Welcome back to Sports and Building Aerodynamics, in the week on basic aspects of fluid flow. In this module we continue our focus on fluid properties. We start again with the module question. If a cyclist would be cycling in an inviscid medium, which means a medium with zero viscosity, instead of in the actual viscous air. His or her aerodynamic resistance would A, be zero. B, decrease. C, remain the same. Or D, increase. Please hang on to your answer. and we'll come back to this question later in this module. At the end of this module, you will understand the fluid property viscosity. You will understand how viscosity changes as a function of temperature, and how viscosity influences cycling aerodynamics. So this module will be exclusively focused on the fifth physical property that we will be addressing being viscosity. First some etymology again, viscosity derives from the Latin viscum, something sticky, birdlime made from mistletoe or mistletoe, or from the late Latin viscosus. It is defined as the resistance of a fluid to deformation by shear stress or tensile stress. It can be indicated by the Greek letter mu, which is the dynamic viscosity, or the Greek letter nu, which is kinematic viscosity. And the difference between those two is the factor rho, which is density. So if you have a high viscosity, this means there is a high resistance to deformation, a low viscosity has a low resistance to deformation. This is nicely illustrated in this animation here, where on the left side you see, a highly viscous liquid, and on the right side, you see, a viscous liquid with less viscosity. You also see some typical values of dynamic viscosity indicated here for air, for water, and for motor oil, at the given temperatures. Viscosity can actually be explained by a rather simple analogy, so let's focus on two trains riding on parallel tracks. And in these wagons, which have open doors, there are two persons standing and they're throwing mass at each other, which can be anything. Boxes or bags of cement, for example. And the blue train is riding a little bit faster than the yellow train. So you could indicate this here. So the yellow train has a speed u. The blue train has a speed u plus du. And there is mass being exchanged. with a certain a velocity in the direction perpendicular to the tracks. What is actually going on, this is not only mass being exchanged but also momentum. m multiplied by u from the yellow to the blue wagon, and m multiplied by u plus du from the blue to the yellow wagon. So the nett exchange is mdu or minus mdu between those wagons. So what actually will happen when you continue increasing the exchange of mass and exchange of momentum. Well, actually, what you're doing is slowing down, because of this, the blue train. Because actually the mass being exchanged from the yellow to the blue one has lower momentum and you're increasing the speed of the yellow train. And finally, when you increase this exchange frequency, what you get in the end is that both trains will be riding at the same speed. So actually what is happening here you could see it as some kind of friction. Some kind of stress acting between those two trains. And this is actually quite similar for what you have with laminar flow. In laminar flow you have layers of fluid flowing nicely parallel, well possibly parallel, to each other. And this is actually similar to those two trains, there is also mass being exchanged in laminar flow. Actually, in laminar flow, it's molecules being exchanged between the different layers. So, therefore also the momentum is exchanged and actually the friction that is caused here that is referred to as the so called viscosity or molecular viscosity. Then a Newtonian Fluid is actually defined as a fluid that behaves according to Newton's law and that means that viscosity is independent of the shear stress or the rate of deformation. So this means that the dynamic and the kinematic viscosity are constant values. You can indicate that in a graph and let's do that for the Newtonian fluid first. So, we have the viscosity as a constant but then there's also other fluids, which can be shear thickening fluids, for example, where self-compacting concrete is a clear example. Or shear thinning fluids, where you see that the viscosity actually decreases with the rate of deformation. And blood and ketchup and paint are examples of this kind of fluids. Let's look at how viscosity changes as a function of temperature. We first focus on water at the pressure of one atmosphere. And then you see here that the actually dynamic and kinematic viscosity have a very similar variation. The ratio between actually those two is the density which is also not varying very much as function of temperature for water. If you look at the same variation for viscosity of air. You see that this is much more pronounced. These values, these ranges are much larger. But what is also remarkable here is that if you compare the graph of water and the graph of air, that for water, the viscosity decreases with increasing temperature, but for air, the viscosity increases with increasing temperature. So this might seem a bit strange, and the question is well, what is actually the reason for this? What is the physical mechanism behind this? Well, if you are looking at gases at normal pressure then you have these molecules that are colliding with each other and also with the walls of the container. So they're not densely packed, and what happens when you increase the temperature is also that the travel distance increases of these molecules. And because well, we have this analogy of momentum exchange that actually explains the viscosity. When you increase the temperature not only the distance between the fluid layers where molecules are exchanged, will increase. But actually also the amount of momentum exchange itself can increase between identical layers. So therefore, viscosity increases with the increasing temperature due to increased momentum change. So, what happens then with liquids or gases at high pressure? Well, there the molecules are rather densely packed as shown in this animation. So, the molecule's motion is less pronounced and actually the molecule layers brush against each other and that actually explains to a large extent the viscosity. However, what happens at higher temperatures, is that these molecules start vibrating more intensely with larger amplitudes so, the molecular movement increases and you actually reduce the brushing effect. So actually the movement of molecule layers compared to each other becomes easier. So this means that viscosity indeed decreases with the increase in temperature for liquids and gases at high pressure. An inviscid fluid is a fluid that has actually zero viscosity. So this means that also the shear stress is zero, so an inviscid fluid is a fluid that cannot support shear stress and flows without energy dissipation. Sometimes it's also called an ideal fluid or a perfect fluid and what is typical for this assumption is that the shear stress is zero but also that you have the so called slip behaviour at the wall. This means that the the speed of the fluid is not zero at the wall as actually it should be, as shown here in the graph on the left side. So let's turn back now to the module question. If you have cyclist that is cycling in an inviscid medium, so with zero viscosity, instead of actual viscous air, what will happen to her or his aerodynamic resistance? Well actually, what happens is that it decreases. Actually it decreases quite a lot. It decreases by 50%. What you see here in this graph is again static pressure illustrated on the body of the cyclist. And the reason why, one of the reasons why it decreases is that while the aerodynamic drag is made up of the so called form drag and the skin friction drag. Where you have zero viscosity, you don't have skin friction. But this only means that there would be a reduction by 7%. There's an important, much more important other mechanism, a second reason. And that is actually flow separation, which is very important for aerodynamic resistance, that that actually changes quite drastically when you make the assumption of zero viscosity. Exactly because we're going to assume slip behavior. And that's the reason why in the theoretical case of zero viscosity, the aerodynamic resistance of a cyclist would decrease by 50%. In this module, we've learned about the fluid property viscosity. We've seen how viscosity changes as a function of temperature and also how viscosity influences cycling aerodynamics. In the next module we will focus on some differences. The important difference between viscous and inviscid flow. Between compressible and incompressible flow. Confined versus open flow. Steady versus unsteady flow. And stationary versus non-stationary flow. Thank you very much for watching, and we hope to see you again in the next module. [BLANK_AUDIO]