 In the last segment what we did is we took a look at the correlation that new salt was able to derive for the conductive heat transfer coefficient for condensation on a vertical surface. We're now going to look at other correlations that extend beyond the laminar flow regime into the wavy and then finally into turbulent flow. And so what we're going to do, we're going to begin assuming that we know the thickness of the film that is forming on the surface that is cooled, the condensation film. So these correlations can apply to either a vertical plate or to a vertical cylinder provided that the radius is much larger than the film thickness that forms on the vertical plate. Now we're going to introduce a new Reynolds number that we will use in these correlations. And if you recall from an earlier lecture we were talking about Reynolds number being defined in terms of the mass flow rate of the condensate running down our vertical surface. And this was the expression that we had. And here, P-E-R, that is the perimeter. And so if you're looking at a vertical plate, the perimeter would be equal to the width of the plate. And we said the unit width would be B, not unit width, but that would be the width that we're dealing with would be little B. And if you're dealing with a vertical cylinder, in this case the perimeter is equal to pi times the diameter of the cylinder. And so with this, what we can do, we can make a substitution here. And I'm not going to go through it, but it enables us to come up with a new form of the Reynolds number defined in terms of the thickness of our film. And so with that, a new salt or you can come up with a relationship for this gamma of X, which is basically quantifying the mass flow rate of the film as it's moving down the plate. But with this we get a new Reynolds number and that will be Reynolds number delta. And it is expressed in the following manner. And so notice we have delta in here. So that assumes that we know the thickness of our film and that becomes the Reynolds number. Now, what we're going to do, we're going to assume that the density of the liquid, which is here, is much larger than the density of the vapor, which is usually the case. When you look at water, typically for atmospheric pressure, it's a difference of about a thousand. And so it's a fair assumption to say that the liquid density is much higher than the vapor. But we're going to make that assumption. So with that assumption, we can then express the following correlations. And we're going to begin with laminar. And so this one would need to be consistent with the one that new salt came up with analytically. But it will be defined in terms of a new salt number. There is our average connective heat transfer coefficient. Now the length scale here, what we're going to do, we're going to use, that is our kinematic viscosity. So kinematic viscosity, remember, is mu L divided by rho L. We're going to make that substitution. So kinematic viscosity squared divided by G raised to the power one-third. And then we're going to divide by the thermal conductivity of the liquid. Let me get rid of the kinematic viscosity. It's just going to confuse things. There we go. And this is then given by the following expression. And this obviously would apply only in the laminar flow regime. And so that means that the Reynolds number has to be 30 or less going on into the wavy regime. And so this would pertain or apply for Reynolds number between 30 up to 1800. And then finally an expression for turbulent. So these are obtained by taking experimental data and collapsing it. That's where the last, the wavy and the turbulent would come from. And this one it turns out has sensitivity to the Prandtl number. And so we see the Prandtl number starting to appear in the relationship. And that would be for the case where the Reynolds number based on delta is greater than 1800. So those are the three correlations that you can use provided that you know your film thickness. What we'll do in the next segment, we'll look at three correlations if you don't know the film thickness. And it would depend upon the particular problem that you're trying to solve, whether or not you would know the film thickness. Sometimes you might know the convective heat transfer coefficient. And then you'd be able to do calculations such as determining what the height of the cylinder needs to be if you know H. And so anyways, that is if you know the thickness of the film, we'll look at another set of correlations in the next segment.