 Welcome to the fifth lecture which is the beginning of capsule number 3. In this capsule we are going to continue further our discussion about fluid mechanics. So this particular capsule is called as basic fluid mechanics part 2 and in this we will look at two lectures today we discuss some fundamental phenomena in fluid mechanics. We discuss viscous flow Reynolds number and boundary layers. The bulk of the content for this lecture has come from this student Atul Vishwam who is a third year undergraduate student from aerospace department. He undertook the same course AE152 last semester and during the summer he has been helping me in creating content for this course. So this particular capsule the first lecture has been created by Atul. So thanks to Atul for helping me out. Let us look at broadly what is our roadmap for today. We start with an introduction to viscous flow and then we proceed to the consequences of viscosity in the flow which is a laminar and turbulent flow. We then proceed to the concept of boundary layer which follows automatically from a discussion regarding viscous flow. We look at types of boundary layers there are two basic types as most of you know we just have a close look at them and finally we look at flow separation. So this is the roadmap for today's presentation. Let us start with a very simple experiment. And in this experiment we are going to see the behavior of a few fluids. So what do we see here? We see four jars filled with four different liquids and in each of them we drop a small ball. So in the third one again we are going to drop the same ball. So look the color can be deceptive and the last one is the one in which it will take the maximum time to reach down. So four jars identical with four liquids but there is a difference in the behavior. So the question is why is there a difference in the behavior of the same ball in the same jar just because of the presence of the fluid and the reason for that is because some fluids are thick and some fluids are thin. When you drop a ball in the thick fluid it takes more time to go down. When you drop it in the thin fluid then it goes much faster. Alright so here is another animation which shows two containers in which two fluids are being dropped. We notice that in one container on your left the light blue color liquid it flows rapidly and tends to fill the container very quickly. On the other hand we have this orange colored fluid which takes much more time to occupy the volume of the container. So which one is thicker it is obvious that the one which is orange in color is thicker because it is taking more time to fill in. So recently we had a very interesting race in which the worldwide hero lost out with Justin Gatlin. But this is just to revive old memories. This is the world record winning race, Noyan Komofkin says the speaker 9.58 seconds. So just like we have these runners who run we also have particles in a fluid that run against a resistance. So let us see and let us see how viscosity the property of the fluid helps us. So essentially what is viscosity? Viscosity is basically a property of a fluid and this property manifests itself through a resistance to relative motion primarily because of friction. So if a fluid is thicker it will have a higher viscosity. If a fluid is higher viscosity it will have a lower flow rate. Let us have a look. Now we measure out equal proportions of our ingredients into our little containers. So you have these small containers. In the first heat of our race we have water, rubbing alcohol and cream. Water finishes first with a time of 0.233 seconds and rubbing alcohol finishes last with a time of 0.4 seconds. In the second heat of our race we are going to be racing olive oil, lamp oil and vegetable oil. Lamp oil finished first with a time of 0.467 and olive oil finished last with a time of 0.633 seconds. In the final heat of our race we are going to be racing honey, maple syrup, corn syrup and dish soap. First across the finish line is maple syrup with a time of 1.33 seconds followed by the blue dish soap with a time of 4.633 seconds. And then slowly but surely the great corn syrup crosses the line with a 19.5 seconds and then finally honey with a 20.767 seconds. Here are the results of our race. Just like we saw the race between at least, you have a race between fluids. Meaning it has the highest flow rate and the lowest viscosity. Honey was last across the finish line meaning it has the lowest flow rate and highest viscosity. Okay, so the same bolt basically is water, it goes fastest. Alright, now a question, throughout this presentation when you see this particular symbol, we will ask a question and I would like you to ponder over this question and answer using the Moodle page. Don't answer here, this is the question to be done. So the question is just like we have viscosity of fluids, gases are also considered to be fluid. So do gases also have viscosity and can you get some information, maybe some videos which shows the viscosity of gases and the effect of the viscosity of gases on the floor. So that is homework proceeding further. Now it is good to know about viscosity and now let us do some basic calculations about viscosity using the Bernoulli's principle about which we have studied. So to do that basically, we just have to go and read the assumptions. Now this was a question in one of, in the quiz last time. What are the assumptions under which the Bernoulli's principle is valid? And one of the choices was that the fluid has to be non-viscous. So does Bernoulli's principle apply when the fluid is viscous? So we have to go and check out. Okay, so let us look at first the most fundamental flow which is a flow in a pipe. In this video, we are going to color the flow using a small die and the speed of the flow is going to increase with time. So you can see the effect of that. So this is low speed flow at low Reynolds number which we have not defined so far but I will define very soon. Slowly the speed of the fluid is increasing. So you can see that the pattern behind, the pattern as you go ahead is changing. Much higher speed flow, the pattern changes much more rapidly. But you can see there is an oscillatory structure and to some extent there is some uniformity in the structure. But as you increase the speed to a very large value then there is a lot of dissipation of this fluid and you can see there is a