WEBVTT

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- Let's talk about the Venturi effect.

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This has to do with water or any fluid

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flowing through a pipe.

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And it turns out, let's say
this water's flowing right here.

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Minding its own business, having
a good day for that matter,

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when it meets a constriction.

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What's gonna happen here?

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Well, the water's gotta keep flowing,

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but it's gonna start flowing faster

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through the constricted region.

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And the reason is, well,
there's a certain amount of

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fluid that's flowing through this pipe.

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Let's say all the fluid
in this region right here.

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Let's say this front part of the water.

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I mean, this whole thing's filled up,

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but just say this
cross-section of the water

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happened to make it from this back portion

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to this front portion in, I don't know,

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let's just say one second.

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So this entire volume
moved through this section

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of the pipe in one second.

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Well, there's a law in physics
that says that same volume's

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gotta make it through
each portion of this pipe.

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Because if it didn't, where's it gonna go?

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This pipe would have
to break or something.

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This water's gotta go somewhere.

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If that much flowed
through here in one second,

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then this much has to flow through this

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little tiny region in one second,

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but the only way that
that's possible is for this

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front surface, instead
of just traveling from

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there to there in one
second, the front surface

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is gonna have to change it's shape.

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But the front part of
the water's gonna have to

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travel from here to here
maybe in 1/4 of a second

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because all of this has
gotta cram through here

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in the same amount of time.

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Because that water's
still coming behind it.

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There's more water coming.

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And the volume flow rate
has got to stay the same.

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The volume per time
flowing through one region

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of the pipe has got to be the same as

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the volume flow rate through
some other region of the pipe

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because this water's got to go somewhere.

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It doesn't just disappear in here.

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It's gotta keep flowing.

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That means...

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The important part is
the water flows faster

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through the constricted region.

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Sometimes much faster through
the constricted region.

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The smaller this is compared
to this original radius,

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the faster the fluid
will flow through here.

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Why do we care?

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Well, because faster moving
fluid also means lower pressure.

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Why does faster moving
fluid mean lower pressure?

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Well, if we look at
the Bernoulli equation,

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Bernoulli's equation says
P one plus row g h one

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plus 1/2 row v one squared

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equals P two plus row g h two

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plus 1/2 row v two squared.

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Oh my goodness this looks frightening,

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but look at P one, we just
pick some point in the pipe.

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Let's just pick this point right here.

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We'll call that point one.

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So all these ones, this whole
side refers to that point.

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Let's just pick point two right here.

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All this whole side refers to that point.

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Now, notice something.

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These are basically the same height,

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and assume height's not
really a big difference here.

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So let's cross out the heights,

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because they're the same heights.

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We don't have to worry about that.

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This says that, alright, if
there's some pressure at one

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and some velocity of the water at one,

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you can plug those in
here and get this side.

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And now look at over here.

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We know that the velocity
at two is bigger.

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We just said that, it
has to be because the

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volume flow rate's got to stay the same.

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So this speeds up in here.

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So this is bigger, this quantity here.

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But we know the whole
thing equals this side.

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So if this term increased,
that means that the pressure's

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got to decrease so that when they add up

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they get the same as this side over here.

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This is actually called
Bernoulli's Principle.

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Bernoulli's Principle
says that when a fluid

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speeds up, it's pressure goes down.

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It's totally counter-intuitive.

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We always expect the opposite.

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We think fast moving fluid, that's gotta

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have a lot of pressure, but
it's the exact opposite.

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Fast moving fluid actually
has a smaller pressure

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and it's due to Bernoulli's equation.

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And this is what causes
the Venturi effect.

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The Venturi effect refers
to the fact that if you

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have a tube and you want
a smaller pressure region,

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you want the pressure
to drop for some reason,

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which actually comes up in a lot of cases,

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just cause a narrow
constriction in that tube.

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In this narrow constriction,
faster moving fluid,

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and it'll cause a lower pressure.

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This is the idea behind
the Venturi effect.

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So the Venturi effect basically says for

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a constriction in a pipe, you're
gonna get a lower pressure.

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While we're talking about fluid flow,

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we should talk about one more thing.

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Let me get rid of this here.

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Imagine you just had a brick wall

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with fluid flowing towards it.

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Maybe it's air here.

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So you've got some fluid
flowing towards this brick wall.

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This seems like a really dumb example of

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Bernoulli's principle
but I'm going somewhere

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with this so stay with me.

