INSTRUCTOR: This screen cast is going to be
a real basic screen cast reviewing
the engineering principles of
quantities and units,
and dimensional analysis,
and how to deal with units
when you are performing engineering calculations.
So, the first important thing to understand is
what is a quantity?
Obviously, if you see the number five,
you ask yourself, "five what?"
You always need to know what you're referring to.
Do you have five apples?
Do you have five cars?
Do you have five people?
A quantity answers the question,
"how many of what?"
A quantity has a value and a unit.
So, a value answers "how many"
and the unit is "of what?"
So, in five apples,
what is the value?
The value's five
and the unit is apples.
So, in engineering,
I know this might seem a little bit trivial,
but in engineering
it's really, really important to carry
both the value and the unit.
And combined, that's something known as the quantity.
So, we have our units:
Treat units like numbers.
So obviously if we multiply two fifths by five,
we have five in the numerator
and five in the denominator,
so those cancel, and we end up with two.
You do the same thing with units.
So meters per second times second,
the second in the numerator cancels
with the second in the denominator,
and we end up with meters.
So, the seconds cancel just like the numbers.
So treat units just like numbers.
Units are as important to a quantity as the value.
Again, it's really important that you carry the units
in any of your engineering calculations.
The numerical values of two quantities
may be added or subtracted
only if the units are the same.
So if I wanted to add five apples plus two apples,
you can add those, or subtract if you wanted to,
because they have the same units: apples.
So we get seven apples.
Five apples plus two oranges,
we could combine the values,
the five and the two,
but since we don't have the same units,
we can't combine those in engineering calculations
because we have different units.
We could, by the way,
combine five meters and five centimeters,
even though those have different units,
they still have the same dimensions.
As in, they're both length scales.
So we could combine those,
but first we have to convert.
And we will do that in a subsequent screen cast.
So we can only add or subtract quantities
if they have the same units.
However, the units can always be combined
by multiplication or division.
So if we had five meters
and we multiply that by five centimeters,
we would get 25 meters-centimeters.
And that hyphen, sometimes you'll see just like a dot,
that designates multiplication.
So five meters times five centimeters we can do,
we'll get 25 meters-centimeters.
And obviously if you're working with
meters-centimeters you'd probably convert
the centimeters to meters,
or the meters to centimeters,
to give you either meters squared
or centimeters squared.
And that's something we can do if we have the same units,
we can do five meters times two meters.
We take the values, which are five and two,
we multiply those together to get the 10,
and then we multiply the units together,
the meters together to get meters squared.
Note that the values are multiplied together
and the units are multiplied together.
Another example, if we had 300 meters
dividing by 25 seconds,
you would take the values, obviously,
300 and 25, you divide those and you get 12,
and then we take the units and we get meters per second.
So, let's take a look at some of the units
that we typically work with.
Now there are the SI units which are
most common in engineering,
there are seven fundamental units.
Now these refer to mass, length,
temperature, the amount of substance, and time.
From these fundamental units,
we can create derived units.
Derived units would be something like area.
It's a fundamental unit
multiplied by another fundamental unit,
or divided by another fundamental unit.
So area is length times length.
Volume would be length cubed,
or area times length.
And we've got some of these other derived units.
For example, pressure is force per unit area,
and another example that's not shown on here
might be something like viscosity.
That's it for this screen cast,
thanks for watching.