very high level of mixing of the die in the water. Let us watch it once again from the beginning. Low speed flow hardly any oscillations if they are symmetric and they are of low amplitude. As the flow speed increases, these oscillations become higher and higher in amplitude. The structure is, now this is actually unsteady flow because it is time varying and what are you seeing? Are these stream lines, streak lines, path lines or timelines? What are these? You can see how the stream lines is a streak line, correct. So what we see is that the velocity of the flow in a pipe affects the flow pattern. So when you have very low speed flow then you have what is called as a laminar flow which has little or no oscillations. When you have a much higher speed flow you have a flow called as turbulent flow where as you saw a lot of mixing takes place and there is a particular speed for a given pipe dimensions beyond which the flow converts itself from laminar to turbulent. So what about external flows? This was inside the pipe. So over an aeroplane wing which does not have any border on the top and the bottom. Do we have a possibility of laminar flow over the wings? So this is another question on the model. Can we encounter laminar flow in actual aeroplane wings? If the answer is yes, you have to give proof of that. It could be a video from a reliable source. It could be some kind of a photograph or a paper or a publication, anything that we can depend on. Please remember there are many frivolous things on the internet also. For example one most common problem that you see is people showing the working of Bernoulli's principle but actually it is Kowanda effect. So you will see many such videos. You have to be very careful. Do not believe anything that blindly that somebody puts up. Do not believe blindly that somebody puts up on the internet. Apply your own logic and justification before you post it because if you post something which is wrong you are responsible for it. You cannot say I found something on the internet. This is not a clerical exercise where you just give a Google search, you find something, you post it. You have to own up to what you post. And if there are mistakes, it is okay. We all make mistakes. I make mistakes so we can rectify our mistakes. So let us see laminar flow over a wing cross section but this is inside of internal. So there are two main sources for this particular presentation. They are marked as double star and I think hash and at the end there is a slide which explains what these sources are. So once I upload this presentation on Moodle you will have an idea what the sources are. So you can see here it is clear visually also that the flow is smoothly going over and below the wing and I do not see too much of disturbance or turbulence behind. So visually it seems that the flow is laminar. But remember this is in a wind tunnel so this is still internal flow. My question was can we have laminar flow on a wing which is exposed to external flow. This is over a cylindrical body. So here also it is almost perfectly symmetric. This is not a computer simulation. These are actual experimental results but using dyes for visualization. So here also we see that it is almost perfectly symmetrical. So here also we can assume that the flow is absolutely or almost perfectly laminar. Proceeding further we have a rectangular block and interestingly even here the flow can be laminar. So the shape of the body alone does not guarantee or insist that the flow will become turbulent or laminar. As we saw over a wing, over a cylinder, over a rectangular block you can still have laminar flow. So shape is important but not very very important. It is not the only parameter. There are other parameters also which decide about the flow being laminar or otherwise. Yes, Mike, intentional this is actually basically an experiment called as a backward facing step. So what you see is a rectangular block but intentionally they have created a small gap because they also want to investigate what happens if you have let us say a water tank over a building which will have some kind of a overhang or a projection behind. So it is intentional. They wanted to study in one experiment flow behind a rectangular body and also flow behind a backward facing step. So that gap is intentional. I think you are talking about this particular gap, this gap, this gap is intentional and notice the flow here is flowing you do not see much turbulence still. So by and large the flow is still laminar. Now let us go to the question that we had asked in the class. We had this question in the quiz, oscillating flat plate. Here the plate is not oscillating, here the plate is fixed but at a very high angle and still you see that the flow is laminar. So this is another myth many people have. Many people think oh if the angle of attack or if the angle at which the body is placed is high the flow will become turbulent not necessary. You can have a very blunt body, you can have a body at a very large angle still the flow can be laminar not always true but can be also true. So in other words the orientation and the shape of the body alone is not responsible for the flow to become laminar or turbulent. This is a question which I would like you to talk about. How can we first of all can we predict when would a laminar flow become turbulent and if the answer is yes we can predict then the question is what is the parameter or what is the mechanism with which you can be very sure. So this was a problem that was being addressed by many fluid mechanics people in the beginning and this person he made some efforts to study this phenomena and we will but then my question is who is this guy. So if you know the answer I would urge you to raise your hands why let us do the following let us have a proper quiz okay. So I will give you four choices and I would like you to tell me now of course all cannot be right all may be wrong that could be a fifth guy who did it and more than one cannot be right because if x did it why did not do it. So here you can use your elimination skills which you have picked up in your examinations right. So please tell me if somebody knows raise your hand and obviously after two answers if they are wrong we do not want to go ahead because then you can guess okay. Take a mic please if there is a mic around just tell me what do you think who is this person Osborn Reynolds