I'll share my screen. All right, kinetic theory is going on. All right, thermal properties, exams next week. Okay, revision for exams. When is your exam, next one? Where is the next exam? 16th is physics. Is there any exam tomorrow? Tomorrow there is nothing, right? Starts on 1st of October, very good. Mute yourself. Who is Shri Devi Guttu? Is there anyone of that name in our class? Pradyun, okay, it's Pradyun. Is it that, that's your mom's name, is it? All right, I think you can't change it now. All right, so guys, we'll start, all right? Today, we have to complete this chapter and very little of this chapter is left and once this chapter gets over, we can get down to probably thermal properties of matter and you have your physics on 15th of October, right? 15th of October and till thermal properties is coming, right? In your exam, till thermal properties is coming. Okay, so I guess, till thermodynamics, till thermodynamics is coming. That's little too much. So what we can do at max that we could just finish up the thermal properties of matter, till that. So thermodynamics, you can do it your own this time round, right? Otherwise, we'll not be able to do anything properly. Whatever we do, we have to do it systematically so that it is useful for next two years, okay? Not just for your UTs, all right? So I hope all of you are agreeing to whatever I'm saying here and do you guys do the homework assignment? Like I receive not more than 50, 60% of students assignment. You can see every week we put it on the group, all right? So those who are not doing it, do it, all right? Start doing it, otherwise it will be a problem, right? So if you're not doing the assignment, please do not expect any marks, any good marks in the monthly test, right? It'll be an unfair expectation that you do not do what is required and then you are expecting good marks in the monthly test. That never will happen, okay? So if you want good marks in the exams, in the monthly exams, you need to do the assignments regularly, fine? And the chemon test is the coming Sunday. You guys are all aware of it, right? Coming Sunday is your main level test. I hope all of you are aware of it, okay, great. Anyways, so let us start this topic of the mechanical properties of fluids, all right? This topic may get over probably in two hours or a little bit more than two hours and once we complete this chapter, we will then look at the probably, we'll solve questions from this chapter rather than starting a new chapter today itself. Once this gets over, we'll be solving questions on it, okay? All right, guys, so this is the section. I will have to reshare the screen. So write down this, the first topic that we are going to discuss is viscosity, right, Tom? When we talk about viscosity, what comes in your mind? Honestly, what comes in our mind? The first thing that will come in your mind, very good. So this is the first thing that come in everybody's mind, honey, right? I'm sure that many of you would have thought about it. All right, so we associate viscosity with honey somehow, all right? Now what it is basically, it is a viscosity is a property, right Tom? It is a property in which we are talking about force between the layers, layers of it. So basically if we assume, if we assume a laminar flow, what is a laminar flow? In the laminar flow, the flow you can think the flow like this. I guess I might have discussed it earlier, but again, it's like when the liquid is flowing, it is moving in the form of layers, okay? One layer is moving relative to the other, okay? It's not that the entire liquid has the same velocity, same together they're moving, it is not like that, okay? Probably this layer has higher velocity than the lower layer. And the lower most layer could be at rest, okay? So there is some sort of shear deformation is happening. You discussed it last time, okay, great. So anyways, so basically, we are talking about this phenomena only for the laminar flow, in which we can imagine the flow as if it is happening in layers, layer after layers, okay? So in this scenario, the every layer, where down every layer will try to oppose, oppose the relative motion of the adjacent layer. This is the phenomena of the viscosity, all right? Now, this is just a phenomena and it is a property of a fluid. This property can be, you know, this property, viscosity is a property that varies from fluid to fluid. So the honey which comes in our mind the first time you hear the viscosity is a very viscous fluid. How can you say it is a very viscous fluid? You can see the way it flows. It flows very, very slowly, isn't it? Suppose you have a honey like this, there's a piece of honey and it starts moving like that. The layer below this top layer will try to resist its motion a lot. So it flows, ultimately entire honey will be flattened out on the surface, but it does very, very slowly, okay? So same thing is not observed with the water or with the oil, okay? It does vary quickly, yeah, previous slide. This one, copy it quickly. All right, so suppose I take this example, the top most surface is moving with velocity V, let's say, okay, and bottom most surface is at rest, okay? It is at rest. The reason why it is at rest because the contact surface, this is the surface which is in contact with the fluid, the surface is at rest, okay? So if the liquid has to make a contact with the surface, then at a point of contact, the motion between liquid and surface should not be there. So the point which is in touch with the surface will have the same velocity of that top surface, which is zero. So the bottom most part is at rest. The upper part is going with velocity V and let's say the thickness, okay? This thickness is, let's say L, okay? Now I have to quantify something related to viscosity, right? Now when you look at this kind of thing in solid, you will have shear modulus coming in your mind or modulus of rigidity, right? Which is what? Modulus of rigidity, you had defined it as F by A divided by what? Divide by X by L. You remember this? X is the displacement of the top most surface. Do you all agree? Okay, now here, when it comes to fluid, you know, when it comes to fluid and suppose this is a fluid body, you are applying force at the top most surface. Can you tell me how much X can be? Does X depends on the force which you are applying on top most surface or X will be almost the same every time, no matter what force you are applying? Everyone, X will always be same no matter what force you are applying or it will be different for different force you are applying because in case of solid, X was different for different forces you are applying at top most surface, talking about a shear deformation, right? In case of liquid, liquid will always, if you wait long enough, if you wait long enough, liquid will always take the shape of the container in which it is in. Or suppose you are putting it on the floor, if you come after a long time, you'll see that entire honey which was a square shape initially has flattened out and spread evenly on the surface. Same thing will happen with the water, same thing will happen with the oil. Only difference is that the spreading of water will happen lot faster than the spreading of the honey. Okay, but ultimately, the spreading if you calculate the, what is the displacement X? It will be as much as possible. So X will be same in all the liquids, okay? So the amount of displacement of top most surface, X, is same for all the liquids, right? So what we do is that, since we know that the rate of deformation is different, not the amount of deformation, rate of deformation is more relevant in case of liquid. All of you are able to understand whatever I'm telling here, a highly viscous fluid will not deform as quickly as a non-viscous fluid will be, okay? So how can you quantify the rate of deformation? This deformation I do not understand. They've got deformation is X, understood? I don't know, deformation is X or you can say no. Strain is deformation, strain is X by L. You can say this is my deformation. Amount of deformation in solid or in liquid doesn't matter. This is what the deformation is. I'm saying X by L, if you wait long enough, will be same for every fluid. The only difference is somebody will get deformed quickly, some liquid will get deformed later on. So rather than calculating the deformation, which is same for every liquid, I will worry about the amount of deformation. I don't know, that is a property of liquid. Liquid will ultimately take the shape of the container, amount of deformation will be same. But the rate of deformation, which is strain rate, if you differentiate it, it will become equal to one by L, DX by dt. Now DX by dt is what? Everyone, velocity, right? So it'll be V by L, okay? So this is the strain rate. So strain rate is more meaningful in the case of liquid, not the strain itself. Strain is meaningful for solids, not for liquids. Strain rate for liquids. So rather than defining the coefficient of rigidity for liquid, we are defining here coefficient of viscosity. Okay, which is what? It is very simple. It is stress, which is F by A divided by, rather than epsilon, I'll have D epsilon by dt. I'll have V by L. This is my coefficient of viscosity. It will be different for different flutes. Everybody understood how coefficient of viscosity is defined? What will be the units of coefficient of viscosity? Units of coefficient of viscosity. Tell me, unit of coefficient of viscosity. You can tell in terms of Pascal's also. F by A is Pascal's, F by A is Pascal. Velocity is meter per second. So it'll be Pascal's second. Numerator has L also. You can do a little bit of dimensional analysis. You'll directly get it, okay? Everyone understood? All of you understood, right? Okay, those who are joining, please mute. Now, what is F? F is what? What is F? Which I've written F here, what it is. F represents restoring force. It tells you the resistance. It is about the resistance. How much the top layer is getting resisted by the lower layer, okay? So this is what that force is, okay? Now, what if I take, let's say this much, if I take only L by two thickness, rather than taking L, if I take L by two thickness, okay? Then will I get the same coefficient of viscosity? Will I get this only or not? What would be my answer then? Everyone, rather than taking L, I take L by two, okay? I am comparing with this layer. Will I get different coefficient of viscosity? Should I get different or not? First answer me that. Should I get the same one or different one? Should it depend on the amount of thickness I am taking in a liquid? It should not, right? It should be same. It should be same because it is a property of liquid, right? It should not depend on how much liquid I'm taking. So, but then if you look at this formula of coefficient of viscosity, the way we have derived it here, instead of L, you