 In this lecture what we're going to be doing is we're going to be taking a look at external viscous flows and we will be looking at external viscous flows that have to be investigated experimentally. So at the end of the last lecture what we talked about was the boundary layer and we talked about boundary layers with various pressure gradients and we found that you can have a condition where you get zero shear stress along the wall and that's when the boundary layer will separate and when you have boundary layer separation that is then the onset of a fully turbulent flow downstream and it's impossible to be able to predict that analytically what the velocity profile might look like. Numerically people are working on it but quite often this becomes the realm of experimental fluid mechanics and and so a lot of what we're going to be looking at will be data collected and collapsed using non- dimensional numbers using experimentation or experimental data. So what we're going to consider are the forces that might exist on a body. So imagine we have some generic body and that kind of looks like a potato but it could be anything and we will have a free stream velocity coming towards that body. Now conventionally what we will do is we draw an axis through the body and the lift force always acts normal to the free stream velocity and so lift forces here. Not all bodies are lifting but we'll draw it that way here and by convention the drag force always goes parallel to the flow direction so that would be the drag force and so lift and drag are the two main forces acting on a body and then we can have a number of moments basically things that cause the body to want to rotate. So we can have lift drag we can also have another force here which that would be side force and then in addition to that we will have moments acting on the body and so there could be a pitching moment and it's called a pitching moment because it causes the body to pitch up or down. Now we can have a rolling moment and finally we can have a another moment that causes the object to yaw and that is referred to as being the yaw moment and a lot of the terminology here comes out of either aeronautical or also looking at ships and hydraulics and navigation of boats and things like that. So rolling, pitching and yaw moment and then we have the lift force, the drag force and the side force. So by convention drag is parallel to the infinity and lift is perpendicular to the infinity so that's just the convention that we usually use and what we're going to be doing in this lecture we're going to be looking mainly at lift and drag so we won't be looking at side forces nor will we be looking at the moments that might exist on a body. So when we look at this body and we have flow coming towards it there are two main sets of forces on the external of the body that will cause it to go and have these forces on it and these two main sources are viscous shear so we have shear along the boundary of the body once we've looked at shear stress and so all along the body we will have shear because it's in contact with fluid and the other force that we have is associated due to pressure so we have pressure forces acting on the body as well and it's this shear so I'll draw a towel wall and pressure that result in all of the forces that are on the body so it's due to those stresses shear stress and pressure which is a normal stress so those are the main forces we also have the body force associated with the weight of the body itself but here we're looking at the forces that would be exerted by the fluid and and so what we have is we have the body surface integrated we will have shear and pressure which we just saw earlier in the diagram and in this representation df shear so it's a vector it's going to be equal to the shear stress distribution on the object multiplied by the area and the force due to pressure you would need to know the pressure distribution around the body and you would then have to integrate and in that case pressure is a scalar and so the area is a vector so those are the forces that act on bodies we will mainly look at lift and drag but what this says is that if you want to know those forces and the moments and everything else you need to be able to resolve what the shear force is going to be on the body as well as the pressure distribution and it gets quite complex and that's why analytically it's pretty much impossible or very very challenging to be able to determine these for any kind of body we can do it numerically but quite often we use experiments in order to collect this type of data so that's what we're going to be talking about in this lecture and we'll continue on and look at different types of flows we'll be looking at drag force and we will be looking at lift force