwiches So I'll just take the udon noodles with the beef stock and some roast beef mix it all together It's kind of plain, but it's good. It's filling and I feel good eating it So in these cabinets is most of the other stuff I eat We'll have to do a supplement update in a month or two, but for the most part it's been the same Coconut oil I cook with Frankie steak seasoning we ran out of the Bolivian rose salt maybe on occasion I'll I'll choose some gum, but maybe not more than a few times a month and then we have some more mastic up to grind up here a few bags of potato chips and behind the supplements we have some of the banana rice crisp bars Organic rice crisp last thing I use the sugar for was the sorbet recipe I had some pancakes yesterday, but I'm honestly not really a fan of them with the birch benders Pancake mix like I'll crave them, but then when I go to actually eat them I don't enjoy them that much These are some canned artichokes. Maybe I'll make an artichoke dip soon Some beans that I use for the artichoke dip miscellaneous coconut milk coconut oil that I'll sometimes put in like cookie recipes and then here's all of our grains We have two different types of rice some oats Barley, which I don't really touch usually just the rice on occasion and then this is I guess I would call my apple cabinet That's the only thing I really eat out of here every meal for dessert. I have one or two organic apples sometimes I put lemon juice in the Lemon sorbet and I try to have it as a natural source of vitamin C on occasion Here are some garlic and onion that I'll cook with sometimes and the rest of this is just like breadcrumbs flour now I actually will use the flex strokes with like some fiber to make a Detox smoothie once in a while, but with how busy I've been I just don't want to risk like Having to use the bathroom more than normal and then on the table over here I have my mastic gum and my water key for grains that I have with every meal I ran out of water, but we have some Mountain Valley left here. I normally drink the fiyuji So that's really it guys not a lot of variety And I haven't been having the bread as much because there's a lot more traffic now that school started and going into the city Just to get the bread it just takes way too long so like the meals or I'm doing the bean dip with the bread or Garlic bread or that type of stuff not having as often just trying to keep it simple. I did buy Rice cooker and some other equipment. So maybe we'll start doing the rice more often Since it's getting colder. It's possible that we'll switch back to the barley soup Not really sure yet, but hopefully this gives you guys an idea of what I've been eating And when you stick to a minimal amount of high-quality foods That's a great way that you can kind of dial everything in because if you're really not having more than 10 different things in your diet There's a very very low margin of error But if you guys would like to support me you can go to frank-tash-to-found-out.com check out all of my businesses We have roast beef and all high-quality meat products on Frankie's French meat. I don't think I showed you guys I do have the goat testicles in the in the fridge as well that I do have like monster twice a week for the testosterone boost Frankie's your range foods a lot of the stuff you guys saw here. We have the salt We have the rice crisp bars of potato chips and a lot of stuff key for grains that I incorporate into my diet on a daily Basis and then you guys can check out organ supplements Wi-Fi shielding Frankie's naturals for everything I use always wearing the Wi-Fi shielding clothing Frankie's naturals products and taking the supplements every morning. So thanks again for joining guys Please drop a like on the video leave a comment down below Subscribe so that YouTube can unsubscribe you next week and be sure to check that notification bell so they don't notify you of my videos Thanks again guys, and I'll see you for the next video


the continuity equation last time and we will see now that there may be a different way of deriving the continuity equation not only one different way but there could be many different ways of looking into that. We will look into one such alternative way of deriving the continuity equation here and in our subsequent chapters we will look into other possibilities. So, more number of different ways we look into it gives us a better and better insight of what is there actually in the continuity equation. So we look into an alternative derivation of the continuity equation. In this alternative derivation our objective will be to look into the entire thing from a Eulerian view point. That means we will identify a specified region in space across which fluid is flowing and that we call as a control volume. So in a control volume of a particular extent let us for simplicity in deriving the equations assume that the control volume is of a rectangular parallel shape. So it has its dimensions along x, y and z as say delta x, delta y and delta z which are small and in the limit we will take all these as tending to 0. So this is a differentially small control volume that is the entity differentially small control volume. Now what is happening across this control volume some fluid is coming in, some fluid is going out and that is occurring over 6 different phases and each phase has a direction normal and basically the mass flow rate across that phase is taking place normal to the direction of that respective phase. So if we consider the flow rate along x then we should be bothered about which phases, we should be bothered about these 2 phases because these 2 phases have direction normals along