will write L by two, because you're taking L by two length. So, the coefficient of viscosity will become half. I got a new formula. What is a catch here? What is a catch? Now, area remains same. The area remains same. It is a square thing. Area is on the top surface area. When you take the shear stress, you take the top most surface, right? L becomes L by two. Force is, see, what you got? Force is between the two layers. Any two layers, this is the force, okay? This F is the force between any two layers, which is same. F doesn't change. Then what is changing here in the equation? Yes, that is correct, Rubau. That is correct. V is what? V is basically relative velocity between two layers that you have considered, two layers that are considered. When you're taking the L, when you're taking the L length, the bottom layer has zero velocity. Top most layer has velocity of V. So, relative velocity is V only, okay? When you're taking L by two, when you're taking L by two length, the top layer has velocity V. Middle velocity is V by two. So, relative velocity is V by two. Are you getting it? So, L becomes L by two, V also becomes V by two. So, coefficient of viscosity remains same. Do you understand all of you? Please type in quickly. So, this remains unchanged, okay? All right, so I hope coefficient of viscosity is very clear. If I tell you coefficient of viscosity of a liquid, you can find out the force between the two layers, okay? And there are certain numericals based on it. So, let us see numerical on that. There is one numerical from your textbook only, which I'm sure you might have done it in your school also, but let's do it again. Anyone has any doubt, quickly type in. It's not opening up. Okay, anyways, here is the question, guys. All of you, I'll draw the figure here. I thought I could directly project it. So, you have a situation in which there is a mass over here, okay? And there is a pulley. Draw it with me, everyone. Do you do the school questions in the classroom itself, in the school classroom? Some of them, okay. See, sometimes now you have to prioritize what you have to do. You may have to wonder, should I do the school work? Should I do the symptom work? Should I prepare for the UT? Should I prepare for the monthly test? So, you know, you have to be mindful about it, okay? If you're spending X amount of time in your school, it requires three times more time than for the community exam preparation. That's how the wide it is. Make sure to do that. All right, so there is a metal block of area. There's a metal block of area 0.1 meter square, okay? It is connected to, this is a metal block, okay? It is connected to 0.010 kg, okay? Mass wire string that passes through the pulley as shown in the diagram, okay? There is a liquid, liquid of thickness 0.3 mm. 0.3 mm is a thickness. It is placed between the metal block and the surface. So, this red one is the liquid. The red color thing is the liquid, all right? Now, when it is released, everything is released, this mass is appeared to be moving with velocity of 0.085 meter per second, okay? You need to find out coefficient of viscosity of the liquid, okay? This moves with constant velocity. Yeah, you can say that this is Newton laws of motion. The entire chapter is a modified form of Newton laws of motion, okay? Metal block has, the mass is not given. For the metal block, the mass is not given, okay? Anyone close to the answer? All right, you know, there is a basic premise here. You guys should start, should continue solving question. I'll write here, every time we will not argue this, I'll write here that the assumption is, okay, Arabi got something, all right? Pascal seconds, Arabi. The liquid in contact with a surface moves with the surface's velocity. Okay, Rubau got something, Parvati got something. Yeah, something like that. Radhiyan also got it. Nobody else? No one else? Okay, so coefficient of viscosity is F by A divided by velocity divided by L. This is the formula, right? So, FL by AV, so F is what? F is the force between the two layers, any two layers, so that has to be equal to the T. Okay, the reason, what is the reason? If you draw the free by diagram of the metal block, okay? It will be getting pulled with tension T. It is getting pulled with by tension T. There is this viscous force. Why there's a viscous force? Because the upper layer is trying to move relative to the lower layer. Upper layer where it is, it is in contact with the metal. So, it tries to move with the metal. So, the layer just below it applies a force F and expression is zero. So, T should be equal to F, okay? And over here also expression is zero. So, MG should be equal to T. So, basically F is equal to MG over here. So, I can write over here MG into L. L is what? L is the thickness of the liquid. So, MGT divided by area of cross section into velocity. I can directly take the velocity of the movement that is the velocity of the topmost surface relative to the ground. Because thickness I am taking from the ground. So, A into V, which is given to us. So, MGT by AV, all right? This comes out to be 3.45 into 10 raise to power minus three Pascal seconds. Okay, everybody is clear about it. Nothing will happen, Siddharth. It is independent of it. All right, so now, you know, when we talk about the viscous flow or the viscosity, another very important thing that we will notice is the movement of object, right? The movement of object inside a viscous fluid. See, we know very well that if it is a non-viscous fluid, what will happen? We have continuity equation. We have the Bernoulli's theorem and we have many other things to take care of. There will be buoyant force, there will be pressure force and all that. But because now we have to consider viscosity also, it is a viscous fluid. There will be another force, additional to the buoyant force, gravitation force, pressure force, additional to all these forces. There will be one more force, which will be viscous force. Fine, and this is what we are going to include now. All right, and in the case of Bernoulli's theorem, do you guys all remember that we had assumed that the viscous or the viscosity is zero? All of you remember that, right? So, viscous and non-viscous, what exactly is the difference between viscous and non-viscous fluid? Rubber viscous fluid has some coefficient of viscosity, non-viscous fluid will have coefficient of viscosity zero. And if coefficient of viscosity is zero, look at the formula for coefficient of viscosity. If coefficient of viscosity is zero, F will be zero, right? So the force between the two layers will be zero. Or you can say that viscous force is like friction force between the two layers, okay? You know, you can treat it exactly like that. So if there is a relative velocity between the two layers, friction will be there in case of solid, right? Similar thing for the fluid also, okay? And when you are applying the viscosity, you are assuming that laminar flow is happening, okay? You are not taking a turbulent flow here, okay? Yeah, in viscous is like frictionless surface. You can say like that, okay? So now, focus here, everyone. Suppose you have a bucket, okay? A deep bucket like this. It is filled with a fluid, okay? Fluid is at rest. The fluid is at rest. Fluid is not flowing. But then suppose I drop an object inside it, okay? Suppose I drop some random object inside it, and it starts to move inside with certain velocity, okay? Because it's density is a lot higher than the density of the, density of the liquid and density of solid. Density of solid is very large compared to density of the liquid. So it starts sinking in, okay? Now, why it is sinking in? There will be a gravity force. There will be a buoyant force. And suppose it is a viscous fluid. Will there be a viscous force, everyone? Will there be a viscous force on this object which is sinking down? If yes, why? And how? How it get developed? Why viscous force is there? Don't tell him because it is a viscous fluid. Of course it is. It moves the layer as it follows. Good, right? Near the object, surface liquid has velocity, good. So yes, now you got the point. So the layers which are in contact with the solid, the layers which are in contact with the solid, these layers are moving with the solid, all right? So there is a relative velocity between the two layers. The layer adjacent to the liquid, layer adjacent to the layer which is in contact with the solid, okay? There is a relative velocity. What I'm trying to say is this, things are very simple, okay? This layer which is in contact with this surface is moving down. This layer is also moving down. But the layer next to it, this one, was not moving. This one is not moving, right? So there's a relative velocity between these two layers, okay? And because of that, there will be viscous force, all right? But if the coefficient of viscosity is zero, viscous force will be anyway zero, no matter there is a relative velocity between the layers or not. If coefficient of viscosity is zero, then it is zero. Anyways, all right. So now the thing is that there will be a viscous force. Can you tell me the viscous force on it, on the object that is moving inside depends on what? Depends on everyone? What should it depends upon? Of course, coefficient of viscosity, it should depend on coefficient of viscosity, all right? Second, what else should it depend upon? Should it depend on the mass? Should it depend on the mass? What do you think, everyone? Does liquid care about the mass when it is applying the viscous force? Does it really matter to the liquid? It doesn't matter, it doesn't depend on it, okay? So does it depend on the area of contact? Area, can I say area? So, you know, when you say area, it also depends on how the area is oriented, right? Whether you're talking about a sphere, a rectangle, a triangle, right? So I would say geometry here, geometry, right? What else? Okay, somebody said velocity. Will it depend on the velocity, everyone? Viscous force, does it depend on the velocity with which the object is moving? Everyone, should it depend on the velocity? Yes, it is, velocity of the object. Surface area and everything comes under geometry, all right? Now, over here, this eta is fine, okay? Eta is fine, coefficient of viscosity is called eta. This is a Greek letter. Eta is fine, velocity of object is fine, but this geometry, because of its dependence, because of its dependence on geometry, the viscous force will be different for different shape and sizes. Shape and sizes. So it becomes very difficult to create a formula that is valid for every shape and size. In fact, it is not possible, okay? So depending on every geometry, there will be a formula, okay? There was this guy called Stokes, all right? There was this guy called Stokes who had derived the formula for the spherical geometry. The viscous force on the spherical object. This guy