 This is the second lecture of the first part of introduction to fluid mechanics and today we are going to look at three giants of fluid mechanics. So, this presentation is mainly going to be looking at some historical aspects after which we try to explain the basic principles behind the work of these three fluid mechanics specialists. So, first let us look at Bernoulli's theorem and we want to create tribute to Daniel Bernoulli. So, first question is we should try to understand who was Bernoulli. As you will see very soon, there are many Bernoulli's not just one, it is a big family of scientists. So, we are talking about one specific Bernoulli, so today we are going to look at Bernoulli's background history and that will help us understand why he was the way he was. First, let us look at some ideas from his early life. The Bernoulli's were a celebrated family of scholars from Basel. It is not just one as I said there are many families. Three generations produced eight outstanding mathematicians. Daniel Bernoulli was one of them. He was born in 1700 in the Dutch city of Groningen where his father Johann taught mathematics. Can we increase the volume? From an early age, Daniel received lessons in mathematics from his father. So, he is working on the abacus. And it soon became apparent that he had the Bernoulli talent for the subject. But his father wanted the most gifted of his three sons to go into business. The Bernoulli's were a celebrate. It is a very typical thing, you know. Even today, parents impose what they think is good for their children on them. So, here we have a young Bernoulli who is an accomplished mathematician ahead of his times. But his father wants him to do business. It is an old story, but it is still going on. In the end, Daniel was allowed to go to university. His father agreed to let him study, but not mathematics. Not maths. 15 Daniel Bernoulli started to study medicine, first in Basel, later in Heidelberg. The young student's interest was particularly aroused by a work by the English physician, William Harvey, on the motion of the heart and blood. In it, Harvey described for the first time how blood circulates in the body. And Daniel developed a special interest in the way in which fluids in motion behave. You will see very soon his experiments with his own blood in Bernoulli's theorem. At the end of his studies, in 1721, he returned to Basel and did a doctorate on a related subject. The Mechanics of Breathing. Mechanics of Breathing. That was his PhD topic. In the end, Daniel... All right. Now, after that, he went to St. Petersburg. He received a letter from Empress Catherine the Great, offering him the chair of mathematics at the newly established Academy of Sciences in St. Petersburg. One thing the Empress wanted Bernoulli to do was apply his special expertise in the construction of cascades and fountains for the Peterhof Palace. At the time, dramatic water features were all the rage at royal courts throughout Europe. Arriving at St. Petersburg in 1725, Bernoulli designed terraced basins based on his early experiments with water pressure and flow rates. You can see he used his knowledge of physics to... Received a letter from Empress Catherine to design waterfalls. And then finally, he returns to Basel. Bernoulli received a message from Basel University, offering him chair of anatomy and botany. In 1734, when Daniel submitted an entry for the Grand Prix of the Paris Academy of Science, he found himself competing against a work by his father, Johann. The two were declared joint winners, and Johann Bernoulli was furious that his son should be rated as his equal. He broke off all contact with Daniel. In 1738, five years after its completion, his work Hydrodynamics was published in Strasbourg. In an attempt to appease his revered father, Daniel described himself on the frontispiece as the son of Johann. Okay, so this is the father-son rivalry. Interesting thing is, here is a person who is offered a chair of mathematics and then a chair of anatomy by another university. And here is a Bernoulli family. And this is our Bernoulli, Daniel Bernoulli, whose theorem we will have a look at today. Okay, he lived for about 82 years and there are many interesting documents that he has published. These mathematical exercises included a study of the velocity of flowing water. Bernoulli analyzed the behavior of water flowing from a hole in a container. He noticed that the speed of the outflowing liquid depends on the height of the water column. It corresponds to the velocity of an object falling freely from the same height, so it also has the same energy. In the case of water, pressure is converted into kinetic energy. The less the difference in height, the lower the pressure. The greater the difference in height, the greater the pressure and flow rate. So these are his basic observations. And then he wrote his most celebrated work. First he experimented with pipes of different diameters and found that flow rate increased where cross sections narrowed. Bernoulli found the explanation for this in the continuity principle, which states that the volume of water that flows through a pipe in a given time is the same at every point. Flow rates at narrower points have to increase to enable the same volume of liquid to be transported. You can see the pressure is rising. At a place where there is a nozzle of energy, this acceleration requires a force which needs to come from somewhere. That is, it causes a reduction in energy somewhere else. Daniel then studied pressure in fluids in motion. And what he found was that pressure rises as velocity declines. An increase in flow rate results in a decrease in pressure. Bernoulli thus found a connection between flow rate and the internal pressure of a fluid. His equation, which sets the two in relation to one another, describes