 Now another aspect or topic of importance within the study of fluid mechanics is going to be a way to be able to define dimensions and units. And we'll be using this later on in the course when we do a thing called dimensional analysis, and that was something that was used quite often, but in order to figure out the non-dimensional numbers that are important for the study of fluid mechanics. So to begin with, a dimension, a dimension is a measure by which a physical variable is expressed quantitatively. So dimensions, we're all aware of dimensions, that would be a length or things like that. And a unit, a unit is the way to describe some sort of calibrated reference for that particular dimension. So it's a way of attaching a number to a quantitative dimension. So examples of both of these, in the case of a dimension, a length is a common dimension that we often deal with, and we could use a length in a number of different ways. We could use it for height. We could use it for displacement. We could use it for distance or other things. So that's an example of a dimension. And now if you're talking about length, what might the unit be? Well, it depends upon the system that you're operating in, but if we're looking at the units for length, it could be a meter for using the SI system, or if we're using British units, it could be foot. So there we have a dimension, the dimension would be length, and we have, if we're looking at the unit, it could be foot or meter. So in fluid mechanics, why is this important? Well, in fluid mechanics, we have what are called four primary dimensions that we'll be using when we do dimensional analysis later in the course. So the primary dimensions that we're going to be using in fluid mechanics, one of them will be capital M, and with the primary dimensions, I'm going to put them in curly brackets like that. Another one is length, capital M by the way is for mass, L is for length, T denotes time, and the last one that we will use is theta, and that will denote temperature. So we have mass, we have length, we have time, and temperature. So if we were to look at these in the different unit systems that we operate with, or that we will be operating with in this course, if we were to look at SI and then the British units, so if we're talking about mass, we know that in SI we're often using kilograms, and that would have the symbol KG, and if you're using British, that would actually be the slug. If you're looking at length in SI, we know that we use the meter, and in British units, it would be the foot, and sometimes that is expressed as being FT. If we're looking at time, time is going to be common between the two unit systems, and if we're looking at temperature, we're usually talking Kelvin in SI, and we're dealing with Rankin, and that's denoted by degree Rankin in the British unit system. So with that, those are our primary dimensions, and then we can express the dimensions for what we call secondary dimensions, and this is a combination of all of the above for whatever it is that we might be looking at quantifying, but the secondary dimensions are composed of m, l, t, and theta dimensions. So let's take a look at an example of what I'm talking about. So let's take an equation that we will use quite often in fluid mechanics. F equals mA, and that becomes the basis of the Navier-Stokes equations, control volume analysis, other things like that, but if we're looking at force, you'll notice that force does not appear anywhere in the dimensions that we have above, so what we need to do is we need to decompose it back into the primary dimensions, and if we know force is equal to mA, we can then express it as being capital M for mass, so we have the mass there, and that would be capital M, and then that is multiplied by acceleration. Now what is acceleration? That is distance per unit times squared, so we can write acceleration as being l, and then t to the minus 2, and what that would give us then for our secondary dimensions for force, it would be m, l, t to the minus 2, and so that is something that we'll see later when we do dimensional analysis in this course, but it's important to mention now because it's one of the fundamental things that we'll be looking at, and it can quite often help you if you're planning experiments, you do dimensional analysis to understand what the key variables are, the non-dimensional numbers that might be governing the experiment that you might be conducting. So those are dimensions and units.