x. Let us see what is the mass flow rate that gets transported across these phases. So there is some mass flow rate that enters the control volume along x. Let us symbolize that in this way. Across the opposite phase say there is some mass flow rate that goes out and that occurs at x plus delta x. If this is x this must be x plus delta x. So how do we characterize the difference between these 2 because what we have to remember, we have to remember the mass balance. What is the mass balance? What is the rate at which the mass is entering say m dot in it may be along x, y or z minus m dot out that also may be along x, y, z. So what is the difference between these 2? Say there is some mass flow rate coming at the rate of 10 kg per second and say there is a mass flow rate that leaves the control volume at the rate of 8 kg per second. So what the remaining 2 kg per second will do? That will increase the mass of the mass within the control volume. See control volume has a particular volume. It does not have a fixed mass. So if it is a compressible flow say it is highly possible that the mass inside these changes. So that remaining 2 kg per second may contribute to the rate of change of mass within the control volume. So we can say that mass flow rate in-out is nothing but the rate of the time rate of change of mass within the control volume. Then why do we use a partial derivative here? Because by specifying the control volume here by some fixed coordinates we are assuming that we are freezing its locations with respect to position and trying to see what happens in that frozen position with respect to time. So that is why a partial derivative with respect to time. So when you say m dot in-m dot out you have to remember that it has like contributions for flow along x, y and z. So we can try to write what happens along x? Similar expressions will be along y and z. So m dot in x. So what is how do you calculate a mass flow rate given a density? So to calculate the mass flow rate you require first to obtain the volume flow rate. So what is the volume flow rate? Volume flow rate is the normal component of velocity perpendicular that is velocity component perpendicular to the area times the area. So the component of velocity along x is u. What is the area perpendicular to that? x delta y x delta z that is the volume flow rate that multiplied by the density is nothing but the mass flow rate. Very straightforward. So when you write m dot out at x plus delta x basically you are looking for the value of this function at x plus delta x. You know the value of the function say at x again you can use the Taylor series expansion. In the Taylor series expansion when you expand it you keep in mind that delta y into delta z is fixed. So what you can do? You can always take it out of the derivative and think about the expansion of rho into u. So this will be m dot in x plus higher order terms. Let us substitute what we can write in place of m dot in x. So that is rho u delta y delta z. So clearly if we write what is m dot minus m dot out along x. What is that? So this term will come in the other side. It will be minus of that into delta x delta y delta z plus may be minus higher order terms just by simple transformation or taking one side terms in the one side to the other. So the minus sign appears. Similarly you get what happens along y and z and you can write therefore the expression of m dot in minus m dot out. We will do that but before that let us see what happens to the right hand side. So what is the mass within the control volume? So we have to write basically the time derivative partial time derivative of that. So what is the mass within the control volume? Let us try to write what is the mass within the control volume? What is that? Yes. So it is the density times the volume. So rho if it is the density that times delta x into delta y into delta z that is the mass within the control volume. So what we can do now? We can write a mathematical expression of this physical balance because we now know how to write all the terms and we take the limit as delta x delta y delta z 10 to 0. So that delta x delta y delta z that gets cancelled from both sides and in the higher order terms some small terms remain which in the limit as that tends to 0 that term will be 0. So with that limit that is delta x delta y delta z all tending to 0. So you will have for flow along x that will be the case. Flow along y what should be the term? Flow along z. So individual velocity components are responsible for flows along certain directions and that is what we have to keep in mind. That is equal to because delta x delta y delta z gets cancelled. So you can write this in the well known form that we saw in the previous class or equivalent vector notation which is the continuity equation. So we have seen at least 2 different ways of deriving the continuity equation and keep in mind these are not the only 2 ways but at least these have given us some insight of what this law or what this equation is talking about. We will have a couple of important observations related to this before we go on to a problem where we illustrate how to make use of such equations. So the first point is that you see this is a differential form. Now let us say that you want to express in an integral form. So how will you do it? We will later on formally see one methodology by which you can convert easily from a differential to an integral form but without going into that formality let us look into a very simple example by which we see that how to do it. So we are now interested about equivalent integral form. What is that equivalent integral form? We will not go for the most general case