the law of conservation of energy for his information. So now he uses his knowledge of medicine to check the pressure of his own blood vessel. Bernoulli also found an immediate application for his findings. He used them to study blood pressure. Here he experimented with fine open-ended glass tubes which he pricked straight into arteries. He found his experiments with water confirmed. Slow flowing blood is under high pressure. Fast flowing blood under low pressure. So that is how you determine the blood pressure. There is a particular speed at which the blood should flow and where the speed of the flow is less you have higher blood pressure. Where the speed of the flow is less you have lower blood pressure. So one way of helping a person with high blood pressure is to reduce the density of the blood. So there are some drugs or medicines which are given to people who have high blood pressure so that the blood becomes thinner and then it can flow faster so the pressure will fall down. So even in medicine we use Bernoulli's principle. So let us look at Bernoulli's equation. When fluid flowing through a section of pipe with one end having a smaller cross-section. So this is the simulation. It shows two pipes of different diameters. The velocity of the fluid in the constricted end must be greater than the velocity at the larger end. Bernoulli's equation applies conservation of energy to formalize this observation. Consider a tube AB of varying cross-section A1 and A2 and at different heights H1 and H2. Liquid is flowing from A to B. B1 is greater than B2. Here A1 is greater than A2. So V1 is less than V2. The force on the liquid at A and at B. Now the work done per second on the liquid at section A and at section B. V1 equals V2 equals V. Equation of continuity. Net work done equals V1V minus V2V. The net work done per second is equals increases the potential energy and kinetic energy per second from A to B according to law of conservation of energy. So this is a very simple derivation of Bernoulli's equation which assumes incompressible flow. It assumes a few things. You notice that you basically allow the conservation of mass and energy. So what are the applications of Bernoulli's equation? There are many applications. The first one is flow through a venturi tube which we have already seen that as a velocity in the venturi tube in the neck increases the pressure there decreases. Then it is used in bottles that we get to spray a deodorant or aftershave or a perfume. So what we do there is we create, there are some bottles available which is a small air bag attached. When you press that air bag, the air is made to go out and because the air goes at a higher speed it creates a loss in the pressure or suction pressure which draws the perfume molecules and throws it out. So this is, such bottles are available. There are many applications in automobile. For example, the carburetor. You have this valve which the throttle valve which when opens creates a pressure difference and that sucks the and then Bernoulli's principle is also used to explain the generation of lift. In a separate lecture, we will talk at the lift generation and there we will touch upon this particular principle in more detail. Now you can derive the Bernoulli's equation. We have done it in the video and I will try to upload this video on the model page or at least the link on YouTube from where it is obtained. You can derive this equation for two assumptions either for incompressible flow in which the density will remain constant and more important the total derivative d rho by dt will remain constant. Or you can do it for compressible flow. But I am not going to derive it in the class. I am going to leave it to you for self-study. I will proceed further to discuss another interesting principle which is the Magnus effect. The Magnus effect is an effect that acts on balls or bodies which are spinning. When a spinning body moves through an object then there is a pressure difference and we will see very nice videos explaining this effect as well as describing. Now when you have a spinning body and because of the spin there is a pressure difference then obviously there will be motion in one direction and therefore the trajectory of the spinning object will change. So let us look at a nice interesting experiment. This is used in many ways. So here is the principle essentially just to remember there will be a motion towards the direction in which the ball is being spun. So if it is a cylinder or a spherical ball because of the difference in the relative motion between the body and the ambient air you can get a force. Another example let us see this very interesting example or a demonstration we have seen this in many football matches that is how it works. How did you do that? Well it is a pretty standard technique in soccer you use the inside of your foot to generate spin on the ball that spin is actually going to make the ball curve into the goal. Let us take a look at how that happens. As Kyle kicks the ball with his right foot on the right side he imparts a spin on the ball. The ball traveling in this direction means air is flowing across it in the opposite direction but right near the ball there is a thin layer of air dragged around As oncoming streams of air pass the ball the side moving in the same direction as the spinning ball is accelerated follows the curve of the ball and is deflected off to the right the side that is moving against the spinning ball meets opposing air and can't continue around the ball. It slows down and goes straight. We end up getting a net flow of air to the right and the ball must move left. Okay got it. Now let me show you another interesting phenomena and let's see if you can answer why this is happening. We blow air between these two balls okay and then they start moving