the answer is wrong this is what I expected this is what I expected people to answer that is why this question because we talk about Reynolds number because we talk about turbulent flow people automatically assume it will be Reynolds oh it is not Reynolds it is a trick question see what is a trick question what does it say it says that I have made some efforts to study he does not say I have discovered it he does not say I am the first person but he is the guy who actually did lot of efforts to study it. So let us go on to yeah someone there my name is Raul it is Prandtl okay Ludwig Prandtl that is also a good guess but it is a wrong answer okay it is a wrong answer because Prandtl is a very famous name in fluid mechanics so it is a good guess it is a intelligent guess that man was great we call him as the father of aerodynamics so he must have done some good job maybe he did this job so now we have only two remaining okay we have Arnold Sambo field and we have so now can you guess now you have only 50-50 chance okay so you toss yeah so the answer is Stokes okay remember the Navier Stokes equation he is the guy half of it Stokes also remember that is a Stokes theorem also that is what we will study we will study about this particular theorem later on okay right so it is George Gabriel Stokes who was the first person to study this but he could not formulate it properly it was Reynolds who came ahead just like Gatlin has overtaken Bolt okay so let us understand Reynolds number basically it is a ratio ratio of two forces and therefore it is dimensionless the inertial force which resist the motion because of inertia and the viscous force which creates a resistance to the motion okay so I would say the other way around inertial force basically tends to follow what is happening and viscous force is opposing so the ratio of that is called the Reynolds number and there is a critical value of Reynolds number for a particular fluid flow condition it is different for pipes it is different for plates it is different for bodies we call that as a critical Reynolds number because that helps you decide or identify the point of transition okay so the transition Reynolds number is called as the critical Reynolds number so this is our key not the shape not the fluid properties alone not the angle it is the Reynolds number of the flow that decides whether the flow is going to be laminar or turbulent so that is the typical values if the flow is internal it is between 3 to 5000 if the flow is external it becomes 100 times more 300,000 500,000 and it is the best measure to compare two flows the Reynolds number and obviously as the Reynolds number increases the flow becomes less and less laminar or the laminar nature reduces till you reach a critical Reynolds number after which the flow becomes turbulent laminar flow stops so if you look at a human blood flowing in the veins and the arteries the Reynolds number is around 100 why because blood is a very viscous vehicle viscous fluid so if the numerator is viscosity and that number is high the Reynolds number will come down so there are people including in our department who are looking at the fluid mechanics of blood flow in fact interestingly we have a PSD student who is an MD in cardiac surgery and he is now a PSD student studying flow of blood through artificial valves so if you get time please visit the aerodynamics laboratory you will find we have created a small setup where we try to mimic the flow of blood through the heart especially through the artificial valves so there we need these kind of studies. A swimmer operates at around 4 million Reynolds number of course it depends upon the length of the swimmer and the speed of the swimmer also but this is the approximate value so from 100 we go to 4 million large ships like this they operate at Reynolds number of a few millions so what is the Reynolds number first of all there is a question there so can you name this ship anybody here who is a fan of ships what ship is this let us go back to Moodle fine you can search and put it on Moodle. Now what would be the Reynolds number of typical aircraft between around 6 millions to 10 million typically 6 to 10 million is the Reynolds number so when we talk about aircraft and about aerospace engineering flows we normally speak in millions these typically UAVs that you fly these remote control planes that you fly what would be the Reynolds number it would be around 0.3 to 0.5 million now interestingly there are many students who take up aeromodelling as an activity and they make these remotely controlled planes is there anybody in the class who has made remote control planes or is interested in making RC planes just raise your hands so in our class we have Saurabh who is actually a very accomplished aeromodeller ok. So Saurabh a question addressed to you because of your experience in your experience of flying remote control planes you must have attempted to get the aerodynamic characteristics of a particular aerofoil from the wind tunnel data or from the reports but when you actually fly did you observe any difference between the reported values of say the maximum lift coefficient against what you actually got what is your typical experience we are actually going ahead we are talking about lift coefficient we are not discussed it yet but just wanted to know. So if I look at lift coefficient in reality it is slightly less because you have got your wing is not completely smooth in reality it is got little notches and things like that and they transit the flow from lamina to turbulent. No that is not the main reason actually even if I make a perfectly smooth wing when I make an aero model I will not get the maximum lift coefficient which I get for the same wing when I make a big aircraft the main reason for that is there is a Reynolds number effect on the aerodynamic characteristics which many students do not know. So what they do is they pick up data about a particular shape or aerofoil from some source they make an aircraft they do calculations and then they say we are not getting the performance and then they assume what you assume that oh it is because of the bad finish etc that is one reason but I will show you there are other reasons also okay let us go ahead. So let us see there is a critical number of 2900 for a pipe let us see what happens to this particular flow when you move so what do we