Hey good morning AP Physics two we are going
to start today with the second part of fluids.
We're going to go get that to where y'all
can see it. OK, so fluid dynamics for AP Physics
2. The learning objective is I can calculate
the velocity of a fluid by applying the correct
formula to the problem and install. The guiding
question is going to be how can I calculate
the velocity of a fluid? Alright, we're going
to hop to the next one. OK, so fluids in motion.
Here's the thing that we're going to work
on. 1st is we've dealt with fluids that are
essentially stationary static. Now we're going
to do with him in motion. What we're going
to be talking bout this entire time is what's
called an ideal fluid, and what that means
is is not viscous, meaning there's no internal
fluid within the internal friction within
the fluid itself. It's incompressible, meaning
that the density of it is constantly entire
time, so it doesn't change. And then the motion
is not turbulent, which means there's no essentially
no friction or any other forces that are affecting
the fluid will play this little video I have
right here, and just so you can see what's
a lameter fluid. OK, and you'll see it looks
like this isn't even moving, but watch with
this guy does here. In just a second. OK,
so that is a real quick just preview of what
a Lamon are. Ideal fluid would look like in
motion was really hard to tell that it was
moving. We're just going to go to the next
step. OK, so first big topic area is what's
called flow rate and flow rate is how much
mass passes a given point in a unit of time
as that is going to be constant anywhere inside
of a pipe, so the flow rate of fluid is constant
every given point. Now having next slide that
will show you that here in a second this is
also called your continuation or continually
formula. And I've got that right here. Density
equals the area of the pipe times the velocity.
Then that's going to be equal to the density
of fluid times the area of the π times its
velocity at a different point. Since density
is the same everywhere, we can simply take
density out and we're left with the area of
the pipe. Tons of velocity equals the area
in a different spot times the velocity in
a different spot. So I want to pull up the
next picture so you have to see it again.
There's that equation. We're going to go over,
basically to conceptual point on this, and
we're going to compare two points in the pipe.
So the first point we're going to look at
is. Over here on the left hand side and we're
going to compare that to a point over here
on the right hand side. So a couple things
just pause the video here for a second one.
I want you to ask yourself is where is the
velocity of the fastest and why? And then
I also want you to ask yourself which point
has the higher flow rate or fluid flow. So
pause and then come back to that. Alright,
now that you've unpaused the higher fluid
flow rate, the flow rate is going to be the
same in the all positions, so the point on
the left and the point on the right had the
exact same flow rate. Now the other question
is which one has? Is the fluid moving faster?
The fluid is moving faster on the point on
the right, and the fluid has to move faster
so that all of that mass can pass through
there at the same amount of time. One more
picture that kind of illustrates that would
be on the next slide. What do you see in a
wide River over on the left hand side versus
the? Kind of narrow stream over on the right
hand side. And why do you think you see this?
Suppose it just kind of take a minute. OK,
why am I seeing this? OK, now that you've
unpaused, the main reason why you're seeing
this is because the River on the left hand
side is very wide, so it has a large area
River on the right hand side is really really
narrow, so it has to move much faster. That's
why the water looks much more turbulent and
much more swift in the picture on the right
hand side. K so example problem spread through
this. Pause the video and then when you're
ready I'm going to run through this example
for you. Go ahead and pause. Alright, now
that you've written down and try to solve
this one, we're going to walk through this
question together so where you want to start
is area times velocity equals area times velocity.
The area. One key thing that you're going
to want to think of it if they give you a
radius which they did in this question, think
of radius and to get the area you're going
to the area of a circle, so that's why I have
π R squared there, then just went ahead plugged
in the numbers that we had. Into both sides
and then solved for the velocity. And since
the units were in centimeters per second,
the unit for this would also be in centimeters
per second. I'm going to hop over to the next
question is going to be another example. Alright,
so this example no real numbers to this, so
just read through it, pause and then once
you think you have it, go ahead and hit Unpause.
Alright, now that you've unpaused the answer
to this one is D. So let's talk about why
so the water water flows through the pipe
and then it answer it, enters a part where
the the area gets reduced by half. So to compensate
for that, the velocity has to double on these.
These are the kinds of problems where if you
want to put in numbers to start with, he could
have used area as one and the original velocity
is 1 and then. It said the. Area gets cut
in half, so area 2 would be 1/2 and you're
essentially solving for velocity two, which
would be doubled or two. Alright, one more
example problem. This one has some numbers
with it. I've so you might want to jot this
down and try to work through this. Go ahead
and pause the video once you think you have
that will come back and take a look. Alright,
now that you've unpaused, I'm going to pull
up the answers for that and just kind of walk
you through it. It was I just start with the
continue iti Continui equation and I went
ahead and just solved it algebraically for
velocity to hear on this step here. If you
want to go ahead and plug your numbers in
and then move your numbers, you can't, that's
up to you and then I just plugged everything
in 10 centimeters cubed for R-squared for
the area, the velocity, and then the other
area of 5 centimeters squared. Multiply that
out and divided by 5 and got a answer of 30
meters per second. Alright, so here is the
next concept. We're going to talk about. So
this is called the Venturi effect. This is
when a fluid moves through a pipe and the
pipe narrows the pressure in the narrow section
is going to decrease. I'm going to show you
several different images that hopefully will
help illustrate that. So this one you'll notice
I've got this part over here on the left hand
side is much wider. The part in the middle
narrows and then the part on the right hand
side widens back out. So we have higher area
of pressure on the left hand side, higher
area of pressure on the right hand side because
it is more. Why'd the inside is constricted?
