 We'll now take a look at another type of general motion within a fluid and that is of angular deformation. So the definition of angular deformation is it is the rate of decrease of the angle and that's the angle between two originally mutually perpendicular lines and we'll define that angle as being gamma and given that we're looking at the rate of decrease and you'll see as we draw a schematic in a moment I'm going to make that a negative and that is going to be equal to the time rate of change of two different lines in our fluid. We'll have one that makes an angle theta and the other one that makes an angle beta sorry alpha and beta. So we have that now let me draw out a couple of schematics that will help to visualize what's going on here. So what we have here on the left shows an image of what the deformation might look like in a fluid as it's moving starting off with a square and then it gets deformed and distorted and then on the right hand side we have the schematic that we're going to use in order to figure out mathematically how to express angular deformation and in the equation that I wrote up here we had an alpha, a beta, and a gamma. The gamma is this angle here, alpha I'm going to draw it as being delta alpha and then beta will be delta beta in here and what we're going to do we're going to use approach similar to what we did for fluid rotation in order to express this in terms of the velocities. So let's work on that. So at this point what I'm doing is I'm coming up with an expression for the time rate of change of angle alpha and I said that it's equal to delta alpha over delta t. I then use the small angle approximation that I'm embedding here and the next step what I'm going to do is use the velocity in the y direction at point a and that was using a Taylor series expansion and look back at this lecture segment to see where I'm getting those from because that's where it's elaborated. So we get partial v, partial x for the time rate of change in alpha and similarly the time rate of change in beta. Again here small angle approximation is being made to relate delta beta to delta zeta and what we end up with is the partial u by partial y is the time rate of change of beta with respect to time. So what we can do we can take those and we can plug them back into our original equation this one here and that will give us an expression for the time rate of change of the angle between the fluid. So that is angular deformation and this is usually something that is related to the shear stress in the fluid and this would then take us towards shear stress which usually we need to know not usually we always need to know the relationship between the angular deformation and shear stress would be viscosity that would link those two together. So that is the angular deformation of a fluid particle and it is one of the general motion types the four general motion types. If you want to see other motion types just click here on the return box if not that will conclude this segment.