towards each other. This is an experiment done by some of my interns during the summer so they try to pass a stream of air in between the two TT balls but they will turn into balls and you can see that they start moving to each other. So what is the principle here and why is it happening? It is the same thing. Just the same thing that on the curved surface you have a gap between two curved surfaces you blow air there the pressure reduces and because of that they start moving towards each other. Alright so now the question is is this Bernoulli's principle or is it quantified? According to Bernoulli's principle wherever there is high speed there is low pressure and when there is low pressure then things tend to move towards the direction of pressure and according to quanta effect if you have is this Bernoulli's principle in action or is it quanta principle in action? And in fact this is a massive confusion if you look on YouTube many many videos which try to explain Bernoulli's principle are actually talking about something called as a quanta effect. So we will move to the next aspect which is the reason why this happens and that is quanta effect. So let us look at this gentleman called Henry Quanta he was born in Romania in Bucharest and he was interested in the technical problems of flight so he made a very interesting aircraft which was basically a kind of a jet powered plane although we do not credit him as the person with the first jet engine aircraft but this was a plane that was powered by jet and look at the year it is 1910. So in 1930 he has discovered this effect called the quanta effect and let us see what this effect is. The effect says that when there is a stream of fluid which is flowing along a curved body it tends to stick towards the surface of the body that is the quanta effect. So if there is a jet if there is a flow jet which is along a curved surface then what you would expect is if you blow a jet it should go straight but it will curve. So let us see why this is happening let us first see this effect you can see here air is coming out from the top and there is this powered body near the jet you would expect the air to flow out of the jet horizontally in all directions but due to the quanta effect the air bends down to almost 90 degrees the air flow is being pushed down by the air above because the pressure of the air in between the flow and the curved surface is reduced by the suction of the air flow this is flow visualization the air is coming out and then starts curving notice at low speed at low speed it did not attack it is only when it became a jet it is coming out but going down now the reason why this happens can be explained very easily by looking at flow along a stream line and looking at the pressure differential between the two sides which will give us an idea that pressure on one side reduces and hence there is a tendency of the air to move towards the curved side now we are interested more in the applications of quanta effect rather than the theory of quanta effect these are some applications for example you can make a ball float in the air by just blowing high pressure jet from the bottom why does it float in the air because air will go on both sides and that will make it stable so when it is on both sides almost equal the ball may dance slightly and when it goes this side the pressure brings it back when it goes that side the pressure brings it back so you can actually have a dancing ball just by a jet of stream below it alright you can try the same thing look at just two coke cans or empty cans try to take a straw and blow the air if you remove the friction by putting straws on the bottom you will see that the cans will start moving towards each other so just by blowing air between two cans so I will be very happy if someone tries the experiment records the video and upload them on model it will be nice to see this just take two lightweight cans remove the friction by putting something soft below like here we have put the straws and do an experiment and upload on the video this is what I already showed you this is the ping-pong ball experiment where we have the area of reduced pressure and hence they move towards each other this is something about which I spoke to you in the first tutorial about components of the aircraft I mentioned about our visit to the helicopter hangar so I located a very interesting video on how quanta effect is used helicopter number one, go on the island, clear on the left here we go at about 12-15% you are going to get light off over here helicopter does not have a tail rotor no tail rotor hello my name is Nick Page we are here to talk a little bit about the Notar on the MD-900 or 902 Explorer what the Notar is is a other way of providing anti-torque for the aircraft how it is generated is the tail rotor which is of course not on the back of the aircraft is actually mounted forward inside the fuselage up here it rotates based on a drive shaft much like it would on a tail rotor off of a conventional helicopter it pumps air down the tail boom in the tail boom there is two slots running along this right hand side one here, see if I can use this and the other one right in here the air is vented out from these two slots and it creates a higher velocity air flow on this side versus the opposite side creating a pressure differential much like the Bernoulli effect on a standard airfoil what it basically works out to though is a quanta effect it is more than just Bernoulli and pressure differential but it creates lift off to this side here allowing for heading control the Notar fan pitch is directly connected to the pilot's pedals as he applies left or right pedal the amount of air flow that is pumped into the tail boom is increased or decreased creating more or less quanta effect out of these slots approximately