Hi. It’s Mr. Andersen. And this is AP Physics

essentials video 88. It is on Bernoulli’s Equation. And a great application of this

is the reason why docks are not solid, why they are made of pylons so water can flow

underneath it. If you were to have a big boat like this, we are looking at it from above,

come into a dock, if it was solid it would force all of the water out of the way. And

that fluid as it is moving faster would have a lower pressure. There would be a higher

pressure on the outside of the boat which would slam it up against the dock. And so

Bernoulli’s Equation is really conservation of energy inside a fluid. And to solve most

of the problems you will first have to understand how the continuity equation works. Continuity

equation is equal to A1 times V1 equals A2 time V2. Where A1 is the cross-sectional area

and V1 is going to be the velocity. So if we look at a pipe like this, and so fluid

is flowing through it from left to right, in two different points. A1 is going to be

the cross-sectional area, so the area of this pipe here. And A2 is going to be the area

over here. And so if we look at the velocity, that is what V1 stands for, since we have

a large cross-sectional area here we are going to have a relatively low velocity. And then

as we move to the right, since we are decreasing that area, we are going to have a high velocity.

And so if you know the velocity at any point in the pipe, since that whole fluid is moving,

if you know the cross-sectional area anywhere else you are going to be able to figure out

the velocity there. An application of this, if you have ever had a hose, as water comes

out of it, it has a large cross-sectional area. If you put your thumb in front of it,

what are we doing? We are decreasing the cross-sectional area. What happens to the velocity? It increases.

Now if we look at Bernoulli’s Equation it is somewhat scary when you see it the first

time. It looks like this. And so this is going to be Bernoulli’s Equation. And it is frightening

to look at. But what we have really added here are simply two things. We have added

y, which is going to be the height of the pipe. Because that is the potential energy.

And then the other thing we have added is rho, which is going to be density of the fluid.

Because those can affect the amount of energy that we have. And so if we break apart this

equation, we have also got one on the left side and two on the right side. If we look

at this first one, P1 stands for the pressure. So inside the fluid itself, how much is that

fluid pushing in on a point inside the fluid itself. So that is going to be the pressure

energy. We then have this, rho g y 1. Now that seems confusing. But let me kind of write

it out a different way. If we were to instead of write rho or density, if I were to say

the mass, this is g, gravitational field strength and then if we were to look at y if I wrote

h there or the height, what is m g h? You know that. That is just the potential energy

of the fluid. And so that second bit of this equation is going to be the potential energy

of the fluid. And then if we write this next one, what is 1/2mv squared? That would be

kinetic energy. But we are writing density since we are dealing with a fluid. So that

is going to be the kinetic energy. And so those are the three ways we can get energy

on the left side of that pipe. It is the pressure of the fluid. It is the potential energy,

how far it is in relation to gravity. And then the last is going to be the speed of

that fluid. And since this is the conservation of energy, in these two points of the pipe,

since we know the energy over here, and we know it is going to be an equal amount of

energy over here, we can solve some pretty complex problems. So for example if we were

to look at this pipe right here, on both sides they both has the same height or the same

y value. So I have taken those out of this equation. And so where is the velocity going

to be faster? It is going to be faster on the right side of the pipe. So we are going

to have a faster velocity on the right side. Slower velocity on the left side. So what

has to be our pressure on the right side? Well to make it equal on either side, conservation

of energy, we are going to have to have a lower pressure. So just like in my example

of the ship, if the fluid is moving fast, then it is going to have a lower pressure.

And so let’s start with a continuity equation, which is simple. We have a phet simulation.

You can see as the fluid is moving, it is moving faster on the right. And so if we use

a flux meter, on the left side the cross-sectional area is 10 meters squared. And the speed is

going to be 0.5 meters per second. So that would be my A1 times my V1. If I move over

the the right side, now my cross-sectional area is 1, what is my velocity? 5 meters per

second. And so I can just solve for the one I do not know and I can figure that out. If

we were to just change the pipe, now the cross-sectional area is 5 meters squared. What is going to

be my speed? It is simply going to be 1 meter per second. And so continuity equation is

very, very simple. If we were to apply Bernoulli’s Equation, what we are really adding to it

is the density of the fluid and then the height of the fluid. And so let me give you a thought

