 Okay, so we just came up with a formulation for the continuity equation in cylindrical coordinates. What we're now going to do, we're going to look at an example problem that involves continuity in cylindrical coordinates. So what we're told is that we have one-dimensional radial flow in the r-theta plane. So what do we know? That means we can say vr is some function of r and we're also told the v-theta is equal to zero. So there's no velocity in the circumferential or azimuthal direction, and we're told that the velocity in the radial direction is a function of r only. And what do we want to do? We want to find requirements on f of r for incompressible flow. Alright, so, and what that means by requirements, what is a functional relationship like? And we know v-theta is zero, so what we're going to do, we're going to start off by looking at the continuity equation for cylindrical coordinates. And that was del dot rho v plus partial rho partial t equals zero. Now we said that it was incompressible flow, and consequently that means density is equal to constant. And the time rate of change term then that disappears, and what we are left with is then quite simply del dot v equals zero. That's continuity for incompressible flow. Let's rewrite that now in terms of cylindrical coordinates, and then we'll play around with the math and see if we can figure out what the functional relationship should be for the velocity in the radial direction. So del dot v equals zero, writing that in cylindrical coordinates, what we have is the following. Now we were told for the problem that v-theta equals zero, and this is one-dimensional radial flow. And so what one-dimensional radial flow implies is that the flow is only going in one direction, and consequently that means that the partial by partial z term, we can assume that to be zero based on the fact that we're dealing with one-dimensional radial flow, and we were told that it was in the r-theta plane, and consequently that means that this term is gone and that term is gone, and what we then end up with is this. So we then get partial by partial r r v r equals zero, and if we integrate that, what we will get on the left-hand side is r v r, and on the right-hand side would be a constant of integration that I'll just call a constant c. So with that, we can say v r is c over r, and therefore function of r is just c over r. So what does that mean? So what does that mean? That means that the velocity is going to reduce as we move out in the radial direction in a 1 over r manner. So if we had our system here, we have fluid flowing out at the center, and let's just show this in our cylindrical coordinate system. So if we were to go to radial location 1, so this here is r equals r 1, and we were to look at the velocity at any location, and that should be in the radial direction. So drawing out the velocity in the radial direction, we might get something that looks like that, and we could write v r at r 1 is then c over r 1, and if we go a little bit further out, so if we go way out here, and this would be r equals r 2 at a further radial location, then here, let me write that, what we could say is that v r at r 2 is then just equal to c over r 2. So what you're finding is that as you go further and further out, the velocity is going down and down and down, just because the area that it's flowing through is getting larger. So by conservation of mass, we know that the velocity is going to drop down. So that's a particular case where there is no v theta, and it's only one dimensional flow going in the radial direction, but applying the continuity equation to cylindrical coordinates.