has found out that, all right? So we will talk about the viscous force on a spherical object, which goes inside the liquid of coefficient of viscosity eta and with velocity V, all right? Surface area comes under geometry or shape. Everything is under geometry, all right? Can you tell me one thing? If velocity is increased, if I increase the velocity of the object, which is sinking down, will the viscous force increase, decrease or remain same? If velocity with which the object is sinking down, if that is increased, that is increased, then the viscous force will increase, decrease or remain same, everyone, it will increase, guys. Why it will decrease? Why it will decrease? Tell me the reason, tell me, tell me the reason. If velocity increases, the force also increases. You remember eta is what? What is eta? Coefficient of viscosity is fL by AV, okay? So if velocity is increased, f has to increase, right? So you can roughly say that, yes, if velocity keeps on increasing, viscous force keeps on increasing, all right? Everyone understand, right? Okay, so there was this person Stoke, who has given us Stokes law. What does it talk about? It tells us, it gives us the viscous force formula. Sorry, viscous force equation for a spherical object, a spherical shaped object, okay? Now that object could be hollow inside or whatever it is, it doesn't matter because viscosity, viscous force between the object and the liquid totally depends on what kind of surface it is, surface area, geometry and everything, okay? So Stokes law gives us the viscous force to be equal to this. All of you write down six pi eta r into v, okay? Where in your textbook, they have taken radius as r or a, let me just find out, they have taken a. So we'll write down radius as a, okay? So this is the viscous force between the solid, a spherical shape object having radius a, a is a radius, v is the velocity with which the object is going down, okay? So this is the viscous force only, okay? This is not the net force. Apart from this force, there'll be gravity and buoyant force also, all right? Now let us try to analyze what kind of motion it will have inside a liquid which is filled in a container like this, which is, you can say the height of the container is very large, infinite you can say, okay? So suppose this is a container, liquid has a density of rho, coefficient of viscosity is eta, this is the property of the liquid and you have a sphere, a metal sphere that is dropped inside, which has radius of a, okay? You can say density of this is sigma, sigma is large compared to the rho and it is a solid object so it will sink, okay? Now, while it is sinking, its velocity will increase or not? Everyone, initially while it is sinking, the net downward force is more than net upward force or not, everyone? So its velocity will increase, velocity will keep on increasing in downward direction, okay? As a by the way, viscous force is always, this is always opposite to the velocity, okay? It doesn't matter where is gravity or whatever it is, it only depends on which direction the velocity is, viscous force will be opposite to that velocity, which velocity it is, it is a velocity relative to the liquid in which it is moving, okay? Most of the time liquid will be at rest so you can say the velocity is velocity of the object only. So viscous force is opposite to the velocity. So now this velocity keeps on increasing. Now look at the expression of the viscous force. Will this viscous force keeps on increasing or not? Because velocity keeps on increasing, okay? It will keep on increasing. This is viscous force, okay? Apart from this force, apart from the viscous force, there will be two other forces. The forces are gravity, mg, and you have a buoyant force also, okay? Buoyant force. Will mg and buoyant change depending on how deep the object is sinking? Will mg and buoyant force depends on what is the velocity and how deep it is? No, it doesn't depend on it, right? But viscous force keeps on increasing. So can you describe the motion of it object when it is sinking down? Tell me, what can you tell? How does it move? Everyone, tell me about its velocity, how it will be? It goes down with constant acceleration. Somebody is saying, okay, acceleration is constant. Don't you see that viscous force? Don't you think that it will keep on increasing? Viscous force is increasing as a velocity is becoming more and more. It will fast at the start and then slow down. What is fast? Velocity is fast or acceleration is more? What do you mean by that fast? Initially, net force is in downward direction. Viscous force initially was zero almost because velocity was very less. So downward force was very large. When viscosity keeps on increasing, do you guys see that downward force keeps on decreasing because viscous force is upward? If it increases, net downward force reduces, okay? There will be a time that the velocity, velocity can become large enough, becomes so large, downward force becomes zero. Can it happen by the way? Can it happen? It will happen if the bucket you're considering is deep enough because before even reaching that velocity, suppose it hits the bottom surface, it will hit the bottom surface and stop, getting it. So if it is deep enough, there will be a time where velocity will be so high and viscous force will become so much so that net force will become zero. And if net force will become zero, what I can say about the acceleration? What is it? Say acceleration is what? Zero, it gives us constant velocity. This constant velocity which is slowly achieved in this process is called terminal velocity. After a long time, this velocity, constant velocity is reached. It is called terminal velocity referred as VT, okay? I want you to find out what is VT, okay? Viscous force is given to you and every other parameter is given. Mass M is not given, okay? You can consider mass M as density into volume. So can you find out what is a terminal velocity formula? Everyone, derive it, it is from your school, okay? Your school exam, this is one of the favorite question they ask. Let's say that velocity is VT. Just equate the forces at that moment. Net force becomes zero, so net downward force is equal to net upward force. Should I solve or should I wait? Everyone, okay. I'll give one more minute. Everyone get the answer. Very important for your school exam, if not anything else. Shethi's got something, others. You haven't done this in school? Not done. All of you have written this. Mg minus viscous force minus bow and fore should be equal to zero. M is what? The density of the solid into volume that is four by three pi a cube into G minus, huh, those who have got it, that is correct. Viscous force is six pi eta a terminal velocity is VT minus bow and force, which is rho times four by three pi a cube into G. In the bow and force you take density of the liquid, isn't it? So pi will get canceled away throughout. Then this will be two, this will be three, this is two, okay. So from here terminal velocity, you can see you'll get two by nine, two by nine a cube into G sigma minus rho divided by eta and one of the a's also gone like this, a square, okay. Oshik, we have done it. Derivation of bow and force, we have done it. Look at the first video of the fluid mechanics, okay. Everyone, so this is the terminal velocity, okay. So we had only, we have in our syllabus only a geometry of sphere to be considered, okay. For other geometries, we don't have it in our curriculum, okay. So only sphere we have learned in which we can find out the viscous force between the sphere and the liquid when the sphere is moving inside the liquid, okay. There is something called Reynolds number also that is defined with respect to the viscosity only.  Let's write down this Reynolds number. Yes, not buoyant viscous force. Okay, do you talk about a Stokes law? Derivation of a Stokes law? No, the derivation is not there, okay. It is empirically found. You can plot a graph and you know, it's not there. You just assume that this is the viscous force, okay. All right, so Reynolds number, there was this person. Name was Osborne Reynolds, okay. So in his name, on his name this Reynolds number is given. Now what does it indicate? Reynolds number will tell us this Reynolds number is RE. Reynolds number can tell us if the flow is laminar that is streamline or turbulent. Looking at the Reynolds number, you can tell that, okay. Now I'll just tell you the, you know, thought process beyond the Reynolds number then we'll discuss what it is, okay. First of all, you tell me if viscosity of some liquid is very high. Let's say I have, I'm telling you that I have two liquid, liquid one and liquid two. Velocity is same. The flow velocity, they're flowing in a pipe, okay, velocity is same. This one has coefficient of viscosity eta one. This has coefficient of viscosity eta two. Eta one is large compared to eta two. And I have told you only one flow is laminar. Which one that can be, which has higher viscosity or which has a lower viscosity, which has more chance of being laminar. That's what I'm asking here. What do you think? There's a split, I could have taken a poll but now it's okay. But Siddish, can you explain why higher viscous has more chance of being laminar flow? What is the reason? That you're saying that high viscosity implies that it has more chance of becoming a laminar flow. See, it is, if not laminar, consider viscosity as in separation is lesser, okay. Good. So see, if well, a viscosity is high. If viscosity is high, it means that the layers, they don't like to get separated. They want to move together, okay. They will try to maintain some sort of sanity in the movement. Together they will move. They'll not start moving zigzag manner, all right. Now you can imagine the, let's say in a pipe, water is flowing in one pipe and honey is flowing in another pipe, okay. And both the pipes velocity is very high. So now you will understand that the smooth flow will be there in the pipe in which honey is there, which has higher viscosity, okay. There is a chance of having a turbulent flow with the water because it has a lesser viscosity. So viscosity actually promotes the laminar flow because the layers will try to be together, okay. They will move in a defined manner, okay. Do you understand this logic, everyone? So good. So if viscous force is more, so viscosity is higher, more chance that it is a laminar flow. Chance of laminar increases, okay. Now suppose you have two liquids, liquid one and liquid two, which has the same coefficient of viscosity, but their velocities are different. Same liquid you've taken into pipes, similar pipes, their velocities are different. V one is more than V two. Where is the chance that laminar flow will be happening at higher velocity or at a lower velocity? Lower, right, lower. Okay, so this is very clear. So if velocity is lesser, then