 We're now going to take a look at external incompressible viscous flows. Now when we look at external incompressible viscous flows, we could be looking at a number of different example applications. Some of these include the following. So one example could be the flow over a semi-infinite flat plate and for that we'll be looking at the boundary layer and boundary layer theory. Another example is flow over a cylinder where you could be looking at the wake behind the cylinder. You could be looking at drag characteristics, bluff body flows, instabilities associated with that as well. And then finally from aerodynamics a common application for an external incompressible flow would be flow over an airfoil and that would be a coupling of the pressure distribution and boundary layer theory that we'll be spending a little bit of time looking at. So what I'm going to do I'm going to begin with a short video clip looking at flow over an airfoil and what we'll be doing is looking at some aspects of external viscous flow pertaining to this airfoil. So what we have here is flow over an airfoil. There's a dividing streamline at the front and the night eventually comes to a stagnation point where the velocity is zero and then on the back side of the airfoil we can see there's a viscous wake. Outside of that is what we would have heard is being a potential flow region where viscosity is not important and we'll be looking at that. So if we zoom in on the top of the airfoil we have the potential flow region again on the outer side and then what I've drawn in is a boundary layer exaggerated and so the boundary layer goes from being laminar at the front through transition and eventually goes transitions to a turbulent boundary layer and so what we're going to be doing in the next few lectures is looking at the boundary layer flow right adjacent to an airfoil and so that's what we'll be spending some time looking at and we'll be studying different aspects of the flow external to it could be it on a cylinder it could be on an airfoil any kind of external flow we'll always have a boundary layer on it so we'll be looking at the boundary layer approximation and and so if we consider that airfoil again so what we have in this flow field we have a number of streamlines coming around an airfoil and there is development occurring on the airfoil beginning we have the dividing stream line which hits the stagnation point where the velocity is zero and the flow some of it goes above the airfoil some of it goes below but if you're called a no slip condition we have zero velocity along the surface of the airfoil and and consequently what happens is there is viscous diffusion taking place and and the region of reduced velocity is what we refer to as being the boundary layer and and so to begin with the acronyms we have sp that refers to stagnation point lbl refers to laminar boundary layer t refers to the transition point tbl refers to the turbulent boundary layer and then finally what we have in the very back side of the airfoil is s and that would be the separation point where the flow could separate from the airfoil and then you have a viscous wake region behind but nonetheless the boundary layer itself would also give you a viscous wake region downstream of the airfoil so that is an example external flow and what we'll be doing in the next few lectures we're going to be looking in great detail at what could be going on in this layer right here if we zoom in and and what you would find that is the boundary layer what we'll find is we have the no slip condition on the wall and then as we go out we get to the free stream so we'll have some external flow out here and then we have a velocity deficit region because here we have no slip so we will be looking at that and we'll be studying the boundary layer using an approximate technique that was developed by Theodore von Karman and then we'll look at boundary layer theory things that were developed by Prandtl and others so that's what we're going to be spending some time on and then we'll move on and we'll be looking at external flow over cylinders and bluff bodies looking at drag characteristics and things like that as well as lift a lift you could have certain bodies that generate lift if they have asymmetric pressure distributions and you could have a lift force up or down depending upon the particular configuration so that's what we're going to be doing in the next few lectures we're looking at external incompressible viscous flows