that we will study later but we will consider a very simple case as an example. One dimensional steady flow. Say the flow is taking place along x maybe just for your visual understanding let us say that the flow is taking place through a nozzle like this. A nozzle is something where you have when the flow is entering it is entering with a higher velocity and as it is moving along it the area of cross section gets reduced so the velocity of the flow gets increased. So you may assume that it is something like a conical shape maybe, frustrum of a cone or something like that. The shape is not important for us we will just keep in mind that there is an inlet section with area ei ai and there is an outlet section with or exit section with area ei and the flow is taking place along x. So one dimensional steady flow. So how do you simplify this differential form? When you have a steady flow the time derivative is not there. When you have one dimensional flow it will just boil down to only the x component of velocity but it may be compressible or I mean otherwise rho may be a function of position or whatever. So we are not committing ourselves to a constant rho and we are just putting the rho inside keeping the rho inside. Now what we will do is we will try to integrate this over the entire volume of the nozzle. So that means what we are trying to do? We are trying to integrate it. So we have a small volume element say a small volume element dv. Why we require a small volume element to consider? Because u is specially varying.  So that is that integrated over the entire volume that should be equal to 0. It is very straightforward if the function is 0 its integral should be 0. On the other hand if the integral is 0 function need not always be 0 but we will see later on that there are certain cases when if the integral is 0 we may say that the function itself is 0 under certain important considerations but not for all considerations. But here it is the other way which is more straightforward. Now when you have it see our objective is to convert this volume integral to an area integral because we are interested about the areas across which the fluid is flowing. So if you recall in vector calculus there is a theorem called divergence theorem, Gauss divergence theorem which converts the volume integral into an area integral or vice versa. So what is that theorem? So if you have say f as a vector function, general vector function. So if you have a divergence of f over a volume that is given by area integral. Sometimes this is also written in an equivalent notation as f dot dA by giving the area directly a vector sense. So that is what we are going to do. Giving an area vector sense is like magnitude of the area times the unit vector normal to the area. So that anyway takes care of this. So when you write dA as a vector it is n cap dA scalar. You have to keep in mind that it is always the outward normal that is considered to be the positive direction of any area. So if you see this theorem, if you want to convert it to an area integral you have to cast its form in a divergence. So say we want to cast it in the form of a divergence. So what should be the vector function here? f. So what f should you choose such that it is in the form of a divergence? Yes? Rho ui. So the divergence of that of the divergence will give you this partial derivative. So we can write this also as divergence of Rho ui d. Now if you look at this theorem, this is the mathematical statement of the theorem but it has a very important understanding. What is this a and what is this v? It is not any arbitrary a and arbitrary v. This a is the area of the surface that bounds the volume v closely. So when you have the volume v here, it is bounded by say lateral surfaces and this cross sections. So when we are writing this in terms of an area integral that area integral should consider a i, a e and the lateral surfaces also. Lateral surfaces at the end will not be important because there is no flow across those surfaces. So those are like irrelevant from flow computation considerations. But fundamentally it is the entire surface that is bounding the volume. So you can write this by using the divergence theorem as how do you write this? Rho ui dot n dA over the area a that is equal to 0. Now let us look into this form. So when you consider this dA that area element, now you have as we mentioned 3 types of like one is inlet, another is exit and another we may call as wall, right across which there is no flow. So when you have the wall, it is not necessary to calculate to bother about this integral for the wall because there is no flow there. So we will therefore break it up into 2 integrals 1 for the area a i, another for the area a e, other areas are not relevant. So when you consider the area a i, what is the n cap for the area a i? Minus i. So you have rho ui dot minus i dA this integral over a i plus rho ui dA. Now what is for a e n cap? It is i. So this dot i dA for a e equal to 0. So you can write integral of rho u dA. So what does it say physically? It says that for steady state whatever is the mass flow rate across this section, the same must be the mass flow rate out across this section. That is what? It is physically saying mathematically the statement is straight forward. Now it is many times convenient to express this in terms of the average velocity because it might so happen that u is a function of the transverse coordinates. Let us say we have transverse coordinate as maybe say r or y that type of a coordinate and it is possible and it is almost always likely that u will be the function of a transverse coordinate because u will be 0 at the walls by no