# Bernoulli's principle

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i decided i want to try to "understand" how a plane can fly. if thats even possible for a layman like me. so ive been watching a bunch of videos, but still so many questions. and you cant ask a video anything.
so, i thought i would try here.
because this is essentially a tricky subject, i thought i would break it up into mini subjects.
so the first subject is Bernoulli's principle.
now i know this is not the whole picture of why a plane can fly, but it is some of the picture.
so, first up i thought it better to try to understand this.

so, as i understand, Bernoulli's principle states that an increase in a fluids speed lowers its pressure.
the thing i cant find on any YT vid is the 'why'?
what is happening on an microscopic scale?

even though my end goal is to try to understand flight, for the sake of simplicity, we should try to keep it to Bernoulli's principle as much as possible, i will make a new thread later for the next part.

try to keep answers in simple language. (im a laymen). but detailed.

thankyou

Try this:

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57 minutes ago, jfoldbar said:

i decided i want to try to "understand" how a plane can fly. if thats even possible for a layman like me. so ive been watching a bunch of videos, but still so many questions. and you cant ask a video anything.
so, i thought i would try here.
because this is essentially a tricky subject, i thought i would break it up into mini subjects.
so the first subject is Bernoulli's principle.
now i know this is not the whole picture of why a plane can fly, but it is some of the picture.
so, first up i thought it better to try to understand this.

so, as i understand, Bernoulli's principle states that an increase in a fluids speed lowers its pressure.
the thing i cant find on any YT vid is the 'why'?
what is happening on an microscopic scale?

even though my end goal is to try to understand flight, for the sake of simplicity, we should try to keep it to Bernoulli's principle as much as possible, i will make a new thread later for the next part.

try to keep answers in simple language. (im a laymen). but detailed.

thankyou

You don't need a microscopic scale to understand Bernoulli.  In fact such consideration is likely to get in the way as you would then need to start considering statistical mechanics.

Plain old standard mechnaics is quite good enough.

The law of conservation of mechanical energy states that "The total energy of (an isolated) mechanical system is constant.

Note an isolated mechanical system is one that is not busy converting its energy into something else, say electrical energy. That is it is purely mechanical.

There are two basic forms of mechanical energy  potential energy and kinetic energy. The total mech energy is obviously the sum of the two.

So if one goes up, the other goes down.

For example as a stone falls under gravity, its potential energy due to gravity reduces but its kinetic energy increases as it speed up.

A fluid is a mechanical system. And Bernoulli is nothing more than the above conservation of energy..
A fluid potential energy is represented by its pressure and its kinetic energy is represented in the usual way by the velocity times the rate of mass flow (or the volume flow times the density)

So to come back to your question, the total energy is constant so if the speed increases it icnreases the kinetic energy, therefore the potential energy must fall so the pressure falls.
A useful term is the stagnation pressure where the fluid has stopped moving and all the energy is potential pressure energy.

Mathematically this stagnation pressure becomes the standard expression of variation of pressure with altitude.

Does this help ?

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It might help to look at the Bernoulli equation to see what studiot is talking about

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Let me give it a try ...

Take a square sross-section pipe of a given length.
Introduce a fluid ( air ) at one end.
In the absence of 'sinks' or 'sources'. we expect the same amount of fluid to come out the other end.

If we now constrict the pipe by attaching two 'D' shaped plates to the top and bottom, we still expect the same amount of fluid out the other end.
But to pass the same amount of fluid through the constriction, the fluid must move faster ( reduced cross-section ).
What can cause the fluid to move faster ? Pressure, of course. It must be higher before the constriction , to cause the fluid to speed up through the constriction where it is lessened, and higher again after the constriction to cause the fluid to slow down.

That is Bernoulli in a nutshell.

We now employ a trick familiar to aerodynamicists. We move the upper part of the pipe, with the 'D' shaped obstructions, out to infinity, and consider only the lower 'D' shaped obstruction and the streamline above it.
The fluid still speeds up going over the obstruction, and as a result, pressure is lessened ( compared to undisturbed fluid far away ).
That is how a 'D' shaped surface, such as a wing, sees decreased pressure above, compared to below, and generates lift.

Edited by MigL
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On 9/8/2022 at 12:31 PM, StringJunky said:

Try this:

thankyou. this was exactly what i was looking for. an explanation as to the "why".

hhhmmm... thinking...

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If you start at the front where the air splits into two halves, the top flow close to  the wing surface, whch is humped and lthus onger compared to the straighter bottom surface, must arrive at the same time at the rear of the wing where they join back up. To satisfy that condition the top flow has to travel faster. Bringing in Bernoulli, the faster air at the top puts less pressure on the top half than the bottom half, giving us lift.

