 Okay, at the end of the last segment we looked at solutions for the laminar boundary layer and we found that in order to get the new salt number over a wide range of parental numbers we needed to start to look at empirical or experimental data. So what I'm going to do in this segment is just introduce us to that and that will then enable us to move onward into turbulent boundary layer flows. So we're looking at empirical force convection. Okay, so what we've been starting to notice is that the analytical methods such as the solution by Blasius only gets us so far and that only works for rather restrictive and limited cases and when we want to get to more practical or flows of engineering interest we need to start to bring in experimental results and that is the empirical data that I'm referring to and so when we're looking at these the empirical data could be in a number of different forms. We could have empirical formulas and an example of that could be new salt numbers so let's say it's new salt number based on some characteristic length scale diameter a plus b Reynolds number to the n. We haven't looked at this one yet but this is convective heat transfer over a cylinder and it's referred to as being Kinz law and if we plot new salt number versus Reynolds number we'll get a curve that would look something like this and so what you do is you collect experimental data and then fit that curve to the experimental data that you have collected and I show a scatter there because all experimental data is going to have noise in it and a little bit of uncertainty so you can come up with empirical formulas like that. Sometimes there are graphical charts and you'll look up data that way but in any event what we try to do is we try to take experimental data and collapse it in terms of these non-dimensional numbers like new salt number and Reynolds number and then when we're doing our curve fitting what we're trying to do we're trying to determine these constants a, b, and n and that would then give us a relationship that would describe the curve that I've sketched in the middle of this Reynolds number and new salt number plot and sometimes what you'll do you'll take the log of both sides of those equations enabling you to determine the constants in a power lot or you can also do numerical methods to minimize the difference between the data that you've collected and the curve that you're trying to fit. We won't be looking at that in this course but that just gives you an idea as to where these relationships are coming from. Okay so when we collect this experimental data and we're trying to collapse the data onto a curve so you might wonder how do you know what the functional form of that curve would be well there are a couple of different tools that we have experimentalists quite often use dimensional analysis we're not going to talk about it in this course but if you want to see things it's called Buckingham Pi look at my course in introductory fluid mechanics and if you find the lecture on Buckingham Pi you'll be able to watch about dimensional analysis and learn a little bit more maybe you've already taken a course that has covered that. Physical insight so Ludwig Prantl when he took the boundary layer or derived the boundary layer equations came up with them that was partially based on physical insight partially based on a doing dimensional reasoning but that enabled Blasius then to come up and solve simplified forms of the Navier-Stokes equations we call the boundary layer equations and then also sometimes what people will do they come up with very simple analytical models and these can sometimes be quite powerful because they will give us an indication as to what the functional relationships might be between the variables that we're interested in so what we're going to do with this we're going to be looking at different relationships for heat transfer over and across a number of different types of objects and bodies and plates so what we're going to be looking at is so this is where we're going in the next few segments and the next couple of lectures we're looking at flow over flat plates and we'll now be moving into looking at turbulent boundary layers then we're going to look at the flow that we call external flow over things such as cylinders and spheres and then we're going to be looking at tube banks and and tube banks are quite commonly found in cross-flow heat exchangers and consequently that is the interest that we have within this course so those are the types of flows that we're going to be looking at we refer to them as being forced convection external flows and then after we go through all of that we'll be moving into internal flow which would be pipe flow but that will be in later lectures so in the next couple of lectures these are the things that we're going to be focusing on and we'll be using a lot of experimental data and consequently what you're going to be finding are a lot of relationships that you may not really understand where they're coming from but don't worry they they've come from experiments the main thing is to know how to apply them and the other thing that I should say and I'll say it again later on in the course when you're applying these relationships make sure you understand how the properties have been evaluated I mentioned the film temperature but that's not always the case sometimes the evaluate properties at other temperatures so just be very very careful to read the paragraphs above and below the equations that you're going to use to ensure that you're applying them in the right way but anyway so that's where we're going in the next segment we'll then move into looking at expressions for the turbulent boundary layer