I'd like to continue my introductory remarks with a few more comments about

the reference handbook.

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

units which I'll talk about in a minute.

Then conversion factors.

Then ethics, safety, et cetera.

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

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

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

There isn't an exact correspondence between them.

For example, there's no section here.

Specifically on hydraulics and hydrologic systems.

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

And the topics in hydrologics and hydrologic systems

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

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

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

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

The first section in the handbook.

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

equation, must be dimensionally homogeneous.

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

must have the same dimensions.

To give a simple example, consider the distance traveled by a particle.

Let's suppose I have a particle which starts out here and

it's moving downwards at some velocity, v0.

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

magnitude g.

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

And the question is,

what is the relationship between the distance d and time.

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

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

Now, in this equation on the left hand side,

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

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

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

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

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

If you have an equation where the dimensions of

the different terms are different.

Then there's something wrong with that equation.

Now, generally in fluid mechanics civil engineering,

we'll be dealing with three primary dimensions.

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

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

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

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

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

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

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

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

or time, or force, length, and time.

You can use either one, but not both generally.

All of the physical variables that we're interested in

can be expressed in terms of these three primary dimensions.

For example, acceleration is length per time squared.

Density is mass per unit volume, or

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

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

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

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

An example then is speed is distance over time.

The fundamental dimensions are LT to the minus 1.

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

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

miles per hour.

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

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

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

So, it's important to be familiar with both systems of units to

successfully answer the questions.

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

units there that are commonly used in engineering and science.

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

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

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

Where k is a constant, and

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

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

and we define 1 Newton as the force which

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

So the fundamental sy, unit of force in metric units is the newton and

the fundamental system of mass is the kilogram.

The second one, the so sc, the so

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

Where gc is the universal gravitational constant which has a value

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

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

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

So the unit of force here is the pound force and

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

M attached there to differentiate between the two.

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

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

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

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

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

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

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

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

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

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

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

Now different disciplines tend to use different systems.

For example, I think that mechanical engineers and chemical engineers

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

aerospace engineers tend to use the slug and pound system.

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

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

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

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

There are a few special units that come up.

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

So, it has dimensions of force over area

in metric units is Newtons per square meter, would be the fundamental unit.

However, we usually give that the special name of a Pascal abbreviated PA.

The Pascal however, is a very small unit.

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

the kilopascal as a unit of pressure.

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

For example, Newton meters per second.

But again, this is given a special name.

A Newton meter per second is a watt.

Another one that comes up sometimes in fluid mechanics that we'll encounter

is absolute viscosity.

And the units of viscosity in metric units are Newton seconds per square meter.

But this you will sometimes see given as a Pascal second abbreviated like this.

The handbook also gives a list of conversion factors.

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

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

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

Because generally,

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

So although the conversion factors are given here,

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

So, here again is the is the outline of the book.

We have units, conversion factors, et cetera.

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

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

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

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

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

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

So that's fairly simple.

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

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

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

is the mass multiplied by acceleration due to gravity,.

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

multiplying those two together, 49.1 and

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

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

So the answer is C.

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

which is hanging from this cable and

the acceleration is 32.2 feet per square, second squared.

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

So here again, we have the same basic equation

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

Which is M times G.

However, now we have to be careful.

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

the gravitational constant.

Substituting in, we have 5 pounds mass times 32.2,

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

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

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

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

Leaving me with an answer of 5 pound force.

Which, of course, we would intuitively know.

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

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

when you're using the US system.

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

And beginning next time we will start a detailed

review of the technical aspects of the different knowledge areas.

Reference Handbook

Fundamentals of Engineering Exam Review

Meet the Instructors