Edited by StringJunky
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so, i was thinking bout this video,  and i have a few thoughts.

the vid shows the a fluid changing from a larger pipe to a smaller pipe. which means an enclosed space. but if this principle applies to the top side of a wing, would the concept be lessened because there is only one side. so when the air atoms are flying over the wing top, some of the atoms will hit the wing direction, but most will fly upwards.

also, wouldnt this concept be lessened too by altitude?

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The flow is running all over the aircraft exterior, so it's reversed , the pressure direction is inwards instead of outwards. They will never fly upwards because there's another molecule above that one. The laminar flow will follow the contour of the aerofoil. You need to think of the air as a smooth fluid because the air molecules are reacting in concert and not in isolation.

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18 hours ago, StringJunky said:

They will never fly upwards because there's another molecule above that one.

but, at 8000m high, wouldn't the ratio of air molecules vs wing molecules be really different?  when theres very little air, how can there be enough air molecules for the ones that bounce of the wing to be crashing into?

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31 minutes ago, jfoldbar said:

but, at 8000m high, wouldn't the ratio of air molecules vs wing molecules be really different?  when theres very little air, how can there be enough air molecules for the ones that bounce of the wing to be crashing into?

The rarer the air, the faster the speed you need to sustain the pressure difference between both sides of the wing.

Crank up the speed, and you will crank up the pressure difference.

But, as studiot said, it's not because the air is made of atoms, but because of energy conservation. Think of the pressure as some kind of internal potential energy.

Fields (continuous media) also have this "internal tension." And they're not made of atoms; atoms are made of fields.

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34 minutes ago, jfoldbar said:

but, at 8000m high, wouldn't the ratio of air molecules vs wing molecules be really different?  when theres very little air, how can there be enough air molecules for the ones that bounce of the wing to be crashing into?

I hate to rain on the D shaped parade, and note you haven't replied to my earlier post.

Nor have I watched the video.

You sensibly asked about Bernoulli, and said your aim was to understand how a 'heavier than air' craft can fly.
I take it that you have seen some explanations using Bernoulli.

Understanding Bernoulli is a good first step, but it is only  a first step since lift is much more complicated than Bernoulli and involves other factors, not present in Bernoulli.

The D shape is often offered as an explanation but it is not necessary.

Take a sheet of writing paper, hold it out  in front of your mouth so it dangles down from your fingers.
Then gently blow over the top.

The sheet of paper will rise and almost straighten out due to the lift force that is generated.

This should be you starting point and can be discussed using Bernoulli

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4 hours ago, StringJunky said:

, must arrive at the same time at the rear of the wing where they join back up.

Why?

Why can't it arrive a bit later?
The air can sort itself out later by swirling about.
It's not like having two queues of people going through customs barriers where the couples need to meet up afterwards.

The "it goes faster over the curved surface so.... Bernoulli... it generates lift" explanation is clearly wrong. You can fly stunt planes upside down indefinitely.

At the very least, you need to consider this as well.
https://en.wikipedia.org/wiki/Coandă_effect

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9 minutes ago, John Cuthber said:

You can fly stunt planes upside down indefinitely.

I was eventually coming to that, but you beat me to it. +1

I have a bit of a quandrary here as the OP question was about Bernoulli, not the mechanics of flight, which is all too often misrepresented.

I believe @jfoldbar is a student but I am not sure where they are in their studies.

Bernoulli assumes what is called laminar flow.     -    Parallel (not necessarily straight) flowlines.

Since the flowlines are parallel they do not get closer together or further apart.

Starting with statics we have a theorem that every system of forces can be reduced to a single linear force and a moment.

The linear force and the moment can vary independently and in particular each can be zero or any other value.

Transferring this to dynamics we have the same theorem that any combination of motions can be reduced to a motion along a line and a rotation.

In Laminar flow this rotation is zero.

If we place a suitable obstacle in the way of this laminar flow it causes the flowlines to bunch up and/or spread out.

This can be equivalent to changing the rotation from zero to some value. I say suitable and can be because some obstacles maintain the flow as laminar.

Without going into the maths, introducing this rotation introduces the lift force that keeps the aircraft up.

Understanding this then allows discussion to proceed to using Bernoulli locally to describe the bunching and spreading in terms of pressure forces.

Fixed wings are always set at some angle to flow to accomplish this.

It is also necessary to consider the statics of the aircraft in terms of a rotation and a line force.

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1 hour ago, John Cuthber said:

Why?