experiment. Let’s say we were to take a half gallon of milk. And I were to pop three

holes in it and quickly put tape over it like that. So the whole thing is filled up with

a fluid. And then I were to simply pull the tape off the side. So what are are going to

get? Streams of milk coming out of the carton. But do you think those streams would look

like this, like this or like that? If you were to look at its from the side? Which is

going to be the correct way the streams are going to come out? Well the correct answer

is C. Why is that? It is because if we look down here at the the bottom, this is like

the second part of the pipe. So on the left side of the pipe we have way more potential

energy inside the milk. And so that is going to be converted to more kinetic energy and

the stream is going to go out farther. Where as if we go to the top it is not going to

have as much potential energy above it. And so it is not going to be able to have as much

velocity. So it is not going to go out as far. And so understanding both sides of the

pipe, where is the potential energy greater? It really helps you understand how Bernoulli’s

Equation works. And so it is written like this. Left side remember is going to be the

pressure energy, the potential energy and then the kinetic energy. And they are going

to balance. So it is the conservation of energy. If we know what is on the left side we can

solve for what is on the right side. So let’s try to solve a problem using Bernoulli’s

Equation. So I have a pipe. I have a left side and a right side. On the left side you

can see the velocity is lower. I am giving you the pressure on the left side. But what

we are going to solve for is the pressure on the right side. So let’s go through this

equation. On the left side I am giving you the pressure on the right side we do not know

what that pressure is. On the left side do we have less or more potential energy in the

pipe on the left side then we would on the right side. Well the density of the fluid,

since it is water is going to be the same on both sides. And since the pipe on the right

side is going to have a higher height it is going to have a higher potential energy on

the right side. What about this? Are we going to have higher kinetic energy on the right

side or the left side? Since it is going faster on the right side, our velocity is faster

on the right side. It is also going to have a faster kinetic energy or higher kinetic

energy on the right side. And since I am giving you the pressure on the left side as 128,

we would expect to have a pressure on the right side that has to be lower, since we

have higher potential and kinetic energy on the right side of the pipe. So let me show

you how I would solve this. I would write it out with the things I know. So the density

of the water, since it is the same fluid, is going to be 1000 kilograms per meter second.

And we know the gravitational field strength is 9.8 meters per second squared. On the left

side of the pipe we know the pressure, 129 kilopascals. We know the velocity and then

we also know the height. And on the right side what we do not know is going to be the

pressure. That is the unknown. But on the right side again we have a higher height,

higher velocity so we have higher energy right there. It should be a lower pressure. So if

I were to write it out I would write it out like this. Now I am not going to include the

units because it simply would not fit on the screen. Watch one thing that could screw you

up since it is 129 kilopascals, I am writing that out as 129,000 pascals because that is

the unit that we are going to use. I then solve it. And so this right here is going

to be my potential energy left side, kinetic energy left side. If we compare that to the

potential and kinetic on the right side you could see on the right side both of those

values are greater. But we are simply solving for pressure 2. And so using significant digits

I am getting around 90 kilopascals on the right side. And that is because I am limited

by this. It is not a very precise measurement in the velocity. So let’s test that and

see if that comes out. On the right side it is around 87 kilopascals. So it is around

90 kilopascals. And so we can use Bernoulli’s Equation not only to calculate but we can

use it to analyze a confusing situations when we have a fluid. So how does a curveball work?

When you throw a curveball it should drop. So as the pitcher tries, or rather as the

batter tries to hit it, it is going to drop right at the end. And so how does that work?

How does a curveball work? Using the fluid of air. So as you through a ball, let’s

say it is not spinning, as it is moving through the air the fluid of the air is going to move

around it. But since it is not spinning, the velocity on the top and the bottom is going

to be exactly the same. But when you throw a curveball you start spinning it so it is

spinning like this and it generates a wind on the top which counteracts the wind that

is already coming in, and so it decreases the speed of the wind on the top. But on the

bottom, since the wind over the ball and now the wind generated by the spin of the ball

are both going in the same direction, the fluid on the bottom is going to be going faster.

