# B Why is the pressure reduced when the fluid flows faster?

#### Kaushik

Look at the above figure. An overhead view of a car passing a truck on a highway. Air passing between the vehicles flows in a narrower channel and must increase its speed. As the speed of air in that narrow channel increases, the pressure reduces (between the two vehicles).

What is the reason behind that reduction in pressure?

Also, using this can we explain the working of wings?

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#### Kaushik

It's called Bernoulli's principle, which google
And yes, it works for airfoil lift too.
Is it because the the fluid surrounding a particular fluid particles is doing positive work on it to increase the kinetic energy of that particle. Hence, the fluid surrounding it loses energy. Consequently, the pressure reduces.
Is my intuition correct?

#### Kaushik

Why is the velocity of the fluid above the wings greater?

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#### russ_watters

Mentor
Why is the velocity of the fluid above the wings greater?
The overall effect can be described qualitatively as a consequence of continuity; conservation of mass and/or volume in a fluid flow.

An object moving through a fluid is a "hole" in the fluid - say in your original example, a car or truck. When the car moves forward by one car length, air that was previously in front of or next to the car has to move back to fill the "hole". So overall/on average, the velocity of a fluid around an object has to be greater than freestream.

And incidentlly this means the image in your first post is misleading. The velocity on the outside of the vehicles will also be above freestream; just not as much as between them.

Now/so, where the velocity is highest (or even if locally it increases or decreases) is a pretty complicated issue.

#### Kaushik

So overall/on average, the velocity of a fluid around an object has to be greater than freestream.
Could you please elaborate the quoted line?

#### russ_watters

Mentor
Could you please elaborate the quoted line?
The entire paragraph preceding that sentence is the elaboration. What didn't you understand?

#### alva3

Pictures help:

Considering the picture above, would you consider the velocity of the fluid to be faster above, or below the ball? Obviously above, correct? Because the rotation of the ball is working with the direction of the surrounding flow, the velocity is faster and as a result, the pressure is lower. But at the bottom of the ball, the rotation is working against the direction of the surrounding flow, which slows the velocity and increases the pressure. Using this concept of competing "directions", try to answer your own question using the first image you provided. Would you say the pressure is greater in front of a moving car, or behind it? Now work it out using this image:

Hopefully that helps.

#### sophiecentaur

Gold Member
Consequently, the pressure reduces.
I think this statement is putting the cart in front of the horse. Cause and effect are easy to confuse.
I would say, rather, that in order to force the fluid to move faster through a restricted space, the upstream pressure needs to be higher than the downstream pressure. That statement makes sense (total copper bottomed sense, aamof) but it is a bit counter intuitive. But, once we realise that the statement of Bernouli's principle refers to the steady state situation after things have settled down. That's a bit like the "how do the resistors in a circuit know how much current to let through" question which is based on the 'switch on' situation.

#### Kaushik

The entire paragraph preceding that sentence is the elaboration. What didn't you understand?
I didn't understand how the preceding line explains 'Why the velocity of the fluid is greater above the body than below?'. I'm Sorry but could you please elaborate.

#### sophiecentaur

Gold Member
I didn't understand how the preceding line explains 'Why the velocity of the fluid is greater above the body than below?'. I'm Sorry but could you please elaborate.
There is nothing fundamental here. You could fly / design a plane in such a way that the air moves faster below it. Net force would be downwards!!
It is a shame that the 'explanations' for flight get bogged down in the details of fluid flow and ignore the fundamentals of Newton's Laws of motion. Also, trying to apply Bernoili 'cold' to the motion of bojects through the air is making life harder for 'the student' than necessary. The first diagram in this thread should be showing fluid flow through a pipe restriction, where the pipe is clearly stationary and the fluid is moving. (I know it's all relative but why make things harder than necessary?)
With a wing or motor car, there is a high relative velocity between vehicle and air - which is not particularly relevant to Bernouli. It's the difference in velocities that counts, due to the lateral distance that the air needs to travel, over and under the wing.
It's no wonder that the OP is still confused because of all the above posts that introduce extra complexity rather than getting to the nub of the situation. He needs a simplified explanation - not a harder one.
I recommend a Google search for Bernoulli Principle and finding a really basic discussion - such as can usually be found in Hyperphysics pages.