Why can't it arrive a bit later?
The air can sort itself out later by swirling about.
It's not like having two queues of people going through customs barriers where the couples need to meet up afterwards.

The "arrive at the same time" explanation has been, AFAIK, debunked. But the air flows faster. If it didn't you'd have higher pressure in front of the wing, which would then force the air to move faster.

1 hour ago, John Cuthber said:

The "it goes faster over the curved surface so.... Bernoulli... it generates lift" explanation is clearly wrong. You can fly stunt planes upside down indefinitely.

The examples are usually for a specific shape of wing (do stunt planes have that shape?), and if you are in a situation where Bernoulli applies, how does it not move faster and still conserve energy?

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An interesting question is how well should a flat "fin" work in air.
A rocket with a fin (on each side) will follow a curve because the fin provides as "sideway" force.
if you turn that on its side the sideways force becomes lift.

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12 minutes ago, John Cuthber said:

An interesting question is how well should a flat "fin" work in air.
A rocket with a fin (on each side) will follow a curve because the fin provides as "sideway" force.
if you turn that on its side the sideways force becomes lift.

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That the cross section of the wing isn't what matters.

The angle of attack is largely responsible for lift.

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Sure John, a flat fin at an angle of incidence would work, and probably produce more lift than a classic streamlined 'D' shape ( like a Clark Y ), but I can't imagine it would do any good for your lift/drag ratio, and you would have trouble keeping it in the air as a result.

I realize there are many factors which contribute to lift, but I thought we were explaining specifically how Bernoulli makes its contribution.
According to Bernoulli, the fluid needs to move faster, creating a localized area of relatively lower pressure, resulting in 'lift'.

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I'm sorry I have just watched that flawed YT video.

According to the video if I stopped the flow by blocking off both ends of the pipe the wall pressure along the length of the pipe would vary with the diameter of the pipe.

This would be contrary to experience.

The problem lies in the explanation as well.

It equates velocity of impact with pressure.

But this is not the case since the larger diameter portion of the pipe will also have a large surface area to impact on and the impact may result in a large force, but that impact force will be distributed over a larger area and therefore a lower pressure since pressure = force/area.

A further problem is that the video describes incompressible flow in pipes.

Pipe flow introduces another complication   -  it is described by the poiseuille equation.

There are no pipe walls in the atmousphere.

Atmouspheric air flow is not incompressible except in very special circumstances.

Edited by studiot
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19 hours ago, studiot said:

Does this help ?

Helped me, Thanks!

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1 hour ago, John Cuthber said:

That the cross section of the wing isn't what matters.

The angle of attack is largely responsible for lift.

A flat fin is a different example, so basically this is a case of "different problems might need different explanations" This happens all the time in physics.

Angle of attack is an application of forces/momentum. Bernoulli is conservation of energy. It's not a case of one being right and the other wrong, since they draw on different concepts in physics. They are not mutually exclusive.

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5 minutes ago, swansont said:

A flat fin is a different example, so basically this is a case of "different problems might need different explanations" This happens all the time in physics.

Angle of attack is an application of forces/momentum. Bernoulli is conservation of energy. It's not a case of one being right and the other wrong, since they draw on different concepts in physics. They are not mutually exclusive.

I think both momentum and energy transfer considerations are needed.

But you have to be careful  with auxiliary variables such as velocity and resistance to movement as with the situation when calculating the KE of a bullet entering a sandbag or plank and apply the appropriate conservation law.

I'm sure we really mean the same thing.

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1 minute ago, studiot said:

I think both momentum and energy transfer considerations are needed.

But you have to be careful  with auxiliary variables such as velocity and resistance to movement as with the situation when calculating the KE of a bullet entering a sandbag or plank and apply the appropriate conservation law.

I'm sure we really mean the same thing.

Probably. I'm saying as long as the equations are applicable, you can often pick different approaches to solving/explaining a problem.

As an analogy, you can discuss a falling ball as speeding up owing to a force on it, or due to exchanging potential energy for kinetic energy. Both are correct. It's not one or the other.

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5 hours ago, swansont said:

(do stunt planes have that shape?)

Stunt plane wings are, I'm told, "thick" because they have to be strong, and more or less symmetrical.
They are pretty nearly "fins".

If you take a flat fin and  streamline it a bit you get the sort of wing you see on aerobatic planes
https://www.amaflightschool.org/getstarted/how-do-i-know-difference-between-basic-trainers-aerobatic-trainers
And if you then tweak it to reduce the drag caused by turbulence behind/ above it, you get a conventional aerofoil.

Nobody cares about the fuel efficiency of stunt planes, but they have wings that look like dolphin fins in cross section.

Edited by John Cuthber

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