the chance is that it become laminar will be higher, okay. So you have two things to look at. You have viscosity to look at and you have velocity to look at, all right. You cannot just look at the velocity and say that it should be a turbulent flow. What if viscosity is very high? Then there's a chance that it can be a laminar flow. And at the same time, you can't just look at the viscosity and say that viscosity is very less. So it will be a turbulent flow. What if velocity is very less? There's a chance that it can be laminar. So it becomes complicated to look both, right. So that is the reason why both of these factors are combined together. Both of the factors are combined together and Reynolds number has been put forward. When you look at the Reynolds number, you're accounting for both the variables together, okay. So it is, you know, as good as, suppose you have to look at a variable X also, a variable Y also. What you do is that you define a variable Z which is equal to X by Y. And rather than looking at X and Y separately, you just look at X divided by Y and depending on that you can say. So whatever it is, let's discuss it again here. So Reynolds number is basically a ratio of, it is a ratio of the inertial force right down by viscous force. I'll come back to it. First write it down, viscous force. It's a ratio between the two forces, okay. Inertial force represents velocity in a way. Viscous force represents coefficient of viscosity in a way. Okay, so in a way you're taking the ratio of two things and it will be dimensionless, no dimension or no units. Okay, now what is this inertial force and what is this viscous force? Inertial force is simply, you know, it is rate of change of momentum is inertial force. Simply put, ignoring the viscosity, it is rate of change of momentum. Now, how do you find out that? If you consider a pipe in which liquid is flowing, let's say if liquid is flowing with velocity V, okay. Then DM by dt is what? DM by dt we have found out earlier, last class only, rho A V. All of you remember this, DM by dt? Everyone? Okay, so if velocity is constant, V DM by dt is your rate of change of momentum. Rate at which momentum is changing is rho A V square. Clear to everyone, this is called the viscous inertial force, sorry. This is the inertial force, rate of change of momentum. Okay, see I'm telling you how it is derived. I could have directly written, but then I thought I should tell you that's the reason why. Now the viscous force can be written in terms of eta. Okay, eta is F by A divided by V by L. All right, so this is F L by A V. So the viscous force can be written as eta A V divided by L. So all you have to do is to take the ratio between the inertial force and the viscous force. You'll get the Reynolds number, okay. So Reynolds number, if you take a ratio rho A V square divided by eta A V by L. So Reynolds number will become equal to rho V L by eta. All right, and if the pipe's diameter is D, if the diameter of the pipe is D, you can write the Reynolds number as rho V D by eta. Okay, now this is a variable which you can use to find out whether the flow is laminar flow, streamline flow, or it is a turbulent flow. Anyone has any doubt in this derivation that we have done quickly? Tell me, by the way, this is there in your textbook, okay. It is there in your textbook under Reynolds number. Somewhere hidden, you just have to read it carefully. Type in quickly, have you understood this? Okay, then all right, so this is a number. Okay, why it is called number because it doesn't have any units. So it is found out, okay. It is found out that when Reynolds number, wait down, that when Reynolds number is less than 1000, it is a laminar flow. When Reynolds number is greater than 2000, it is found to be turbulent in nature. This is turbulent flow, okay. And Reynolds number between 1000 and 2000. Don't ask me exactly at 1000 what happens, exactly at 2000 what happens, okay. It is, it gives you a range, okay. It is, it's not that a very sharp line is there, that one point this side laminar, one point that side turbulent. It doesn't suddenly transition. Just give you an indication, okay. So Reynolds number between 1000 to 2000, it is a transient flow, transient or you can say unsteady flow. The flow is getting transitioned from laminar to turbulent. It is, you can say half laminar, half turbulent, something like that you can say, okay. These ranges you should remember and this is true every time. This is true, not just the flow in a pipe, this is true for any kind of pipe. Let's say you're considering a pipe which has, let's say cross-section like this, a square cross-section and water is coming out through it. All right, so you can use a Reynolds number formula, rho VD divided by eta and find out the Reynolds number, okay. What you'll take D as if you have certain irregular shape, let's say hexagon is there instead of circular cross-section. If there's circular cross-section, you will take D as diameter. But if it is not, then what do you take D as? If it is not a circular, then what do you take D as? Then you'll take D as hydraulic diameter. It is given as four times area of cross-section divided by perimeter, okay. Four times area of cross-section divided by perimeter. In case of circle, it comes out to be two R, which is diameter only, okay. In case of any of the cross-section, you can find out hydraulic diameter to be equal to four times area of cross-section divided by the perimeter, all right, and use that over here, fine. Anyway, so there is a numerical on whatever we have just done. Let us take that from your textbook. Anyone has any doubt, quickly type in, meanwhile, why we use diameter again? See, it is not that you have to use diameter, only you could have used radius. Then Reynolds number range will be different. Reynolds, if you take radius, Reynolds number range will be less than 2000, greater than 4000, okay. Just that we have assumed, let's take diameter. Then the numbers will be changed accordingly, all right. That is not required, a shortage, that discussion is not required. Just take it as it is, hydraulic diameter. You learn that in engineering, this is flutes. But any, that hydraulic diameter is anyway not part of your curriculum itself. I thought I could just tell you because you might be wondering what if the cross-section of the pipe is not circular. So just additional information. Okay, I want you to solve this, solve this question. Okay, do it completely yourself and do it. All of you should do it. You will see the kind of calculation errors probably that could creep in. You need a lot of practice in calculation itself. Forget about the concepts. It should be good with numbers. So I'm seeing that a lot of you are making silly errors in calculation that require some practice. Are there any liquid with zero viscosity? You can say near zero, okay, some of the oils. But yeah, that is an ideal scenario. That doesn't happen naturally. Basically they're asking you whether the flow is laminar or turbulent. So first tell me the Reynolds number. You can modify the equation of Reynolds number in terms of flow rate also, if you want. Anyone close to the answer? Okay, Harabi got something. Others, did you get any notification from school reopening? As in physical classes? Do you want school to get reopened? No. Except start at 10 a.m. Now it will be very difficult to wake up early and attend the classes, travel and attend the class. See the main problem you guys face is that you have not seen the hard work which is required along with school managing the symptom and the comedy exam becomes more difficult for you. Okay, because you're anyway complaining that the time is very less. Now when school starts, travel is there. You get tired also. So you're not used to that kind of rigor. So probably that may have some impact. Anyways, Reynolds number is four times. See, I have modified the Reynolds number formula in terms of flow rate. Do you all see that? Why have modified? Because flow rate is given to me. Isn't it? That's the reason why. Density is thousand. What should I write instead of q? I have to write in meter cube per second, right? So 0.48 into 10 raise to power minus three that is meter cube. This is per minute. Per second will be divided by 60 into pi into eta that is 10 raise to power minus three into dia that is 1.25 10 raise to power minus two. Anybody calculated this? What is this equal to? See, do the calculation yourself.  Do not look at the textbook and all that. It's very easy to fool yourself, okay? And make you believe that, yeah, you got it. Do it yourself. What is the answer you're getting? Even if you get the wrong answer, it is fine. It is, at least you've tried it. Calculate this quickly. All of you, let's see how well you can deal with the numbers. Everyone, all of you understood, right? How it comes, no one has any doubt in that. Understood, all of you, this is understood, right? Whatever I've written, okay, get the answer. You want me to solve? Parvati got something, Arrabbi got something. Nobody else got anything other than these two. Anyways, 10 raise to minus three is gone. One zero is gone. It's 12.8, is it? It is 12.8, that less. What can it be? 81.56, Gurman is saying, okay? So this is four into 48 into 10 is part two divided by six pi into 1.25. How much it is equal to?  You're not able to, everybody's getting different if I answer. This is very bad. It will impact you during the exam. All right, anyways, so this will be 815.2, roughly. If you do your calculation properly. So you can be proud of yourself, look at this. You're not able to multiply or divide, add, subtract. It'll not lead you anywhere. So make sure you are practicing a lot of calculation here and otherwise someone come from grade five will beat your hands down because of the calculations only. All right, so this is the Reynolds number. So this is laminar or turbulent? Everyone, laminar or turbulent? Laminar, it is less than 1,000, right? Now, if the flow rate is increased to three liter per minute, what will be the Reynolds number then? Do we need to calculate it again all over again? Reynolds number will be what? If the flow rate becomes three liter per minute. Do we need to calculate it again? Everyone, what should you do? See Reynolds number is proportional to q, right? Proposal to q. So three divided by 0.48 times 815.2, like this you can do. So 0.48 flow rate, Reynolds number is 815. So for three flow rate, it'll be three divided by 0.48 into 815.2, okay? So it is roughly six times of the earlier this thing. So Reynolds number will come out to be around 5060. Okay, 5175.5, okay? 5175.5. Now, this is a turbulent flow, right? So if you increase the flow rate to this much, your flow will become turbulent, okay? Anyone has any doubt on the viscosity, whatever we have done till now? Typing quickly, is it clear to everyone?