#### russ_watters

Mentor
I didn't understand how the preceding line explains 'Why the velocity of the fluid is greater above the body than below?'. I'm Sorry but could you please elaborate.
Generally, the velocity is greatest where the airflow is smoothly deflected or constricted most. It isn't always obvious looking at objects, but for an airfoil the sharp trailing edge enforces a top/bottom surface split of the airflow at the leading edge, which is rounded, so it can't enforce a split. Thus at higher angles of attack you will see flow in front of the airfoil curving upward to go over the top of the wing.

Note however that depending on the shape and angle of attack, the pressure and velocity on the bottom surface may be increased or decreased.

Edit: Caveat I shouldn't need: this description applies to typical airfoils in typical conditions. Special airfoils and conditions may show different behavior.

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#### sophiecentaur

Gold Member
Someone really ought to mention that forces generated when fluids flow are there because of Newton's Third Law of Motion. It's rather blinkered to put it all down to low pressure over a wing (etc. etc.) when you realise that there must be a downward flow of deflected air and the continuing change of momentum of the air as the plane flies along. But, somehow, this is allowed in the case of a helicopter. The resulting reduction of pressure over the wing is interesting and quite valid (of course) but it tends to be quoted as an article of basic faith, rather than to be given its proper status in the whole cause / effect chain.
Fluid Flow experts always seem reluctant to acknowledge this but you guys have to admit; reactionless forces just do not exist.

#### russ_watters

Mentor
Someone really ought to mention that forces generated when fluids flow are there because of Newton's Third Law of Motion. It's rather blinkered to put it all down to low pressure over a wing (etc. etc.) when you realise that there must be a downward flow of deflected air and the continuing change of momentum of the air as the plane flies along. But, somehow, this is allowed in the case of a helicopter. The resulting reduction of pressure over the wing is interesting and quite valid (of course) but it tends to be quoted as an article of basic faith, rather than to be given its proper status in the whole cause / effect chain.
I think it is mostly a matter of convenience. A helicopter rotor traces-out a discrete, easy to identify circle and generates a coherent, uniform downward-flowing column of air. This makes the lift calculation using Newton's third law easy and precise. The same cannot be said/done for a wing of an airplane; There's no identifiable volume and no uniformity of velocity.
Fluid Flow experts always seem reluctant to acknowledge this but you guys have to admit; reactionless forces just do not exist.
Depends on what exactly you mean. I think people mistakenly conflate Newton's third law with conservation of momentum. A book sitting on a table is a Newton's 3rd Law force pair as well, and involves no motion: just because the table is being pushed downward doesn't mean it moves downward. So, no, there is no explicit Newton's 3rd Law requirement that downwash cause all lift*. This is best seen in ground effect, where downwash is blocked by the ground and lift increases.

In a free airstream (not constrained by an obstruction) or close to a wing it can be accurate to assume downward airflow and conservation of momentum fully account for lift, but again it is essentially impossible to identify a specific mass flow rate and velocity of that downwash. That's why I prefer to view it in terms of pressure integrated over the surface.

But please note that for a surface and an air molecule, pressure and momentum change per unit area and time are the same thing.

*IMO, this should be considered as one of those "lift fallacies" that people like to cite.

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#### sophiecentaur

Gold Member
I think it is mostly a matter of convenience.
Yes. Exactly.
We use approximations all the time, for convenience, and yet mostly we acknowledge that the bigger picture is there. The lift force is there because of the downward motion of a lot of air and, in the case of a fixed wing, that air is spread over a long portion of the aircraft flight path. But it is there, still. It happens that the Bernouli effect can be identified as acting closer to the aircraft and that is handy. There is a similar situation with a radiating em dipole where we jump from the currents and potentials close to the wires to a far field radiating field. But there is not the same 'act of faith' which I can always read into the way that the action of a wing is described.
Perhaps I have become over-sensitised to this? It's a big endians and little endians thing.

"Why is the pressure reduced when the fluid flows faster?"

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