0:10

Here is the table of contents and as you can see it begins with a discussion of

Â units which I'll talk about in a minute.

Â Then conversion factors.

Â Then ethics, safety, et cetera.

Â And a number of topics related to the the knowledge areas.

Â However, this table of contents doesn't correspond to the list

Â of knowledge areas, the 18 knowledge areas, which I mentioned exactly.

Â There isn't an exact correspondence between them.

Â For example, there's no section here.

Â Specifically on hydraulics and hydrologic systems.

Â Instead, many of the topics in hydraulics are found within fluid mechanics.

Â And the topics in hydrologics and hydrologic systems

Â are contained within the sections on fluid mechanics and civil engineering.

Â So, the topics particular areas are scattered somewhat throughout the manual.

Â And, as I mentioned before, somewhat hard to find sometimes.

Â Basic to all of this is the idea of dimensions and units.

Â The first section in the handbook.

Â And, the first thing that's important of course, is that any physically realizable

Â equation, must be dimensionally homogeneous.

Â And what that means is that all additive terms in an equation

Â must have the same dimensions.

Â 1:41

And, we'll suppose that it's subject to gravitational acceleration of magnitude,

Â magnitude g.

Â After some time, t, let's suppose that this particle has fallen a distance d.

Â And the question is,

Â what is the relationship between the distance d and time.

Â Well, that's a very easy problem in kinematics, I'm sure you can do that.

Â And the answer is d, the distance is v0 t plus one-half gt squared.

Â Now, in this equation on the left hand side,

Â d is obviously a distance, it's a length.

Â V0 times t also has dimensions of length, and gt squared,

Â I'll leave you to put that, also has dimensions of length.

Â So each term in this simple equation has dimensions of length.

Â They're all the same, and that must always be so.

Â If you have an equation where the dimensions of

Â the different terms are different.

Â Then there's something wrong with that equation.

Â 2:46

Now, generally in fluid mechanics civil engineering,

Â we'll be dealing with three primary dimensions.

Â Either mass, length and time, which we denote by M, L,

Â and T, and we usually place within square brackets to denote that we're referring to

Â dimensions in that case, and also possibly F, force.

Â However, force is not a fundamental dimension because force is related to

Â mass and acceleration by Newton's second law, F equals ma,

Â from which you can see that the dimensions of force must be the same as

Â the dimensions of mass multiplied by acceleration MLT to the minus two.

Â 3:30

So, there are three fundamental dimensions involved here, either mass, length,

Â or time, or force, length, and time.

Â You can use either one, but not both generally.

Â All of the physical variables that we're interested in

Â can be expressed in terms of these three primary dimensions.

Â For example, acceleration is length per time squared.

Â Density is mass per unit volume, or

Â ML to the minus 3 et cetera, for all of the other variables here, power,

Â energy, et cetera, are all expressible in terms of three fundamental dimensions.

Â And generally we'll mostly be using the MLT system.

Â However, equally you could use the FLT system, but not both of them at once.

Â An example then is speed is distance over time.

Â The fundamental dimensions are LT to the minus 1.

Â But the particular unit you use depends on the the unit system you're, you're using.

Â For example, the units might be feet per second, or meters per second, or

Â miles per hour.

Â This is the section on units and if I can just expand, blow up the first part here,

Â it says that the FE examiners handbook use both the metric system of units,

Â in other words SI, and the US customary system, USCS.

Â 4:59

Now, more generally though, there are three main systems of u,

Â units there that are commonly used in engineering and science.

Â And the difference between the two we can illustrate by means of Newton's second law

Â again, which I'll generalize by putting a constant of proportionality.

Â So, instead of F equals ma, I'll write F equals kma.

Â Where k is a constant, and

Â the value of that constant depends on what particular system of units you're using.

Â 5:30

So firstly, the metric system or SI units, we put k equals 1,

Â and we define 1 Newton as the force which

Â gives an acceleration of 1 meter per second squared to a mass of 1 kilogram.

Â 5:56

The second one, the so sc, the so

Â called US customary system puts k is equal to 1 over gc.

Â Where gc is the universal gravitational constant which has a value

Â of 32.174 units of pound mass foot per pound force, second squared.

Â So in this case we define 1 pound force as the force which gives an acceleration

Â of 32.2 feet per second squared to a mass of 1 pound mass.