slip condition and then u will change maybe maximum at the center line. So it is expected that along the transverse direction u will vary. So it is not that we are talking about a cross sectionally constant u. It is rather a cross sectionally variable u. Now if we assume that rho is not varying across the section as an example. So let us take an example where rho does not vary over a given section but it may vary from one section to the other. So rho does not vary over a given section. That means you can take that rho out of the integral and you are left with these types of terms. For example for the left hand side it will be rho at the inlet surface, inlet section times this integral. Now there is a definition which is called as average velocity. So how the average velocity is defined? The average velocity is a cross sectionally average velocity. So for a one dimensional flow it is like u average.  So it is basically integral of u dA divided by A. What is the physical meaning of this? Physical meaning is see the entire section has a variable velocity. With that variable velocity it has a volume flow rate. Now if you have the same volume flow rate with an equivalent velocity that would have been uniform throughout then that uniform equivalent velocity is the average velocity. So what we are basically doing? We are equating the volume flow rate. In one case it is a variable velocity, the real case. In the other case it is an equivalent idealistic case where it is a uniform velocity but the end effect the volume flow rate is the same and then that equivalent velocity equivalent uniform velocity over that section is known as the average velocity okay. So we can replace this integral or this term by what? We can write this as rho i into ui average into Ai. Therefore we can clearly say that this equation this boils down to a very simple form rho i Ai ui average is equal to rho e Ai ui average. If the densities are not varying specially then rho i and rho e get cancelled out. So you get Ai ui average is equal to Ai ui average which is like A1 V1 equal to A2 V2. These types of equations you have used earlier for solving simple problems. Now what you realize here? See whenever you come up with an equation again I am saying you have to keep in mind that what are the assumptions. So if you have say an equation like this Ai ui is equal to Ae ui. So what are the assumptions under which it is valid? See we have of course we may go on deeper and deeper into the assumptions but let us talk about only the major assumptions. What are the major assumptions? First rho is a constant, the density is a constant. Then we are talking about these velocities not local velocity at a point but cross sectionally average velocity. If it is an ideal fluid flow then it is possible that local velocity is same everywhere because the velocity gradient is created by viscosity. So if you have no viscous effect then the effect of the wall is not propagated into the fluid and it is possible that there is a uniform velocity profile. So then the average velocity and the local velocity may be the same. So if you consider say a cross section like this, now let us identify 3 different points say these 3 different locations. At these 3 different locations the velocities are different. So when you write say Ai ui bar maybe sometimes in your previous studies you have written it as the velocity at this point. Fundamentally that is incorrect that is wrong. When you get rid of that wrongness by only one thing either you are writing you are although you are thinking that you are writing velocity at that point actually you are writing the average velocity over the section or even if it is velocity at this point that may be okay if the velocity is not varying over the section that is a uniform velocity profile if it is there across the section. That means you are implicitly treating it as an inviscid flow. So these are some subtle important concepts that go into the equation that is why I always say that try to get rid of whatever you have learnt for the entrance exam preparations because you know the end formula but many times you do not know that what are the restrictions under which you are using that end formula and that may be dangerous that may be more dangerous I would say it is worse than not knowing the formula. So let us keep that in mind. Now next let us look into another issue that we have discussed about the continuity equation in a general vector form but we have not looked into the other coordinate systems. We have looked into the Cartesian coordinate system but let us say that we are also interested about the cylindrical polar coordinate system. That coordinate system many times is important if you have something of say a cylindrical symmetry some body of cylindrical symmetry. We will not go into the detailed derivation of the continuity equation for a cylindrical coordinate but I will tell you how to do it and I will leave it on you as an exercise to complete it. So if you consider say cylindrical coordinates cylindrical polar coordinates. So in the cylindrical polar coordinate you have a polar nature that means you have the r theta coordinate system just like the polar coordinate and you also have a 3 dimensionality. So you have the axial coordinate system given by the z. So r theta z coordinate system and let us say that these have their unit vectors as given by epsilon r epsilon theta and epsilon r epsilon theta and epsilon z just like ijk. Now we can so we have to see that what are the differences in the Cartesian system and in this system. So first we have to know what is the del operator in this system.  