So Bernoulli’s Equation, what happens to our pressure if the fluid is going faster,

pressure is going to decrease. Since we have lower pressure on the bottom there is going

to be a force pushing it down. So that is how a curveball curves. And so did you learn

to construct an explanation of Bernoulli’s Equation using the conservation of energy?

Remember on the equation left side equals right side. Could you use it to make some

calculations and solve some problems in a moving fluid? And then finally could you use

it to show where the pressure changes? So in a dock, in a curveball or in any fluid?

I hope so. And I hope that was helpful.

great but way too fast for a beginner to this

Thank goodness! You explained it so well that I, a retarded p6 person, understood it clearly despite of not attending our intervention😀. Thank you sir!

this helped more than khan academy!

ok you earned it with first video i saw. subscribed.

How is potential energy using density not mass, same for kinetic energy?

Thank you for the great tutorial

What is the name of the program that you use?

bro you are the freakin man, great explanation even a numb nuts like me understood that

Great video; I think you can do even better. I think you should make a video that focuses on how Bernoulli's principle works with airfoils. Don't focus on angles of attack, axxys or airfoil design. I think if you stick with the core equation but show viewers the resultant, through visulaziation, fluid mechanics, and that mind of yours, thousands of cfi's would love you.

But doesn't the potential energy use Joules, kg m^2/s^2 instead of kg/ms^2?

These videos are made by The God himself.

THANKS FOR HELPING THE POOR HOOMANS!

That was very helpful, thank you so much

When you explained pgy, I was gob smacked at how much I understood the equation! Thank you. Thank you so much.💗💜💗

Great teacher. Simple and easy to understand explanations! GJ!

Super educational system

9:10 but why does a ping pong ball flies for longer when I apply a spin in that same direction?

Shouldn't it just drop if the faster flow is on the bottom?

<3

This guy is literally my savior

essentially its the same as me sticking my thumb into a hose to get the water flow to shoot out faster like a jet stream?

Excellent

7:19 Isn't density supposed to be meters cubed?

great work to sir Bernoulli. even if he died but his principle will never die. we use it even in medicine especial

in anatomy and physiology .when blood stream reaches in constricted area of vessel the velocity increases but total mechanical energy remain kept constant.i am a medical scientist from RWANDA.

thank you very much 5 star plus

THANK YOU SO MUCH THANK YOU

Excellent theoretical presentation. For an unusual demonstration go to https://youtu.be/37mA3sc2O8w Just skip over the print making stuff.

great video! which software are you using to show interactive the velocity in the pipe? I am wondering, what is happening with the pressure in detail.

What type of software used in this Bernoulli's equation

How do I solve this when the velocity is missing?

what program is this

I think you should explain convergent/divergent rocket nozzles and why the divergent part is needed.

Great! Thanks!

Can you please explain to me how 1/2(1000)(.9^2)=1620

If anyone is willing to provide the explanation, you can also send it with an email at [email protected]

Kind regards

Why is the density of a fluid "equal" to the mass of a solod when dealing with energies?

In spite of errors in the example problem, this is an excellent explanation of Bernoulli's equation. For demonstrations go to this video https://youtu.be/WfANou3DbG0

Well explained, thanks!

YOU ARE AMAZING! I'm not even an english native speaker and I understood it better than reading in my mother tongue. Seriously, awesome!

just Incredible, thank you

I've got to challenge the curve ball explanation. Think of putting a curve on a ping pong ball and you'll see it does the opposite of what he says.

Density unit is kg/m3

respect from a ib student

How come no one teaches anymore? The reason this is intimidating is because you’re a bad teacher. It’s not because you’re smart and you understand a complicated problem. This is a simple problem. Just show a bunch of ship docking to start. Then show a water hose. Math and physics does not exist in your head you fuck

It was very helpful thank you

How come that they have they same height or y-values if the opening of the tube is bigger than the other side of the tube? Please, enlighten me.

what app/software is that… the moving dots in the pipe?