I was kind of hoping that there wouldn't be a ton of people, not because I didn't want to speak in front of a lot of people, but I was thinking about this, you know, I got such a positive response, the idea of this talk, and it sort of broke my heart to think that that many people might really be that burned out and I really need this. So you know, I'm not a super experienced speaker, I really hope that I can do this topic justice, because it seems like something that a lot of people need to hear about. The bad news is that I'm not a self-help guru or a motivational speaker, a licensed clinician, any of those things. I don't really have any official capacity to tell you how to relieve your stress. What I do have is some common sense, some stories, a little bit of advice from my own stories that I think might help. But I have this feeling, you know, if you're here and you're already identifying as being burned out, you probably already know what you need to do to change that, but sometimes it just helps to hear it from someone else. So I hope that I can help. If you're here at JangoCon, you're already a part of a really thriving community. It's a very active community. You're already, you know, part of open source, so you used to give me your time and energy very freely. Well, why we do that is probably a topic for another talk at another time. I know that most people that I know outside of open source don't get it at all. You know, we give all of our free time. We work a lot in our free time where we, you know, there was a tweet that I saw from PyTex this weekend about leaving, you know, to go off on your Labor Day holiday weekend to go and write more code. That's what a lot of us do. And maybe it's so that you can improve your programming skills or make some new friends, take part in this community and meet really amazing people. There could be a lot of reasons. Maybe you're just drawn by the energy and excitement of all the knowledge share that we do. Those reasons have really been discussed and discussed and dissected. And, you know, I don't really know. One thing that I do know is that we all have this very common passion. Everyone's very excited and they love what they work on. But that passion has to have limits. I think we've all discovered that at some point. So I'll start by telling my story. A few years ago, probably three, four years ago now, I just moved to Austin. I started and finished one contract job and then started another permanent job. I started a relationship. I was blogging or trying to. I had just begun doing Young Coders, which is the kids' Python class. And we teach at PyCon. I started developing that. I was teaching beginner Python classes here and, you know, and all over at small conferences around the South. I had gotten involved with the local CSTA, that's Computer Science Teachers of America. I was volunteering with them to try and help, you know, work to improve local computer science teachers in class or computer science classes in classrooms here in Austin. I was volunteering with a local program, Central Texas Discover Engineering, that brings technologists into classrooms to speak and to teach and kind of get kids excited about STEM. So I spent a lot of time doing that. In between all of those things, I was doing some technical review. I had a couple of friends that were doing Python and Django books. I was spending a lot of time reading. And I founded the PyLadies chapter here. So I was spending a lot of time doing meetups in classes to try and get that group growing. So as you can imagine, I was stretched to my limits pretty much. I was really exhausted most of the time. My relationships were suffering a little bit. My friends and relatives, I was not seeing very much of them. I started developing some health problems, which I will never go into here. I was traveling, sure, but the only travel that I was doing was for comrises. I used to joke that I was seeing the world, one PyCon and DjangoCon at a time and not much more than that. It started to take time away from my actual job, the day job that pays the bills. I was not getting to do any of the things that I love outside of programming. And so after a while, after a couple of years of this, I started to really dread every meetup, every class. My God, it was like pulling teeth, dragging me out to a meetup two, three nights a week was awful.  I was very involved, and I didn't want to. I really wanted to run away a lot of days. So it took a couple of years of this before I realized what I had to do, and that was just to scale back. I handed PyLadies over to some other very capable women here in Austin, and Inda's continued to grow to this day. It's been really amazing. I cut my teaching schedule back very dramatically. I stepped back from all of that volunteering, which was heartbreaking. It was a real shame, but I've been able to get some other people involved in my stead, and I started saying no to a lot of requests for my time. And eventually, things got sane. Things calmed down, and I was able to breathe again. So we know that burnout really is a result of long-term exhaustion. And everyone can have a busy day now and then or a busy week. So just when those weeks start turning into months and years, and you're doing the same thing, and you're struggling to get it all done, and you're taking on more over and over, you're being spread too thin for too long, and the result starts to feel a lot like depression. You start to dread what you're doing. It gets hard to get up out of bed some days, knowing what you're going to be facing. So it should surprise no one that that kind of thing can lead to really terrible performance. But what I think a lot of people don't realize is what a serious health toll it can take. Every time I open a browser, I see more news about new stories, new studies that are being done about the effects of overwork on the brain and the body. It's pretty scary stuff. Oh, by the way, the links in these slides. I'm going to post these slides to my blog, mechanicalgirl.com, after this. And there are going to be links. So you can actually read some of these articles in depth, take a look at these studies and see the kinds of things I'm talking about. So when you're juggling your day job and your open source work, and your personal lives, usually the first thing that gets sacrificed is sleep. I know that's true of me. I was at one point sleeping maybe two or three hours a night. It was scary stuff. So I wanted to talk about some of these articles that I found. So this one up here, this UC Berkeley thing that was posted in this episode back in July. This is actually a reference to the study over here from the Journal of Neuroscience. It's a very formal study conducted by UC Berkeley. I just really loved the sensationalist headline. When you're overtired, you perceive friends as enemies. And it kind of got me thinking. I wonder if that's where flame wars come from. People who love each other and respect each other suddenly find themselves at each other's throats when they're under the pressure of trying to get a pull request in. And then also, you guys know the XKCD cartoon. I can't go to sleep yet. Someone's wrong on the internet. Well, what if they're not really that wrong? What if they just seem wrong because you haven't gone to sleep yet? So there's that. And then this one over here, this is an article from mic.com from last year. This actually came accompanied with a really great infographic. It was too large to put in a slide here. I think you would not have been able to read it even up on this big screen. But I can give you some of the highlights. Sleep deprivation can lead to things like hallucinations, cerebral shrinkage, lost memories, false memories, lost focus. I think we're all pretty familiar with that. And ultimately brain damage is something that you can suffer from. But one of the stories that really caught my eyes, this last one here from NPR back in May, it's actually a story about another sleep study that was done by the University of Washington. One of the examples that they cite is the Exxon Valid Ease Crash. Now that happened back in 1989.  By some estimates, there were something like 40 million gallons of oil spilled. Hundreds of thousands of animals were killed, including orcas. There were a couple pods of orcas that were decimated. There were seabirds, seals, sea otters. I deliberately did not get any photos from the disaster.  I just couldn't do it. These are very happy, alive seals, not covered in oil, but in water. I just want to point that out. But yeah, I mean, the fact is this disaster had a lasting impact on Prince William Sound. 