So for the first component that is for the component along r it is just like component along x for the Cartesian coordinate. For the component along theta it will be this one because you have to keep in mind that the line element along theta is like r d theta that is the length element. Not only that even if you forget about that fundamental consideration just look into the dimensionality right. It is 1 by length. So it has to be that this unit should be length. So when you write that theta derivative theta is like it does not have a dimension. So you have to adjust it with a linear dimension. So just from the dimensional arguments also like these things I am telling because if you are confused that you are not being reminded that what should you write. At least these common sense things should guide you that what should be the correct way of writing this and then so in the continuity equations is the first term is the time derivative. So the time derivative you do not care much you know that like it is not dependent on these operators. The time derivative of the density but the next term is you have the divergence of low v. So there calculation with the del operator will be important. Can you tell where does it fundamentally differ from what you do in the Cartesian system? Yes? There is only one fundamental difference and if you keep that difference in mind it is just a straight forward exercise. In the Cartesian system when you have i, j, k those are invariant in direction whereas when you have epsilon or epsilon theta these are not invariant in direction. So if you consider say a point which is located at a position r. So how do you write it epsilon r and epsilon theta? So this is the radial direction. So this will be the epsilon r and perpendicular to that will be epsilon theta. You go to a now a different point. Let us say you go to this r. Even if you keep the radial magnitude same now what will be your epsilon r? Your epsilon r will be this and your epsilon theta will be again perpendicular to that. So if i and j they are invariant but epsilon r and epsilon theta they actually vary with theta but theta is the angular coordinate. So when you differentiate so this del operator is basically for differentiation and when you differentiate you have to keep one thing in mind. What you have to keep in mind? So when you write v you also write v in terms of its r theta and z component.  So when you are differentiating it is possible that you have to find out these quantities and these ones. These kinds of quantities they were not relevant for Cartesian system because invariant direction unit vectors. So we will find out one. Let us say you want to find out the derivative of epsilon r. So how do you look into that? Let us say that you have epsilon r for a particular angle theta as this one and let us say that epsilon r has changed with the angle theta plus d theta. So let us say this is epsilon r for theta and let us say this is epsilon r for theta plus. We can write d theta straight away or if you want to be more fundamental let us consider it as delta theta in the limit as delta theta tends to 0. So let us say that this is at theta plus delta theta where theta plus delta theta is the corresponding angular position. So you can see that in a scalar form actually magnitudes of these are the same. Both are unit vectors. So length of this is one, length of this is one. What has changed is the directionality. So what is the delta epsilon r? What is the change in the epsilon r? That is nothing but delta epsilon r. The change in epsilon r. What is the magnitude of this delta epsilon r? So if this angle is delta theta, so magnitude of delta epsilon r is like 1 into delta theta. So for small delta theta it is just like arc of a circle. So it is 1 into delta theta. What is its direction? You have to keep in mind that we are talking about the limit as delta theta tends to 0. Some of the 3 angles of this triangle is 180 degree. This is an isosceles triangle. So these 2 angles should be equal. So when this tends to 0, these 2 tend to 90 degree almost. That means delta epsilon r has a direction epsilon theta that is perpendicular to epsilon r. So we can say that delta epsilon r is like delta theta. Now you give the directionality epsilon theta. Sorry, now you get rid of the magnitude. Now on the basis of this you can find out what is delta epsilon r delta theta. That is you can take limit as delta theta tends to 0 delta epsilon r delta theta. That is epsilon theta. So this is nothing but okay. Similarly, if you work this out, it will be – epsilon r. Very same. I mean I need not work it out again because it is just very very similar. So now when you plug in those considerations in this del operator, in this divergence operation by considering this as the del operator for the cylindrical polar coordinate system, you will get a form of the continuity equation in r theta g system. I would advise you that you complete that exercise and then in your book you will see that the final form is written in the r theta g system. So you check or verify your final expression with that. That will give you a confidence that you have done it correctly in terms of the cylindrical polar coordinate system. So we have got some preliminary understanding of the use of the continuity equation. Whether the understanding is good enough, let us try to work out a problem and see. Let us say that you have a plate like this. You also have a bottom plate that say the top plate is a rectangular plate with the dotted line representing the axis of symmetry. The bottom plate is a very special plate. It has some holes. We call it a porous plate. So it has some pores or holes and the idea of keeping these holes