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### Course: Properties of matter (Essentials) - Class 11th>Unit 3

Lesson 6: How does a cricket bowler make the ball swing?

# Bernoulli's equation derivation part 2

This is the second of two videos where Sal derives Bernoulli's equation. In the second half of the video Sal also begins an example problem where liquid exits a hole in a container. Created by Sal Khan.

## Want to join the conversation?

• HI! I'm Ashwin from India. The service you provide for clarifying doubts is great!!
I have a question on the application of Bernoulli's principle. When air flows over a foil/paper, why is it that the air flowing on the upper surface of the foil(though has a higher velocity) has a lower pressure than the air flowing on the lower surface of the foil?
Thank you.
• It is not because they have to cover the same area in the same time. In fact the air on the top of the wing will reach the trailing(back edge) of the wing FIRST. NASA talks about the incorrect theories floating around. http://www.grc.nasa.gov/WWW/k-12/airplane/wrong3.html

The way I understand it is(you will want to talk to someone who actually does experiments in a wind tunnel, not just a lecturer and definitely not a pilot as they are the worst offenders), the air impacts the front of the wing imparting a velocity to the fluid both upwards and downwards, creating low pressure directly ahead of the wing and perpendicular to the direction the air at the leading edge of the wing was just accelerated. Now the air moves over the wing through the area of lower pressure that was created by the leading edge. The movement of the air over the wing surfaces again causes low pressure over the top AND bottom of the wing. However the bottom of the wing does not allow air to flow past easily if it is inclined and so the air tends to create high pressure under the wing. Above the wing the air wont be stopped and is free to continue accelerating to the trailing edge of the wing. Because of its high speed the air at the top of the wing will flow downward off the trailing edge because the wing is not there to support it and it is traveling with a lower pressure and higher velocity than the air around it. The high pressure air under the wing will try to flow on top of it but can't get over the trailing edge because sucking is different from blowing(try to suck out a candle)and it can't turn the sharp angle. It can get over the tips of the wings though and does cause drag.

I am not an expert but that is what I understood someone who worked for NASA to be saying. If you want to know definitively ask someone who DOES ACTUAL EXPERIMENTS. And remember air is a fluid acting and reacting continuously with itself to create vortexes.

Also I thin the magnus effect has to do with rotation and friction slowing a fluid down and creating a difference in pressure that way, and not how an airfoil would generate lift.

Oh and the more general idea this falls under is "Bernouli's principle".
• In fluids Part 2 we learned that Pressure-in equals Pressure-out. Doesn't Bernoulli's equation contradict this, where there is lower pressure in a zone of restricted diameter?
• Good question! I think the difference is that Pascal's principle (pressure in = pressure out) applies to "confined fluids," that is, static fluids. Bernoulli's equation applies to fluid dynamics, or fluids in motion.
• i still don't understand why pressure is low when velocity is high ? i get the thing about keeping height fixed but how did we come up with that inverse relation b/w vel. and pressure?
• I like to think about it like this: if the velocity is high, this means that the fluid is moving very fast right? If the fluid is moving fast, the fluid particles have less time to collide into the walls of the tube, so they exert less force on the tube. Pressure = (Force/Area), so less force exerted on the walls of the tube means less pressure for fast moving fluids.

Of course the other factors come into play, but for quick thinking I hope this helps :)
• At , wouldn't the liquid just stay inside because the hole is the only way for air to get in?
• not only that, but a vacuum would have negative pressure wouldn't it? unless outside is a vacuum too.

the liquid would just turn into a vapor and fill the container.
• Is it just me, but why is the (rho)*g*h looks vaguely familiar?
• because it is the equation for pressure due to gravity: density * acceleration due to gravity * height
• So would an object that is moving underwater experience less pressure than the same object when it is still?
• I would imagine that moving forward would cause the object to experience force against its front (like how air slows down a ball flying through the air). This force spread over the area of the front of the object would then be pressure. The pressure the object feels from every direction should remain the same (unless for some reason the pressure on its back would decrease because of the forward motion (I don't know if this is the case). Could anyone elaborate or correct my thinking?
• How does pressure decrease when going into a more constricted area of the pipe? If pressure is Force/Area, wouldn't having a smaller area just create an even larger pressure? Also, does the pressure increase=velocity decrease apply if there's a change in height?
• You are right, P=F/A when a force is applied over an area. In this case we are actually more concerned with conservation of ENERGY.

OK, you need to take a look at the Bernoulli equation. See that the total energy in the system remains constant. So if there is an increase in kinetic energy (or gravitaitonal potential) then there will be a decrease elesewhere, hence the decrease in pressure P.
• the rho v. wade part was really funny