26 years later, there are still thousands of gallons of oil in the water, in the sand. Most of the animal populations have not recovered. There was an entire oyster bed, I think, that was wiped out, that has started to come back, but that's about it. And I remember, I was in college at the time, I remember the rumor that was going around was that the captain of the ship was drunk and that he ran the ship aground. What came out later was that the captain wasn't even there. He was not at the helm. It was the third maid who had been up and working steadily for 18 hours at that point. And he was not the only one. The crew was accustomed to that kind of sleep deprivation, working 18-hour shifts and getting a couple of hours of sleep and then going on again with no breaks, no weekends. So they were pretty overworked. And the result of that was this huge environmental disaster. So it kind of made me wonder, I know people who have stayed up as long as 18 hours hacking on a project. It's not that uncommon, especially when you're young and eager and new to the community. It made me wonder, imagine working for that long and that hard and being that tired and your open source project crashing like that, what a disaster that could be. Not on the same scale, obviously. I don't expect that you would kill animals, but really giving your most tired self to a project is not good for that project. The people that you're working with, the people that are working around you deserve better, you deserve better. Your self-care is so much more important than getting that next line of code written. Sometimes you just need to step back and refresh and then come back to it with a new passion and if you're not going to do that for yourself, please do it for the otters. So if you take nothing else away from this talk, remember this phrase. This is probably the most important thing that I can tell you. When it comes time to recover, the first step is to simplify your life. You need to spend some time thinking about what it is that you really want. Do some soul searching. Make a list if you have to. Figure out what are the things that are really important to you? What's fulfilling to you? What's giving you joy? What are you doing that is really bringing you fulfillment? And if the answer is none of these things, well, maybe it's time to start jettisoning those things and look to something new. Or keep the one thing that you find that is really important to you. When I was feeling burned out and I needed to shed all of those projects, the one thing that I held on to was young coders. Because I started out my career as a teacher and teaching kids and teaching them programming is the one thing that I love the best. So that is the only thing that I do these days, aside from occasionally speaking, obviously. I focus on teaching and I develop curriculum and that's it. I say no to everything else. And there's one thing that I wanted to point out to you, another important point. When you are evaluating what's important to you, whatever you do, please do not compare yourself to other people that you know in this community. We all know someone who seems like they have a hand in every project. They're doing all the things. And you can't possibly know what they're going through behind the scenes. You have no idea if they are fulfilled or if they're struggling. So don't judge yourself by other people's contributions and other people's performance. Just focus on yourself and focus on what you want out of life. And I think ultimately you'll be happy. And then once you've made all those decisions and figured out what you want, get ready to start practicing this phrase. If you are overloaded and someone asks you to speak at a meetup, you can always say no or actually better thanks, but no. Be polite about it, firm but polite. If someone asks you to teach a class, same thing, you can say no. Then if people want to contribute to their project, and I know this is hard because everyone wants to be involved in these code projects. But if you're overloaded, you can say no, and it's okay. I'm giving you permission. Maybe you're worried that someone might be upset if you say no. And it's possible, that can happen. But if they are, anyone who's gonna be angry at you for turning down an offer or saying no to something is someone that is not worth your time, trust me on this. I think your mom would agree with me. And sometimes no just means not saying yes. You don't have to respond to every letter or every tweet that comes your way, every email. Sometimes just listening in on the conversation is enough. You don't have to participate. In fact, this is something that I feel really strongly about. I think that it took me a while to realize that any unsolicited email that I get really is just a big ask for my time that I didn't agree to. And it takes a lot of time. We want to be generous, we're conditioned to be generous with our time. But really, at the end of the day, you don't owe anything to anyone. You don't have to answer that email if it wasn't something that you agreed to do. But note that I said unsolicited. I mean, if you're organizing an event or you're leading a project, you've kind of implicitly signed up to deal with those things. And so those emails that come your way, they are for you. But that's something to keep in mind before you make your next commitment. Remember that those are the kinds of things that you're going to be burdened with and so maybe you don't want to commit to that project or that event, just, and also as I check my notes here. Saying no isn't a license to flake either. Do the things that you say you'll do.  And you'll be a happier person, I swear. And those people that all seem to be doing all of the things, there is one thing that you can learn from them. They're very good at delegating and asking for help. The irony is not lost on me that everyone here is at the start of a conference, the start of DjangoCon, you're going to be exposed to a lot of new ideas and projects and you're going to want to get involved in all of them because they are all really cool. And you don't necessarily have to say no to all of them. Just, I think my best advice to you is just to be judicious. Guard your time carefully, be judicious with your commitments, really evaluate whether or not this project is going to be something that you'll enjoy or that you can offer something to you or that will be good for you before you jump in. You don't necessarily have to say no to things, but you might have to relieve yourself of some responsibilities before you take on new ones. And I have a couple of examples. So the first step towards giving yourself a break might be just mentoring someone new. So I have a story. Over this past year, I've been traveling a lot, doing a lot of conferences, and I've talked to lots of other women who are tech speakers. And I found much to my core that there are some of them that are traveling around the country, break next speed, doing as many as 15 to 20 conferences a year. That is no way to live. But right now, there's a big push in the community, in all of open source, really, to increase the visibility of women. And that's a very admirable thing. The problem is that these same 10 to 15 women cannot be doing all of these talks. So I think maybe we need to mentor some new ones, do some teaching, bring some people up and get more people involved and get more people talking about their experiences that are women, specifically. And then the same thing goes for that code library that some of you out there have been maintaining for many, many years.  But maybe you've convinced yourself that no one else can do that job. As well as you can. Well, I have some news for you. There are a lot of fresh faces and a lot of developers in our community who just really want a chance to stretch and grow. And they just need that chance to get in there and get started. What's old hat for you is going to be very exciting for them. And they might make a few mistakes and they might stumble a little bit. But they'll be all the better if you spend the time to mentor them. So reach out to your user groups, reach out to mailing lists, find people who might be interested in filling your shoes. If it's something that you really want to get rid of, bring some new blood in. Don't be afraid to do that. And then hand the job over.  You're gonna be able to take a deep breath for the first time in a long time. And it's gonna feel really, really good. No, I have another great anecdote here, this is terrific. So something to remember if you're the one asking for help. Over the summer, I was at a party in Brooklyn hanging out with some other developers. It's pretty much the only people that I hang out with these days. It was a different community, different language altogether. But I was spending some time with some other people who are also very, very sought after speakers. And they had some horror stories to tell me. They get so many requests to come and speak at these conferences that they've had to start making excuses. They have to start lying about having personal commitments or a death in the family or something else that they have to do to avoid saying no. Because just saying no has stopped being enough. Applied, thank you, but no, I just don't have the time. It's not cutting it. There are some organizers out there that are actively hostile. And being like, well, so you'll do so and so's conference, but not mine. Well, nah, nah, nah, nah, nah, you know? And it just, it drove me crazy. I've never experienced that. And I couldn't imagine someone being that mean. But the point that I want to make is that if you're that person doing the asking, just be very careful that you don't cross over the line from being welcoming and encouraging into pressuring and bullying in some cases. Don't do that, please, please don't be mean. And by the same token, if you find that you're in the position where you're being pressured to contribute to talk or contribute to a project, you can push back gently but firmly. Some people may not know that they are putting on that much pressure until you tell them. So finally, we get to the good part. There are actually some things that you can say yes to. Once you're clear your plate, there are a lot of things in life that are out there to enjoy. You can go outside, for example, your inbox can wait. No, no, no, sorry. That outside, that's the one that you want. It really is that beautiful sometimes. The point is though that when you let go of all those things that are weighing you down, you can go out and take on the things that you really love. And this is just a quick sentence cloud that I put together with a handful of things that I enjoy doing that have nothing to do with code. I'm sure you can think of hundreds more. Make a list and work towards that. And then finally, I know, I know, this is probably one of the most annoying acronyms in the history of humankind. It's been used to justify a lot of obnoxious behavior and I felt really bad about including this. But if you think about it, there's a kernel of truth there. You only get one life and you really owe it to yourself to make the best of it. And that is it.