is to blow some fluid. We will see that it is not just a mathematically defined idealistic problem. Many times it is something which is followed in technology. I can give you one example. Let us say that this is a heated electronic chip and you want to cool it. So it is possible that you blow air through a porous plate which goes into the chip and tries to keep it cooled. So it is not a very hypothetical type of a situation but the way we will look into this particular problem is abstracted from that any specific application but more into the fundamental that what goes behind this. Let us say that this is a uniform velocity with which it enters. Say we call it v0. So this is a porous plate. The gap between these two say is h. The length may be this is l by 2 and this is l by 2 and let us say that we have x coordinate like this and y coordinate like this. We make an assumption that it is an inviscid flow that is given. Assume inviscid flow. What is your objective? Your objective is to find out the velocity components u and v as functions of x that is number 1 and number 2 what is the acceleration of fluid at a given x or maybe at a given x, y. So when we say x maybe let us make it generalized say it could be x as well as y. So let us first physically try to understand that what is happening. Whenever you are solving a problem we can of course start putting equations but that is not always necessary. First you have to understand. So what is happening? Some fluid is entering. Now the fluid cannot leave through the top because of what? Is it because of no slip condition? No because no slip ensures that it has no tangential component but it simply it is a no penetration condition because it cannot just penetrate through the wall and go out because it is just a fully covered solid wall. So no matter whether it is slip or no slip you cannot actually penetrate it and go out along y. So only way this fluid can move in a steady condition is it can move sideways. So whatever fluid enters now may be half enters right and half enters the left okay. So what we can say is that we may write a gross overall mass balance. So when you write a gross overall mass balance what we have to keep in mind that very simple equation just like rho i into ui average is equal to rho e into Ae into ue average. So here let us say that rho is a constant. So that is another assumption that we make rho equal to constant. So when we make the assumption of rho equal to constant it is we have to just consider the area times the average velocity is same as what enters is same as what leaves. So we have to fix up a control volume to write that expression because you require specific surfaces. So what control volume we may choose? Let us say that we choose this control volume. See it is symmetrical with respect to the y axis. So I mean if we consider only one part of the domain half of the domain to the right of y axis the same happens to the left. So let us say that we consider a control volume like this which is say located its end phase is located at a distance x. So its local x coordinate is x. So with respect to this control volume what are the phases across which fluid flows? Can you tell? One is the most straight forward is the bottom phase. Yes through this fluid flows. Another straight forward is the top phase through which fluid does not flow. This one? Yes or no? How many will say yes and how many no? Think again think physically. See the fluid enters here fluid does not know whether to go to the left or to the right. So it is equally probable and it is actually equally so that may be half will try to go to the right and half will try to go to the left because it is perfectly symmetrical. So if it tends to go to the right with a velocity say plus u similarly it will have a tendency some fluid particle located at the same position to go to the left with minus u. Net effect is that at this axis of symmetry of no u, u is 0 because it is just like balanced from what you so whatever enters it has a balancing effect of going to the right and to the left. So there is no net flow across this. So when you have there is no net flow across this there is only so this one has a net flow. So when we say i and e maybe this is the surface i and this is the surface e. So for the surface i what is so we can write again so here rho is a constant. So we can write ai ui is equal to ae ue. So what is ai? Let us say that the length that the width of the plate perpendicular to the plane of the figure is b that is the width. So what is ai? What is this ai? b x. What is this ui average? It is v0 because it is a uniform. So average and local everything is same. Now come to these ones. What is ae? So h x b. So this is and what is ui average? See for that this assumption of inviscid flow is important. So if you do not consider inviscid flow then you have to know what is the velocity profile in between you have to integrate that to get the average velocity. But when you are given that is inviscid flow your inherent assumption is that it is a uniform velocity profile like this. So u is not changing with y. It is locally changing with x but along y it is uniform because it is inviscid. You can see that with inviscid flow you cannot impose no slip boundary condition because if it is if it has to be uniform suddenly it cannot go to 0 at the wall. So it is not no slip here at the wall but no penetration at the wall that is sufficient for solving this problem. So no slip is not a necessary condition here and in fact it will contradict if you say that it is an inviscid flow. You cannot have no slip and inviscid simultaneously. So there is some slip. So this velocity so it does not