Â So the unit of force here is the pound force and

Â the unit of paw of mass is pound mass with subscript F and

Â M attached there to differentiate between the two.

Â There is a third system, so called British gravitational system,

Â which also puts k equals 1, and in this system, we define 1 pound as the force

Â that gives an acceleration of 1 foot per second squared to a mass of 1 slug.

Â So in this system the unit of force is the pound, and

Â we don't really need to put an F on the end there to distinguish it anymore.

Â The unit of force is the pound, and the unit of mass is the slug.

Â 7:14

But here as I mentioned in the FE exam we use predominantly the first two of these.

Â So, these are the basic units in the first in those three systems

Â unit of mass in SI is kilograms, USCS is pound mass, and

Â BG is slug, length is meters, feet, and ce, and feet,

Â time is seconds, and force is either Newtons, pounds force, or pounds.

Â 7:45

Now different disciplines tend to use different systems.

Â For example, I think that mechanical engineers and chemical engineers

Â tend to use the pound mass and pound force system, whereas civil engineers and

Â aerospace engineers tend to use the slug and pound system.

Â So we just have to be aware of the differences between these.

Â 8:08

So, one way to remember that is that a slug is approximately 32.174

Â pounds mass and the Newton, which is not generally a familiar,

Â a Newton, a unit, a Newton you can think of is a order of a quarter pound.

Â 8:28

There are a few special units that come up.

Â For example, pressure is a normal stress, or a normal force per unit area.

Â So, it has dimensions of force over area

Â 8:53

The Pascal however, is a very small unit.

Â So more, more usually, we use a thousand Pascals, or

Â the kilopascal as a unit of pressure.

Â 9:02

Power is rate of doing work, or force times distance over time.

Â For example, Newton meters per second.

Â But again, this is given a special name.

Â A Newton meter per second is a watt.

Â 9:40

The handbook also gives a list of conversion factors.

Â And here I'll just expand on a part of that.

Â But generally speaking, I don't think we need to be concerned with that.

Â For example, con, converting acres to feet or miles to meters, et cetera.

Â Because generally,

Â all of the problems will be given in one system of units with the properties given.

Â So although the conversion factors are given here,

Â I don't think they're a concern for the exam.

Â 10:19

And let me do an example to illustrate how the units of mass and force work.

Â So here's a simple example, we have a map, a sphere, which weighs 5 kilograms and

Â it's suspended say from the ceiling by a cable and

Â obviously there is some tension force in this cable to hold it up.

Â So the question is if the acceleration due to gravity is given the tension in

Â the cable is most nearly well, which of these alternatives?

Â 10:51

So that's fairly simple.

Â The tension in this case must be just equal to the weight of the sphere,

Â which is hanging downwards for that to be in equilibrium, and

Â the weight of an object is just the force of gravity acting on that object,

Â is the mass multiplied by acceleration due to gravity,.

Â So in this case the mass is 5 kilograms, gravity is 9.81,

Â multiplying those two together, 49.1 and

Â the automat, the units in that case automatically work out to Newtons,

Â because we've been consistent between kilograms in this case.

Â So the answer is C.

Â 11:35

Secondly, the same problem, but now we have a sphere of 5 pounds mass,

Â which is hanging from this cable and

Â the acceleration is 32.2 feet per square, second squared.

Â The tension in the cable is most nearly which of these?

Â 11:54

So here again, we have the same basic equation

Â that the tension is equal to the weight of the object.

Â Which is M times G.

Â However, now we have to be careful.

Â Because of the units here, we have to divide that by GC,

Â the gravitational constant.

Â Substituting in, we have 5 pounds mass times 32.2,

Â the acceleration due to gravity, divided by the universal gravitational constant,

Â which I'll round off to 32.2, and has units as shown, and,

Â as you can see here by checking the units, pounds, mass, pounds cancels,

Â feet, feet cancels, second squared, second squared cancels.

Â Leaving me with an answer of 5 pound force.

Â Which, of course, we would intuitively know.

Â So, the answer in that case, is 5 pounds force.

Â So, this just an illustration of where you have to be careful with the units,

Â when you're using the US system.

Â This concludes my brief overview of the exam and some issues involved with units.

Â And beginning next time we will start a detailed

Â review of the technical aspects of the different knowledge areas.

Â