I have a question, doesn’t high pressure want to be in low pressure? So the baseball will go down, because my teacher taught me in Bernoulli’s principle that when a plane is about to fly, there is fast air on top (low pressure) and slow air on the bottom (high pressure) of an airfoil. So the slow air automatically wants to connect to the fast air which pushes up the airfoil and makes a plane fly. And you need thrust and lift for a plane to take off and fly. So slow air is on top and the fast air is on the bottom of the baseball which makes the slow air automatically connect to the fast air which makes it go down right? I’m in grade 6 and I’m tryna be ahead of my class and be the best, so please explain to me how Bernoulli’s equation works in a simpler way that a grade sided can understand. I hope you can help me to be the best in my classes. Thank you.

it seems some unreasonable if area is same at both end, how can the velocity be same even though height is increasing. if we assume velocity is diffreent from each other, then pressure would be same at both end, which is also unreasonable.

We are working on bringing freshwater by pipeline from Laos to Australia:

𝐓𝐡𝐢𝐬 𝐩𝐢𝐜𝐭𝐮𝐫𝐞: http://bit.ly/2PojPiO 𝐬𝐡𝐨𝐰𝐬

Adding to Tropical Cyclones: bit.ly/2L81Udo:

➕ The monsoons/rains:

↦ from the Indian Ocean,

↦ from the Gulf of Thailand,

↦ from the Huge Pacific Ocean,

➕ The return of evaporation,

➕ the melting Ice from Tibet,

⏩ Confirm the warm tropical monsoon climate region of SE Asia, Laos has too much freshwater with most under not too deep under mountainous ground stored, flowing down, refilled each year since eons.

But nearby, Thailand has too much freshwater only for a short period during the monsoon season but does NOT have enough storage capacity for its own year-round usage.

For 300km/h (83m/s) speed, what should be the hight of the tower considering a pipe about 4m diameter?

I still dont understand the equation part :'(

IMHO, milk carton explanation should have done in terms of Pressure instead of Potential Energy.

the ball analysis is the same as aircraft wing since the upper surface is bulged more , it creates higher velocity so low static energy and viceversa for the lower wing surface. so this lifts the aircraft among with another factors.

I am flabbergasted. This is amazing sir. Thank you

Nice video. very informative. Can you make an explanation of Navier stoke equation?

The height at which point should be taken? and with respect to what surface?

i need the application please, for my research

how can i get the simulation?

This is possibly the clearest explanation of Bernoulli's equation and its application I have ever seen. I honestly don't know how anyone can top this.

In Bernoulli’s equation why is volume not multiplied by the density when substituting for mass?

Superb

this was a great video

Hi Bozeman Science, Paul Anderson and Team, Thank You for your explanation of Bernoulli's Equation.

It helped me sort out that rho=Density, and the potential and kinetic energy variables of the equation.

Oh well back to the Pump Test Stand…..<sigh>

I'll pass the information along to other members of my Pump Unit Assembly Team.

simply the best …. understood bernoulli's equation in just 10 minutes

Very well done. Please do more!

does anyone know the name of the simulation software he used

paul, youre great. Where does the hydrostatic pressure come into the equation?

Where did you get that interactive calculator?? That thing is amazing!

to long

Sir why P1 is high? By P= F/A. If area increases pressure decreases right. Then why we take p1 is high and p2 is low? Please answer

cool

Hello 😀 i would like to ask you if you have any links where i can find a resume of hydraulics of liquids ofc 😀

cheers dad

excellent … thanks !

Very well explained!!!

So this makes planes fly

Thank you !

Great Video

Aye aye captain! it was very helpful and easy to understand! :-))

There are people who are very knowledgeable yet can't dumb things down for the layman, but you sir have a gift of teaching /explaining your explanations are simple and clear.

Ground effects bois.

I like trains

Very good explanation thanks a lot, but density unit kg /m3

So many nerds pointing out a square instead of a cube, yet nobody (not even the professor) knows the difference between a curveball and a slider…

If only traffic could flow like that.

so i should get a smaller diameter cold air intake??? these rules would apply???

Thanks! this video was very helpful for understanding this concept. I liked the visual demonstration and the calculation you went through. They explained everything in a concise yet comprehensive way.

I am from India

Hi! What software do you use to create these great videos?

Very clear and helpful, thank you! 😀

I learned about the Flying Bernoulli Brothers in jump school. We gave thanks to them every time that T-10 cracked open.

Thank you!

Some of this is bad science, in the case of a ship that is not a closed path as your pipe example – to assert that a continuity equation even applies in the first place is beyond me. To assert that because the fast water has a lower pressure, o.O

aweesome

It's neat how math makes common sense complicated. 👍

Gradient pressure….