two thirds of the heading control of the aircraft is from the air flow out of these slots while at a hover then what we have on the very back end of this is a rotating cone which also turns when the pilot is pushing the pedals and it vents out the remaining one third and it provides a measure of precise additional control to the heading control provided by the two slots forward this is how the aircraft works at a hover as you're transitioning into forward flight you get above 60 knots then your verticals pick up much of the load from the Notar itself in addition to the other aspects of the Notar what we also have here are vortex generators which have been added to this tail boom along with a 21 inch extension plug vortex generators what do they do well as we progress forward down the tail boom you can see more of them and what they do is they allow the quanta effect to work to a higher lateral amount of hovering speed than would be able to be had without them what they do is they just keep the air flow from the main rotor adhering to the surface area of the tail boom longer or higher speeds that's how the vortex generators work on this tail boom ok so if you have understood basically there are two slots longitudinal slots on one side of the boom and there is a free turbine which is at the beginning of the boom inside the boom that turbine is just throwing air behind the air is coming out from these two slots and because of quanta effect it starts going along the boom curvature and it leads to a pressure difference so the helicopter boom will start moving towards the direction of the air in addition they have provided on the rear side one small rotating nozzle which can be also used by the pilots for providing additional control what do you mean by propulsion you can see you cannot create propulsion but you can create forces quanta effect generally gives you force ok so it's a very indirect way of producing force it might be easier to produce force directly this is a very indirect way of producing force so what we use it mainly for providing small amount of force now because of the length of the boom you get a moment arm so you can get the required moment so in principle yes but it will be a more complicated way of producing thrust or a force anybody else ok let's go ahead I also found a very interesting video about I would say a device or an aircraft which flies on the basis of quanta effect it's called as a quanta effect saucer and I just want to show you it's a very interesting video and for those who are interested the plans of this particular device are available for those who are hobbies, aeromodulars I will upload the plans on the Moodle page for those who are interested this website gives you a complete description on how to make it using 3D cutting there are complete information available so this is a patent which was given by Henry Quanta very good example of quanta effect you can see that using a simple vacuum cleaner you can show that when the air is coming out from that nozzle because of the curved surface there is a pressure so it just goes up and when there is no air coming out because of gravity it comes down so you can also check this effect so you can see where the velocity is very large the value is shown in the red colors and where the velocity is low is shown in the greener colors ok now this is a model which has actually been built and very soon we will see videos of this aircraft being by remote control by the pilot I think it is a very fascinating it is a very fascinating model if someone is interested in narrow modeling I would urge you to make something like this it is really really interesting I remember in the aircraft design laboratory which I conducted a few years ago one student wanted to make something like this you can see there are flaps on the bottom which allow you to give a lateral velocity so this particular contact saucer will not have very long range probably but it will have extremely good ability to stay at one place so if you want something which can hover for a long time at one place this may be a good thing to try out but you can see it is very difficult to balance it because of the forces which will be fluctuating so then if there is somebody interested in providing stabilization system this is another very challenging platform try to make something that can go up and remain rock-steady at one particular place interesting project the principle used here to generate the lift force is a condi effect so there is a single rotor in the center and there is kind of a covering around to create a jet of the air the jet of the air goes out of the bottom of that thing and goes down there are these straighteners to allow it to go like a jet and that gives it a force and then you have these flaps to give it lateral imbalance ok this is something which enthusiasts can make alright now we move yes sir how do they control its rotation like what is providing anti-torque there is no anti-torque required here because the air is coming out equally from all sides there is a central rotor and there is this kind of a wall around it with a small gap so the air is being sucked by the fan and thrown out equally on all sides of this particular saucer along the sides so there is nothing like rotation here plus there are those small vertical members all around the side to analyze the flow so that it comes down straight any tendency because in a whirling fan there is always a tendency of even the flow also come in a whirling fashion so to cancel that they have put those vertical members all around that straightens the flow ok so that is it there is no side force but you create intentional imbalance by moving those flaps which allows you to move on one side or the other it is a good project I think someone should try to make it in their spare time