Venturi effect and Pitot tubes

- Let's talk about the Venturi effect.

This has to do with water or any fluid

flowing through a pipe.

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

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

when it meets a constriction.

What's gonna happen here?

Well, the water's gotta keep flowing,

but it's gonna start flowing faster

through the constricted region.

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

fluid that's flowing through this pipe.

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

Let's say this front part of the water.

I mean, this whole thing's filled up,

but just say this
cross-section of the water

happened to make it from this back portion

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

let's just say one second.

So this entire volume
moved through this section

of the pipe in one second.

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

gotta make it through
each portion of this pipe.

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

This pipe would have
to break or something.

This water's gotta go somewhere.

If that much flowed
through here in one second,

then this much has to flow through this

little tiny region in one second,

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

front surface, instead
of just traveling from

there to there in one
second, the front surface

is gonna have to change it's shape.

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

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

because all of this has
gotta cram through here

in the same amount of time.

Because that water's
still coming behind it.

There's more water coming.

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

The volume per time
flowing through one region

of the pipe has got to be the same as

the volume flow rate through
some other region of the pipe

because this water's got to go somewhere.

It doesn't just disappear in here.

It's gotta keep flowing.

That means...

The important part is
the water flows faster

through the constricted region.

Sometimes much faster through
the constricted region.

The smaller this is compared
to this original radius,

the faster the fluid
will flow through here.

Why do we care?

Well, because faster moving
fluid also means lower pressure.

Why does faster moving
fluid mean lower pressure?

Well, if we look at
the Bernoulli equation,

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

plus 1/2 row v one squared

equals P two plus row g h two

plus 1/2 row v two squared.

Oh my goodness this looks frightening,

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

Let's just pick this point right here.

We'll call that point one.

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

Let's just pick point two right here.

All this whole side refers to that point.

Now, notice something.

These are basically the same height,

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

So let's cross out the heights,

because they're the same heights.

We don't have to worry about that.

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

and some velocity of the water at one,

you can plug those in
here and get this side.

And now look at over here.

We know that the velocity
at two is bigger.

We just said that, it
has to be because the

volume flow rate's got to stay the same.

So this speeds up in here.

So this is bigger, this quantity here.

But we know the whole
thing equals this side.

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

got to decrease so that when they add up

they get the same as this side over here.

This is actually called
Bernoulli's Principle.

Bernoulli's Principle
says that when a fluid

speeds up, it's pressure goes down.

It's totally counter-intuitive.

We always expect the opposite.

We think fast moving fluid, that's gotta

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

Fast moving fluid actually
has a smaller pressure

and it's due to Bernoulli's equation.

And this is what causes
the Venturi effect.

The Venturi effect refers
to the fact that if you

have a tube and you want
a smaller pressure region,

you want the pressure
to drop for some reason,

which actually comes up in a lot of cases,

just cause a narrow
constriction in that tube.

In this narrow constriction,
faster moving fluid,

and it'll cause a lower pressure.

This is the idea behind
the Venturi effect.

So the Venturi effect basically says for

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

While we're talking about fluid flow,

we should talk about one more thing.

Let me get rid of this here.

Imagine you just had a brick wall

with fluid flowing towards it.

Maybe it's air here.

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

This seems like a really dumb example of

Bernoulli's principle
but I'm going somewhere

with this so stay with me.

This is flowing towards here.

What's going to happen?

Well, it can't go through the wall.

It's gotta go somewhere.

Maybe this just goes up like that

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

It's closer to go that way.

This side maybe just goes down.

This is actually kind of what happens.

But there'll be a portion in the middle

that basically just terminates.

It hits here and kind of just gets stuck.

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

where it's just not moving.

What if we wanted to
know what the pressure

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

We could use Bernoulli's equation again.

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

Let's pick this one, point two.

Use Bernoulli's equation, it says this,

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

so that height is not a big factor.

And if these terms are the same,

then we can just cross
them out because we can

subtract them from both
sides, they're identical.

Now, what can we say?

We know the velocity of the air at two.

It's not moving, got stuck here.

It got stagnant.

And so v two is just zero.

And we get this statement
that the pressure

at two, which is sometimes
called the stagnation pressure,

so I'm gonna call it
the stagnation pressure,

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

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

"I thought the air had to go somewhere?"

Well, it's all going somewhere.

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

It get stuck and air starts passing it by.

And so, what's this pressure here?

Well, up here we just read it off.

All these went away.

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

has gotta equal P one,
the pressure over here,

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

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

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

People do it all the time,
because you can build

a pretty important instrument
with this called a Pitot tube.

And the Pitot tube looks
something like this.

Let's get rid of that.

So why would someone use this system?

It's called a Pitot tube.

People use it to measure fluid velocity

or, if you're moving through the fluid,

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

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

Let's say you're in an airplane.

You mount this on the airplane.

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

So that mean air is rushing
towards this section here.

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

So you'll notice air flying past you.

A Pitot tube always has
this section that's facing

into the wind or into the air.

This air would be directed
straight toward this region,

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

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

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

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

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

There's no out here.

And then there's another region.

Up here you've got a second chamber

where the air flows over the top.

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

You've got another chamber.

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

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

between the pressure here
and the pressure there.

If you had some sort of membrane in here,

something dividing these
two sections that could

tell you the pressure differential, right?

If the pressure on this
side is a little bigger

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

one of these is measuring
the pressure here

and one of them is measuring
the pressure there.

What is the...

Mathematically, what's the relationship?

It's the one we just found.

Right here, this is the
stagnation pressure, right?

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

We know the v is zero right here.

And so the stagnation pressure
equals the pressure up here.

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

Let's say this is a very small device

and it's not like 10 meters tall.

So any height differences are minuscule,

and we would just have
our same equation before.

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

And this is how you determine the velocity

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

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

minus the pressure at
one, that whole thing,

times two, divided by
the density of the air

and then a square root because you have to

solve for the v one.

So this device lets you determine this

pressure differential right here, check.

You need to know what
the density of air is

and this gives you a way to determine the

velocity of the fluid, or in other words,

the velocity of your aircraft
flying through the air.