It’s impossible to have a vacuum of space next to a positive pressure system without a solid barrier.

Gravity is a state sponsored hoax and space is fake.

A Vacuum of Space next to a positive pressure system violates the 2nd law of thermodynamics.

Bravo!

@3:58 he says "if the fluid is moving fast, it's going to have a lower pressure." I guess what's left unsaid is "in a given situation"? Because a general rule that says faster moving fluid has a lower pressure makes no sense; there are plenty of high pressure, high velocity systems.

This is why I didn't do well at math or physics.

Density is not kg/m2. You stupid.

Paul,

Unfortunately, you have three errors.

1-

The boat-dock is improperly analyzed and, as it was stated, is encouraging the common fallacy that fast moving fluid has a lower pressure than any nearby slower fluid. This can all be easily confirmed with a simple demonstration described below.

As the boat approaches the wall-dock, the pressure is increased first at the side of the boat because a surface advancing on a fluid causes an increased pressure at the surface and it is this increased pressure that is the force which accelerates the water away from the side and toward any nearby lower pressure regions. This is simply Newton in Fluids.

This water in this gap, because it cannot instantaneously move out of the way due to the dock, gets deeper as well. This supports this higher pressure. It is not unlike the bow wave of a sailing ship which precedes the boat or the same thing on an aircraft wing. The water level rises there; deeper water has more pressure.

Because the water outside the gap is lower, the gap-water will flow out the ends. Euler showed us that a pressure gradient is what accelerates a fluid. Again, Newton in fluids.

The water in the gap starts out at a HIGHER PRESSURE than ‘ambient’.

If we move the boat in at a constant ‘closing speed’ the exiting volume leaves at a constant rate. However, since the cross section is shrinking, the speed of the exiting water also steadily increases over time. The increased pressure in the gap accelerated this water out of the gap faster and faster.

If we try to stop the boat, the water’s mass/inertia/momentum will keep it moving out of the gap. This

WILLdrain the gap, lower the water and lower the pressure since the level will now be lower than outside the gap.The fast moving water exits because it has a higher pressure than ambient.

You correctly identified ‘P’ as the pressure at a point as noted by Euler.

—

What so many people miss is that the smaller pipe section is a restriction to the flow which increases the pressure in the wide section, _UP STREAM_. The thumb-hose water is faster because the pressure upstream is now higher.

If you magically widen the narrow pipe section, the pressure in the wide section will decrease.

While the energy shifting is certainly true, that talk is quite obscure. You missed an opportunity to mention that the milk carton has higher pressure at the bottom and this is what actually accelerates the fluid more, so it exits faster. People generally know about water pressure at depth and think of it as intuition, though it is actually learned.

2-

The exponent error at time 7:15 pointed out by others THREE YEARS AGO. (Rho should be Kg/m^3 and not Kg/m^2)

3-

Curve Ball: Bernoulli says nothing about the relative speed along a surface and those Curve-Ball speeds are also incorrect. The upper air is ‘dragged along’ by the ball’s surface, in the direction of travel, faster than below; relative to the ground and still air. The higher speed difference of air and surface causes the upper air to separate and not follow the curve behind the ball.

Below the ball, the ball’s surface is moving much slower in the direction of travel or even in reverse (if it is spinning fast enough), so that surface and air is either stationary or drawn in reverse (left in your image). It is the Coanda Effect which is responsible for this lower pressure where more air follows the convex curve. Coanda himself acknowledges the lowered surface pressure in a convex flow.

—

Lastly, I want to also emphasize that an equation never shows cause and effect. They only allow calculating values and were originally determined by a proper analysis of the science/physics concepts involved. A proper understanding of the physics is required to correctly apply an equation.

Boat-Dock Demo.

Fill a sink or straight-sided fish tank with water and use any straight-sided board or rectangular cottage cheese container as a boat. Add some glitter for visibility. Push smartly toward the side. You can see the water rise. It may be more obvious in Slo-Mo.

Regards

Honestly, i could figure it out in 15 minutes. TKs for helping me out

Where d fuq did you get 1620

great vid……but surely density is kg/m3…..not m2 ?

PS…I see someone already commented….apologies.