Let's talk about trigger Properties of triangles Some of the angles in a triangle is 180 for any triangle some of the angles in a triangle is 180 degrees The only triangles you like this pizza. No, I'm pretty sure you like other things other triangles For sure triangles come into play everywhere Do you like music? Trigonometry, do you like light shows trigonometry, right? for right-angle triangles a bc Keep in mind there's six pieces of info in a triangle Pieces slices aren't triangles They're sectors of a circular circular technology But they are related to triangles because triangles are related to circles, right? So triangles definitely are related to pizzas because if pizzas come in circular sizes They're circular shape, then that's trigonometry as well, right because and The unit circle the way we find ourselves in a coordinate is through triangles Right the triangle is also the only shape where the sum of the angles are 180 Every other shape is 360 for this reason triangles have more structural integrity They have and they're that's why you have tripods like tripods are stable more stable, but with triangles Triangles are the building blocks of all polygons Right. It's like the prime factors of polygons or triangles. For example, if you have this Here's a polygon, right? What's the sum of the angles of this polygon? Right That's your hydro Right. Well break it down into into his prime building blocks. It's just the same thing as H2O H2O is H2 and O and H and H right the building block of H2O is HHO The building block of 12 is two times six and two times three Right The building block of this is One triangle Two triangles Three triangles one two three sorry four triangles, right? So there are four triangles that this How many shapes sides one two three four five six six sided polygon is made of right Well, what's the sum of the angles in this triangle is a hundred and eighty times six Right you can break all polygons into into triangles and then from there You can work out their angles or whatever it is if they're regular polygons. This is Not to scale not regular polygon, right? So triangles are your smallest building block of a polygon. That's why they're super important one of the other reasons They're super important, right So take a look Let's kill this as well Triangle has six sides or sir six bits of information Why times six? Did I say times six or did I say times four? Oh, I should set times four poop. I made a mistake That was a brain for it. That was a chicho brain for it. That should have been a hundred and eighty Times four there was four triangles, right? Gotcha. Yeah chicho brain for correct my brain for its police Okay, I make I end up making because I'm mentioning other numbers and other numbers all of a sudden enter the My calculations oops don't do that on exam. Don't do that on homework, right? There's six pieces of info in a triangle, right three sides and three angles and an angle controls the opposite side So this angle This guy controls it. So we're gonna call this capital B So this angle is called capital B and it controls small case B side, right? this angle We're gonna call a because it controls this side and this angle we're gonna call C because it controls that side Let's put the a here too. So we're consistent, right? So this angle controls this side this angle controls that side that angle controls that side Okay The smallest angle controls the smallest side the medium size angle controls the medium side and The largest angle controls the largest side if you got a right angle triangles the 90 degree angle is the largest side Hence C is your longest side Okay, and don't forget gang Free as such free as such free as such Julian Assange is a publisher and journalist that has been crucified for trying to Try to bring transparency and accountability of capital's power to humanity Support him Right. So in a right angle triangle, we have the following other relationship as well Which is the Pythagorean theorem, right? We got one relationship Angles in all triangles equals 180. Hello Mac 650 For right angle triangle, we have the Pythagorean theorem, which is a squared plus B squared equals C squared That's the relationship that exists between a B and C Okay, and C is your hypotenuse. So the two legs of a triangle squared add it together equal the hypotenuse squared That's another property that we have There are three other properties of a triangle Features of a triangle right angle triangle that we also deal with we should call the trig important ratios Right, so three trig Ratios ratios Right, which are sine of an angle is equal to the opposite side divided by the hypotenuse Coase of an angle is equal to the adjacent side divided by the hypotenuse 10 of an angle is equal to the opposite side divided by the adjacent side Okay, those are the properties of a right angle of the trig ratios adjacent side Mac I never like math. Do you suggest a book that makes you like math? Maybe? It really depends what you're into Mac. What's your interest in life? No matter what your interest is in life Mathematics can relate to it All right, if you're interested in business look into mathematics of investing and stuff like this if you're interested in music look into Mathematics of trigonometry really frequencies waves and stuff like this if you're interested in engineering There's tons of books out there and engineering If you're interested in pure mathematics, just look at the algebra as problem-solving Right, we just had a problem. We just did a problem where It was complicated. It was cool, but together we're able to solve a problem So if you like puzzles mathematics is the place to be right So what do the trig ratios mean? ratio is something Compared to something else now remember yeah, there's a difference between a fraction and ratio fraction and ratio The difference between a fraction and a ratio is this I can give you the following Two over three. What does two over three mean two over three means part of a whole Interesting investing yes, I like the math and finance, but it's simple compared to you are explaining on advancement. No Financial mathematics investing can be extremely complicated Some of the most complex mathematics ever done have been in the realm of Investing personal finance right you can start off with some simple stuff But it can go into very complicated stuff mathematics is a tool You can build a shed in your backyard or you can build a skyscraper Right if you want to do a comparison mathematics is limitless And you can apply it into extremely complex levels on any topic Even art like paintings and stuff like this hues of colors and play around with that stuff Fraction two over three is part of a whole so if I have a whole thing I break it into three pieces I'm gonna eat two of them Two out of three right Two parts of a whole. Okay. Thank you. Sorry for no no worries Mac, right as far as math books again Nothing really comes to mind I have certain math books that I've used to learn certain topics If I write down a ratio two over three Ratio two over three is a comparison of two or more things so two over three if it's a ratio it means two circles versus two triangles Okay, it's a comparison right Two versus three Okay Keep that in mind. So these Trig ratios are not fractions. They're ratios. It's a comparison of one thing to another thing Right, and what are these two things comparing? Well the formula tells us what it's comparing It's saying that the sign of an angle, right? the sign of an angle is Equal to the opposite side of that angle Divided by the hypotenuse of that angle of that triangle, right? So I'm gonna erase this part So trigonometry says this if I have a triangle Like this Right right angle triangle and these only work for right angle triangles. Okay. They don't work for non-right angle triangles If this is my theta the sign of theta is the opposite side Opposite divided by the hypotenuse So what does this mean? The ratio why is this important? Well, it's important because of the following if I say that Let's assume. This is 30 degrees right and This is a right angle triangle and let's assume the hypotenuse of this is five Right. I want I want to find this X Okay What I'm gonna do is say Use this formula to find X. This is an absolute It means that for any triangle Right So let's find here. Let me just tell you what sign of 30 is sign of 30 degrees If you punch that to your triangle, you're gonna get this. There's a special triangle called this 30 90 60 1 root 3 2 if you punch in sign of 30 You're gonna get 1 over 2. It's equal to 0.5 Okay Really right here, we're gonna punch it in let me punch it in make sure I didn't do any brain farts here 30 degrees and you're gonna go Sign of that is 0.5 right So sign of 30 degrees is 0.5 Now sign of 30 degrees is not 0.5 Just for this triangle or for this triangle sign of 30 degrees is 0.5 for any Any try no matter how big it is how small it is.  Yeah, a lot of people right? So if I give you a triangle like this I Say this is 30 degrees and I ask you what the ratio is between this side and this side You will tell me that it's 0.5 The ratio of this side. Let's call this the opposite side and let's call this a hypotenuse The ratio of this divided by this opposite over hype Is equal to 0.5. That's what I wrote down here by the way. Where is it? Right, so if you have one of these you can always find the other one so If the hypotenuse is five you just put five here oops Then the opposite side is going to be 0.5 times five which is 2.5. So we know this is going to be 2.5 So the ratios the trigger ratios are an Absolute for specific angles. It's the relationship of one side of a right angle triangle Relative to the other maybe adjacent versus the hypotenuse Opposite versus the hypotenuse or opposite versus the adjacent it could be this divided by that that divided by that or this divided by that Or it could be this divided by that that divided by that or that divided by that There's six different combinations you could do with this right and That's what the trigger ratios are They're not Some people think these are magic. They're not Right, it's just a way of saying instead of saying what's the really? What's the ratio between the opposite side of an angle and it's hypotenuse? That's the definition of sine theta but that's Too long right as I've said before mathematicians are some of the laziest people you'll find and They try to simplify things and they end up calling these things sine cosine and tangent Where they got those names wrong haven't looked into the history where the name came from I Hope that's clear. Is that clear does that make sense? Would you like expanding on that I Forget who was asked that Trigonometry I'm just going up to see who asked about the Triggs Trig ratios and by the way if you already have The opposite and the hypotenuse so let's assume you have a triangle here Let's erase this Let's assume you have a triangle You already have the two sides or two sides are trying to compare. Let's assume you have this is six and this is 15 and you want to find angle theta well You want to find this angle and The two sides that you have is this and this Remember if this is not 90 degree triangle you can always find this just using a Pythagorean theorem, right? But right now we don't care if we're trying to find theta So if you're trying to find theta What am I looking at mathematics if you're trying to find theta? Well, what sides of this triangle do you have?  Oh, we got this one opposite and hypotenuse. So just fill in the blanks So you got sine theta is equal to six over hypotenuse is 15 right So how do you isolate? Now the only variable you need to get by itself now is Theta and the way you isolate this on your calculator you got something called second function of the sine sine inverse So the way you separate the sine and the theta you got theta is equal to sine inverse of six over 15 and if you punch that in you'll find out what the angle is and that's the ratio of What the opposite side is relative to the hypotenuse of This angle and if you punch that in here, let's punch it in six divided by 15 and you go Trigonometry second sign is 23.6 degrees So theta is equal to 23.6 degrees. So any triangle that has an Angle any right angle triangle that has an angle of 23.6 degrees its ratio will always be six over 15 which is really two over five point four So the relationship between this side rather than this side that divided by that will be point four All right What does that mean? What's 15 times point four? It's six. So the opposite side will always be 0.4 40 percent of the length of the hypotenuse Okay No, we only open up a black hole and we divide by zero If you divide by zero black hole pops and the universe explodes Right. That's where the black hole comes in from. That's what the black hole is Why can't we travel at the speed of light? Enigma why can't we travel at the speed of light? Do you like sci-fi? I hope you like sci-fi Why can't you travel at the speed of light? for anyone that's like Star Trek Star Wars any any sci-fi infinite mass right If you try to travel at the speed of light you get infinite mass. Do you know why you get infinite mass? I'm gonna erase this


