 Another one of the forms of general motion of a fluid particle is that of linear deformation. An image to show what is happening with linear deformation is something like this. And this is the case where the fluid particle is changing in terms of its volume as it's convecting or moving about. So we can have different types of linear deformation but that's one that we've shown here. And it turns out that this occurs dependent upon the derivative, the spatial derivative of the velocity components. And so it turns out that the element will deform if partial u, partial x, partial v, partial y, or partial w, partial z exist. And these represent the strain rates, longitudinal strain rates in the principal directions of our coordinate system. So when we're looking at this, I can read out an expression. Now this one kind of makes sense. If we're changing the lengths of the sides of our fluid element, that means that the volume of the fluid element is changing. Now when we looked at vector relations, we did look at a relation, the divergence, that what we said is that it quantified the time rate of change of volume of the fluid element. So what we said is that the time rate of change of a volume element or a fluid element per unit volume is given by del dot v. And that was the divergence vector operator, which we said operates on a vector. And if we write out divergence del dot v, that then gives us a quantification of the volume dilation rate. So either the fluid element is getting larger or smaller, but the volume would be changing. Now that would obviously be for a flow that we would call compressible, one where the volume could change. Quite often we're dealing with incompressible flows. So if we do have an incompressible flow, recall when we looked at the continuity equation, we said that for incompressible flow, del dot v was equal to zero. And that's basically saying that the dilation or the volume dilation rate for compressible flow is zero, which would make sense. Because what that means is that for incompressible flow, the volume remains constant. That is, it does not change as the fluid element convects and moves. So that would be for incompressible flow. And if we do have volume change, then we would have it's not always just compressible flow. You could have non isothermal flows where you have heat transfer. And you can get volumetric heating of the fluid, in which case it would expand as well. So you don't need to have the high Mach numbers. You could actually have this at very low Mach numbers, but still with non isothermal flow have volumetric heating. So that is linear deformation. If you want to go back and look at the other general forms of motion in a fluid particle, all you have to do is click on the return key that I've just put there. So click on that with your mouse and it'll take you back. If not, the segment will end shortly.