It's reduced down in area so you're going
to have a lower pressure in that area. Two
other photos that just kind of illustrate
this same thing. This time it has the gauges
with actual numbers on it, but it's doing
the same thing. And then there's bottom image.
What you'll notice is you'll see that the
water in the middle doesn't go to as high
of a height. The reason that happens is there's
less pressure to push it up. Remember, pressure
is force divided by area. If there's less
pressure there, there's less force so that
that liquid is not going to get pushed nearly
as high. In that one. So that's kind of the
second concept for today. So first concept
was the continued continued equation in the
Venturi effect. We're going to go over Bernoulli's
equation. This one is going to look really
really long. This is really a conservation
of energy concept with a fluid. So this equation
applies when there's a fluid in a pipe and
then you have a change in height. Think of
this just like conservation of energy, where
total energy before and total energy after
are conserved. So here's the equation. I kind
of want to walk through this and I want you
to think of it in terms of energy. So you'll
see one arrow pop up here on the left hand
side. Hopefully we look at that. That kind
of looks like 1/2 MV squared, well. Is essentially
the. Kinetic energy of a fluid? You'll notice
that's on both sides. So you have essentially
the kinetic energy of the fluid on both sides.
You also notice hopefully one other term that
looks fairly similar. I've got an arrow popping
up on that one. It will ro GH. Hopefully that
looks very similar to mge or our potential
energy equation. Notice both of those show
up on each side, so you have potential energy
on both sides. You have kinetic energy on
both sides. The one thing that was new is
going to be pressure. So pressure is kind
of our 3rd way that we can. Store energy,
I think it wants you to think that is almost
like another way you can store energy are
going to take a look at this as an example.
So you got an example, just a little pipe
and one of the things that you'll notice is
it's going uphill and it's getting constricted.
So this maybe when you see a problem this
would be a time when you go OK I'm going to
use Bernoulli equ.nderstanding. Guys, we're
going to pick up with one of the annuities
questions with some numbers and everything,
so take a minute, try to work through this
one. This one will be your first attempt at
a Bernoulli's equation. So take a look at
that and see where you think you should start
going to the hidden. Pause here to start.
Work through it, and then when you are ready
I will walk you through the steps on how to
do a question like this. Alright, now that
you have unpaused, we're going to walk through
the solution, so the first thing you want
to do is figure out the velocity of the fluid
in the other area of the pipe so you're going
to hear continuation equation, or you can
do your continuity equation. Have that, therefore
you can plug in the area in the velocities,
and then will solve for the missing velocity,
so that'll be part one. Second part is to
use our Bernoulli's equation that has all
of these terms in there. One thing you'll
notice is height one is 0, so that will actually
drop out equation. So we're going to worry
about that part. So here's the next part.
So we've got pressure 1. They were trying
to sell for pressure too, so I went ahead
and moved everything over, so pressure two
is by itself and then plugged in the numbers
and then solve it. So if you need to pause
it here to take a look at how those numbers
work, feel free and then we're going to look
at one more thing. It's called Tor Shelly's
theorem, and then we're going to walk through
that. Alright, last new idea of this is called
Torricelli's theorem. This is going to apply.
This is Bernoulli's equation but it's reduced
down very very simply and this has allows
us to figure out how fast a liquid would be
traveling with leaves something with a hole
in the side. So when you see this you'll have
something that's filled up. It will have a
hole in the side and you'll be able to figure
out what the velocity is V1, which is the
velocity as it exits. Is the square root of
2 G and then it's basically the difference
in height from the spout up to the top of
the fluid and then as that fluid empties the
height will get reduced, which means the velocity
will get reduced as well. OK, so concept question
first on this and then we'll go with some
numbers. Alright so content concept question
first. Attainment kind of read through that,
and then we'll come back and talk about it
here in just a second. So two concept questions.
And then we'll suppose. And then we'll talk
about it. Alright, the answers to these the
velocity as at water drains will decrease
as well the distance it lands away from the.
Jars coming out now we're going to do this
same concept, except this time we're going
to use the numbers. We have some equation
we're going to actually use the equation,
so take a minute to read through this pause.
See what you come up with for the exit velocity
on this one. Alright, now that you have unpause,
we're just going to walk through how to do
this. I've got this up here for you, so there's
the equation there at the top. I went ahead
and plugged in all of the numbers. You'll
notice there wasn't a Y one, so if you don't
have a Y one, you can use 0. So I just walked
through those numbers there, plugged everything
in there and I got 9.9 as the velocity that
it left at. If you use 10 for your acceleration
of gravity would get a slightly higher. Velocity,
and that's fine as well. OK, where can you
find these equations? If you are looking on
your AP Formula chart, you have all those
equations here at the top, under the fluid
fluid mechanics and thermal physics you'll
notice A1V1 equals a 2B2 is right there. You'll
also notice there is Bernoulli's equation
all written out for you. The only inflation
that's not on there is that or Shelly's equation.
So I would go ahead and just add that to your
formula chart or memorize it. Whichever one
you want to do. As a reminder, please make
sure you're doing your exit ticket in canvas
for attendance, and that will wrap us up for
today. You'll have a wonderful rest of day.