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This is flowing towards here.

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What's going to happen?

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Well, it can't go through the wall.

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It's gotta go somewhere.

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Maybe this just goes up like that

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and this, you know, I'm gonna go this way.

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It's closer to go that way.

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This side maybe just goes down.

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This is actually kind of what happens.

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But there'll be a portion in the middle

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that basically just terminates.

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It hits here and kind of just gets stuck.

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So there'll be some air
right near here in the middle

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where it's just not moving.

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What if we wanted to
know what the pressure

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was there, based on the variables
involved in this problem?

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We could use Bernoulli's equation again.

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Pick two points, let's
pick this one, point one.

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Let's pick this one, point two.

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Use Bernoulli's equation, it says this,

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and again let's say these
are basically the same height

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so that height is not a big factor.

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And if these terms are the same,

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then we can just cross
them out because we can

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subtract them from both
sides, they're identical.

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Now, what can we say?

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We know the velocity of the air at two.

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It's not moving, got stuck here.

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It got stagnant.

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And so v two is just zero.

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And we get this statement
that the pressure

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at two, which is sometimes
called the stagnation pressure,

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so I'm gonna call it
the stagnation pressure,

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because the air right here
gets stuck and it's not moving.

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You might object, you
might say, "Wait, hold on.

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"I thought the air had to go somewhere?"

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Well, it's all going somewhere.

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The point is, there's some air
right here that gets stuck.

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It get stuck and air starts passing it by.

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And so, what's this pressure here?

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Well, up here we just read it off.

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All these went away.

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P two, which is what I'm
calling the stagnation pressure,

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has gotta equal P one,
the pressure over here,

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plus 1/2 row v one squared
and we get this formula.

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You might think, "Why
would we care about this?

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"Who is regularly shooting
air at a brick wall?"

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People do it all the time,
because you can build

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a pretty important instrument
with this called a Pitot tube.

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And the Pitot tube looks
something like this.

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Let's get rid of that.

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So why would someone use this system?

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It's called a Pitot tube.

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People use it to measure fluid velocity

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or, if you're moving through the fluid,

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it's a way to measure your
velocity or your speed.

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So what happens is you've got this set up.

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Let's say you're in an airplane.

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You mount this on the airplane.

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You're flying through the
fluid, which is the air.

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So that mean air is rushing
towards this section here.

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Rushing past you, let's say
you're flying to the left.

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So you'll notice air flying past you.

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A Pitot tube always has
this section that's facing

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into the wind or into the air.

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This air would be directed
straight toward this region,

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and the key is this is
blocked off at the end.

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So there's air in here,
but it can't be moving.

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The air in this section
can't be moving all the way

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to the front because, I
mean, where's it gonna go?

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We just said if fluid flows
it, fluid's gotta flow out.

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There's no out here.

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And then there's another region.

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Up here you've got a second chamber

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where the air flows over the top.

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And this is directed at a
right angle to that air flow.

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You've got another chamber.

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And again, in here, fluid's not flowing.

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The key is this gives you a
way to determine the difference

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between the pressure here
and the pressure there.

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If you had some sort of membrane in here,

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something dividing these
two sections that could

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tell you the pressure differential, right?

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If the pressure on this
side is a little bigger

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than the pressure on this side,
and this would bow outward,

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one of these is measuring
the pressure here

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and one of them is measuring
the pressure there.

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What is the...

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Mathematically, what's the relationship?

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It's the one we just found.

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Right here, this is the
stagnation pressure, right?

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The air's not moving in
here, it flowed straight in.

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We know the v is zero right here.

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And so the stagnation pressure
equals the pressure up here.

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Again, I'm assuming there's
very little height difference.

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Let's say this is a very small device

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and it's not like 10 meters tall.

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So any height differences are minuscule,

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and we would just have
our same equation before.

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This would just equal the
pressure plus 1/2 row v squared.

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And this is how you determine the velocity

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or the speed, because now we
can just solve this for v.

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I'd get that v one equals P
s, the stagnation pressure,

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minus the pressure at
one, that whole thing,

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times two, divided by
the density of the air

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and then a square root because you have to

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solve for the v one.

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So this device lets you determine this

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pressure differential right here, check.

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You need to know what
the density of air is

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and this gives you a way to determine the

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velocity of the fluid, or in other words,

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the velocity of your aircraft
flying through the air.