vary with y. So we can say that it is like u just a function of x from the inviscid flow consideration. So this is like that u which is a function of x. So no more it is a function of y from the inviscid flow consideration. So from here you can say that what is u as a function of x it is v0x by h. Which point? Inviscid flow how see when you are considering inviscid flow see what does the viscous flow do? See we have earlier discussed always keep this qualitative concept in mind. What does viscosity do? It propagates the effect of a momentum disturbance. So here you have momentum disturbance imposed by the wall. So if the fluid has a viscosity that will be propagated from the wall to the inside and it will in effect try to slow down the fluid elements which are close to the wall and as you go more away and more and more away from the wall the velocity will be more and more. So the velocity profile in that case will have like 0 value at the wall and then increasing away from the wall. But if you have no viscous effect then the effect of wall is not propagated in the fluid. Fluid does not know that there is a wall and therefore it tends to maintain a uniform velocity and that is why for an inviscid flow you have such a kind of uniform velocity profile. So when you have such a kind of a profile so you have this like you have u only function of x but not function of y. Very idealistic situation but like simple one to begin with. Now how do you find out v? So you know u. How do you find out v? So you have the continuity equation that relates you with v. So what is the special form of the continuity equation with rho equal to constant and it is a 2 dimensional flow. So when rho is a constant the first term the time derivative is 0. The next one is if rho is a constant so you have like this plus this that is equal to 0 for a 2 dimensional flow so w is not there. Rho being a constant it will come out of the derivative so it will be this equal to 0. Now so you know what is u as a function of x. So you can write the partial derivative of u with respect to x. What is that? v0 by h. So now you can integrate this with respect to y to find out how v varies with y. So if you integrate it what will you get? v equal to v0 y by h plus what? Maybe some function of x also. It is a constant of integration but since it is a partial derivative when you are integrating it you are integrating it partially with respect to y. With respect to that integral x is like a constant. So you could have in general a function of x. Within that there may be a constant. It may itself be a constant but for generality it is better to write it in this way. Now you can find it okay minus yes this is the minus and then this one. Now you can find out this with a boundary condition. So what boundary condition is there? At y equal to h you must have v equal to 0. This is no penetration boundary condition not no slip again I am repeating because it cannot penetrate physically through the boundary. So that if you substitute so minus v0 plus fx therefore fx becomes equal to v0. This means that you have v is equal to v0 into 1-y by h. So you can see here that u is a function of x, v is a function of y only. And see look at this equation you can do a mathematical simple mathematical jugglery with it. So the left hand side u is a function of x so this is a function of x only. v is a function of y so this is expected to be a function of y only and ironically you are getting a situation where left hand side is a function of x only right hand side is a function of y only. It is possible only when each is equal to a constant. Otherwise you do not have a way by which you can cancel x and y from both sides. So only way is you may get it as a constant. So there are I mean these are just ways of views of looking into a problem. It is not just a matter of solving a problem there are nice interesting concepts and remarks that you can get from a problem. Now the next is so we have got u and v acceleration is very straight forward. So how do you calculate the acceleration? Let us do that. So what is acceleration along x? This is acceleration along x. This we derived earlier. So it is not a 3 dimensional case so the w term is not there. So first of all it is u is not a function of time. So this is 0. Then you can just substitute what is u here? v0 x by h and so this will become v0 by h. The other term will be 0 because u does not vary with y. Similarly let us write the y component of acceleration again because v is not a function of time. This is 0. Then v is not a function of x. So this is 0 and here you have so v as a function of y. So what is v as a function of y? You have v0 into 1-y by h and what is dvdy-v0 by h. So you have final concrete expression for acceleration components along x and y. So you have acceleration component along x as v0 square x by h square. Acceleration along y-v0 square by h into 1-y by h and the acceleration vector is axi-ayj which is a function of both x and y. So this is the acceleration at a point. So if there is a fluid particle located at some x, y that will locally be subjected to that acceleration because locally the fluid particle and the flow behavior is identical. So you can clearly see that although the velocity components are not functions of time still you get an acceleration. That is what is the important implication that we get from an Eulerian approach because the entire acceleration component has horizon because of the convective component of acceleration because of the variation of velocity with respect to position. It is not because of change in velocity due to change in time. So we stop here today. We will continue in the next class.