normally do basically is so this is a flow in a pipe this is not a computer simulation this is just a photograph or a sketch okay. So this is a non viscous flow in a pipe is it possible to have non viscous flow is it possible to have a fluid with no viscosity that is the reason why I cannot show you a video nor can I show you any of course I can show you a computer simulation in any CFD tool I can put viscosity 0 and get some results but I chose not to do it I chose just to show you a sketch. So this is theoretical flow you will never see this in real life that you have a pipe and the flow continues along straight lines parallel it is only in theory okay what will happen if you have viscosity tell me what do you what do you think will happen because of viscosity yes. If the pipe is circular it is it is a circular cross section pipe so there will be a parabolic velocity profile okay why will it be parabolic because of the velocity gradient which is created due to the viscosity like the fluid at the edge which is in contact with the surface of the pipe top and bottom okay will have a smaller velocity as compared to the fluid. So if I correct you do you think it will have any velocity or will it be zero velocity technical rate is zero that is what we call it it is a boundary condition it is a no slip condition it is a no slip condition so that means essentially we have something like this okay. So in the center of the pipe the friction is only between the two fluid particles at the edges you have friction between the fluid particles and the pipe wall so you typically get this kind of a variation of velocity okay now the question is is it laminar or turbulent do not go by just the looks there has to be some logic so let us see okay. So if the flow is laminar which is what it appears to be then what will be the response number will it be low or will it be high it has to be low okay it has to be low so one can keep on increasing now let us see let us see a video about viscous flow over a solid surface this is an experiment so you introduce a small pipe in the flow you touch the floor and then you release the fluid and you take it up slowly. So interestingly the fluid which was there at the bottom has remained stationary this is the proof of what I was suggesting to you that in case you have a flow over in a pipe or in any container the fluid that touches the surface is at rest that is why we need a brush to clear off that the presence the particle remains okay the fluid is flowing but the particle remains why is it flowing because you can see those things moving but on the surface it is not moving that means the surface velocity is 0 so this is because of friction the friction between the fluid particles and the surface now let us go to the flat plate. So you have a camera which is stationary so it is Eulerian approach the camera is stationary and there is an automatic carriage that tows a plate so the channel is stationary the camera is stationary but this plate is moving in the fluid plate with sharp edge so the camera is stationary it takes a picture. So you can see now the plate velocity is very low and you inject fluorescent dye notice how the structure of the flow field changes as the velocity of the fluid is increasing and hence the Reynolds number is increasing now you go to higher Reynolds number see the difference in the flow field so this is the name given to this particular phenomena where you have a very large mass called a turbulent bulge and then you have these vertical structures inside you can see those vertices which are continuously generated and they are bursting also so when we study these things in more detail that is when we look at these kind of pictures. So here is just a snapshot of some CFD calculation CFD stands for computational fluid dynamics in which we simulate the fluid flow using certain standard equations that can be used to model the flow so you can see that the fluid is almost stationary very very low values of mark numbers on the surface and as we go above and when you go to the thin region outside you have a very much higher speed flow of 0.712. So with this basically you can say that when there is a flow over a flat plate the flow pattern can be divided into two clear cut segments one segment is the red area where the fluid velocity is uniform equal to the free stream velocity of whatever 0.172 or 175 and the viscous effects are limited only into a small area below the yellow and green curves lines so that is the only area. So if you want to do a very simple analysis let us say you have some equations available with you which are applicable only for inviscid flow and you have a flat plate to be investigated. So what you can do after looking at this picture we can conclude is if I replace the flat plate with the body of that shape what shape the shape below the yellow colored and if I do an non viscous analysis on a body of that shape I will probably get the same results as on a flat plate with viscosity because the viscous effects are confined only in that small area. So this is called as flow partitioning and this is the contribution of Prandtl Prandtl was the person who first observed these boundary layers and he said oh we can divide it into two segments and then live with in viscous calculations in the non boundary layer area. This particular area may appear to be very small but what is happening inside is very very drastic and dramatic okay. So basically viscosity has spoiled the flow field yeah the answer is here. So you have a flow acting over a flat plate and we see that the effect of viscosity is confined only in this small zone which is colored yellow green and blue where the velocity of the flow is lower than 0.172. So what is happening here is the free steam Mach number is something like 0.172 or 0.175. So ahead of the plate there is no problem the flow is still not sonic so there will be no effect felt so the flow will remain at the same Mach number. But when the plate starts a small area starts getting built up over the plate in which the flow velocities are reducing and finally they reach the red value. So analysis of a flat plate in viscous flow is equal to analysis of a body of that shape shape equal to the shape of this yellow green band put in non viscous flow. So this is what it is so this person said why do not you split into two regions and that is called as a boundary layer.