are you eating kfc how do you feel watching that while you're eating that did you see this this was in the guardian newspaper this morning can you leave the restaurant yeah of course do you want to come and look at are you the manager yes do you want to come and talk about it then all right so we're just out the front of kfc here in Leicester Square London we've got the investigation footage that Matthew Glover and VSC gathered from one of kfc's flagship farms moey park so you really do care about these yeah we do tell me what about these chickens do you care about birds like these three here we're going to go show people at the front of kfc where their chicken comes from so let's do it kfc torture animals kentucky fried cruelty kfc torture animals this is one of kfc's farms this is what kfc do to birds this is kfc suffering animal suffering this is one of kfc's farms it was just recently exposed uh today actually if you look in the guardian this morning you'll see the expose and that this is one of kfc's flagship farms that they were touting as one of the the best most humane farms and my friend went in there with a investigation team and brought out these images they're called vfc the vegan fried chicken they exposed one of kfc's farms yeah so it's a kfc farm was exposed this morning it's gone brother do you work here yeah are you a manager okay what's this did you see in the guardian this morning where in their guardian newspaper this morning they exposed kfc farm yeah yeah this is what one of their the farm they did the advertisement with investigators went in there and exposed it yeah i don't think so yeah no this is look in the guardian i'll show you the guardian newspaper kfc expose hey this morning dead chickens everywhere suffering and dying this morning in the guardian newspaper you can look it up right now on your phone it's true see how long i can stand here before someone's come maybe i'll show did you see this this was in the guardian newspaper this morning expose on kfc's flagship farm do you ever see that commercial with nico do you know youtuber nico hello my friends i'm nico and i'm on a farm kfc have been improving chicken welfare for years yeah well this is the commercial kfc did called behind the bucket and uh uh matthew glava from vfc this is this interests you this should interest you yeah of course do you want to come and look at you the manager yes do you want to come and talk about it then thank you very much what do you think about this but what do you think about this so but what do you think about this yeah but do you think what do you think about the cruelty though thank you tell me what you think about cruelty and i'll leave the restaurant okay thank you that's pretty bad though isn't it it is cruel cruelty caves everywhere kentucky fried cruelty no no only a kfc no all animal products no only the vegan ones okay thank you yeah okay we'll stand just here thank you we'll just stand here for another hour now kfc torture chickens just letting you know about that this is a kfc farm this is one of their farms investigated this morning much yeah kfc torture animals kentucky fried cruelty what was that it's not working are you losing customers you're making bank i know this isn't going to stop kfc they make their own choice even if that choice is this this bad their choice the animals don't have no choice though is that true the animals have no choice kfc torture chickens just letting you know this is their farm kfc torture animals did you know that yeah pretty common knowledge this is a kfc farm vegan shoes good work you're vegan are you bless you kfc torture animals this is one of their farms it's disgusting isn't it what is it that's one of kfc farms that was investigated this was a commercial they used that nicko to do the do the commercial but some investigators went there and showed what was really going on they're using the chickens yeah they all chicken farms will abuse the chickens because they grow so big and they can't support their weight and they fall down and die yeah do you see chicken yeah this is a kfc farm that's what you're eating suffered birds would anandos farm be the same yeah all chickens in the uk a factory farmed at the moment the vast majority so but you can get vegan fried chicken so and kfc do a vegan burger as well yeah you don't like animal cruelty a i don't do you think animal cruelty is worth it for a sandwich quick sandwich what do you think you're thinking about it what do you think like for you like when you have a sandwich it's a quick sandwich and you get some flavor but for that bird it's a life of suffering do you think it's worth it it's not good enough yeah but then i don't know anything else do they they're born there so yeah we forced them into that sometimes they can have a better life so they have a size of an a4 piece of paper in this shed but you know this youtuber nico yeah you know they used him as an advertisement and said oh it's all humane in and then vfc went in there and uncovered this vfc is vegan fried chicken so humans still eat chicken though yeah but you can get vegan chicken as well but you know what would humans are going to still do it probably yeah you're right but what about you is he still gonna not as much as just a bit of cut it down just a bit of cruelty then a bit of animal cruelty in your life what's right you're gonna have to have a lot of people to not if people still eat it then like it's not going to stop we need more people like i'm just concerned about what you guys think about it at the moment because me i don't i don't um contribute to i've been vegan for nearly 10 years they're conscious beings they have blue eyes blue eyes and a brain so when you experience the world they experience the world too but all they experience is suffering so someone can have a sandwich a quick sandwich it's not good enough don't listen to the lies when they show you a commercial don't trust them they're trying to sell you stuff this is the truth no worries guys good to meet you good to meet you my friend take care i want to tell you that i think it's a good idea to um tell people that is so all right first i think i'm from germany you're from germany yes nobody do so so i think it's um a good activity to do so to share the truth with people you mean yeah so but i think um i um before you taught me so i didn't knew it you didn't know next time i see you maybe in germany you'll be vegan maybe that's it see you brother see you see you kfc cruelty that's what kfc do to birds this kfc's farm this kfc what they do to chickens kfc torture chickens birds they're tortured birds kfc torture animals hey this is one of their farms this was the farm they put in their commercial their advertisement this is their advertisement my friends went there and filmed it filmed all the chicken suffering in there all animal products kfc torture animals this is one of their farms it's a kfc farm there's planting seeds brother planting seeds 82 82 years right 82 years or years 82 years i know i know torturing animals for a long time haven't they kfc have been torturing animals for 82 years apparently the very fact that these animals have to exist in the bodies the way they are is torture in and of itself like they don't have to be in there physically torturing them for their existence to be torture this is the kfc's farm yeah kfc kentucky fried cruelty kentucky fried cruelty kfc torture animals in their farms we exposed the kfc farm here bfc did this is the suffering that was in their farm see that's like i want them to see like the birds suffering and when i say kfc so they know that they make the connection but you know it's not just kfc by the way like it's just that kfc were putting this silly humane washing campaign out there but uh it's all chickens in the uk the vast majority of the factory farmed exactly like this it's very standard this isn't just an isolated incidence in a kfc farm this is very common this is what you see when you go into a chicken farm go into any broiler shed you'll see dead dying chickens overgrown chickens collapsing um under the weight of their bodies they can't support themselves their little baby birds in overgrown bodies this is just so common it's standard practice i'm just showing the patrons the footage while they're waiting for their kfc the line has gotten smaller in there though hasn't it kfc's farm are you me too kfc torture chickens in their farms this is what really happens and don't believe the advertisements this is kfc's farm oh yeah it was exposed by vfc who's a vegan fried chicken brand went in there with investigators and exposed their farm are you eating kfc how do you feel watching that while you're eating that i don't think he likes it anymore right i showed him there the this is kfc's farm okay the reason this is big is because this is youtuber named nico i don't know if you know youtuber named nico nico you know the one he does pranks and stuff yeah they used him they paid him money to go into their farm when all the birds were really young to say oh look how humane and nice it is so then vfc went into the farm two weeks later and all the birds have grown really big because that's what they do they grow fast and they're all in there dying on their faces and suffering so don't believe the lies they tell you you know all the chicken here is factory farmed right now over 95 percent usually but right now they're all indoors factory farmed because of bird flu anyway but so wherever you buy a chicken you go to the butcher get chicken they're coming out of here you're not getting free-range meat chickens if they're suffering it's bad but if they're happy it's bad it's worse to kill them it's bad to kill a happy animal imagine a happy dog and you just kill them imagine a happier person and you just kill them animals aren't food they're animals we've been taught their food for generations and generations and but they're conscious beings they don't want to die he said being vegan is like the alternative right yeah but like the thing is here like you see the protein isn't the same protein yeah so the animals that you eat get their amino acids from plants to begin with okay so if you're eating a wide range of plant foods you can get enough protein you can get protein rich plant foods like beans and the protein is not like a whole protein if that makes sense yeah when it comes to like a plant protein so every single plant has all the amino acids in varying varying degrees so it's like they won't have not every plant's going to have them all in like the highest degree so you just have to eat a variety of food which everyone eats a variety of food anyway if you want to like tofu tempeh and you can get the soya uh the soya meat which is like super high in protein so you can get protein it's just it's much more efficient to get protein from animals like so not necessarily like i've been vegan nearly 10 years man so how did it feel when you went vegan it was amazing i felt amazing when i first went vegan for sure now it's just normal to me because i went for like a lot of raw food so i was eating a lot of fruits and vegetables and i was just like because i was i got out of prison and i was like i used to take lots of drugs and be on eating heaps of meat and that but when i got out of prison i got sober and went like raw vegan and i was like wow i was like i was on drugs it was i felt amazing but now i look i just eat like normal vegan food like what you probably eat what's your source of protein what's your whole grains beans uh but i like uh vegan meats tofu all right take care take care good talking to you say peace man hey pretty cool i like them i like them a lot all right so another huge thank you to vfc for this powerful expose they did please share it far and wide actually keep sharing this video tag underneath the original kfc propaganda piece they did with nico so that the people in the comment section can see the truth and uh you know just be vegan just being vegan is the only way you can avoid this don't listen to the liars and the propaganda and eat vfc instead of kfc