How dynamic and static pressures are related

[thetexan]

I teach aerodynamics and I’m looking for a way to explain how d and s pressure are related.

I understand that as dynamic increases static decreases with the total sum remaining the same.

With dynamic being zero the total goes to static. As dynamic increases the static pressure decreases. But why? Dynamic is measured parallel to the surface and static measured normal to the surface. And dynamic is related to velocity of the air.

Is there a way to explain this relationship between velocity and dynamic pressure and between dynamic and static pressures that are relatively easy to present?

It as if when velocity across the surface (wing) increases the fluid (air) doesn’t “have time” to spend exerting static pressure perpendicular to the surface. And the slower the velocity the more normal pressure that can be exerted.

I’m looking for a good way to explain this phenomena.

Any help would be appreciated.

Thanks

Tex

 

[CWatters]

I don't teach aerodynamics so I could be wrong but I thought static pressure was independent of velocity. What I mean is for something like an aircraft or submarine its related to height/depth only not the velocity of the fluid flow.

 

[thetexan]

Well...

There is a relationship between fluid velocity and dynamic pressure...the faster the velocity the higher the dynamic pressure although I don’t completely understand how velocity and viscosity fit into the dynamic pressure formula.

And...consequently, the higher the dynamic pressure the lower the static pressure. And that is what I want to know how that works. The total pressure equals total dynamic pressure plus total stati pressure...and the total sum of dynamic and static pressure is a constant for a given situation.

I don’t understand that and how it works and it makes it hard to explain it to students.

I need help

Tex

 

[CWatters]

Ah Ok you are talking about Bernoulli's principle. It derives from conservation of energy.

A unit of water flowing into a section of pipe has some energy. It has KE and PE (which includes static pressure). If the pipe narrows, forcing the water to speed up, it gains KE. Conservation of energy means it must loose PE (which includes static pressure).

 

[bkercso]

"As dynamic increases the static pressure decreases. But why?"

When applying impact pressure to a fluid or gas, it is accelerated, after that its pressure decrases because of energy conservation (Bernoulli law). Static pressure is the pressure you could feel inside this fluid or gas. Dynamic pressure is what you feel when try to stop this flowing medium.

 

[boneh3ad]

There is a relationship between fluid velocity and dynamic pressure...the faster the velocity the higher the dynamic pressure although I don’t completely understand how velocity and viscosity fit into the dynamic pressure formula.

Viscosity has absolutely nothing to do with what you are asking here.

And...consequently, the higher the dynamic pressure the lower the static pressure. And that is what I want to know how that works. The total pressure equals total dynamic pressure plus total stati pressure...and the total sum of dynamic and static pressure is a constant for a given situation.

I don’t understand that and how it works and it makes it hard to explain it to students.

Dynamic pressure isn't really a pressure at all, but a measure of the kinetic energy of the gas due to bulk motion per unit volume. After all, look at the equation,
q = \dfrac{1}{2}\rho V^2.
It's the same as the physics 1 equation for kinetic energy, except it uses density, so it is basically a kinetic energy density. If the kinetic energy due to bulk motion changes, that had to come from somewhere. Barring a change in elevation, the only other source is the pool of kinetic energy that exists due to the random motion of air molecules, otherwise known as static pressure.

Dynamic is measured parallel to the surface and static measured normal to the surface.

What does this even mean? Both of these quantities are directionless. They are scalar.

Dynamic pressure is what you feel when try to stop this flowing medium.

Under no circumstances can you "feel" dynamic pressure. Dynamic pressure cannot be felt or directly measured. In that sense, it is a somewhat abstract quantity. If you, say, stick your hand out the window of your car and feel the pressure on it as you drive, that is total pressure or stagnation pressure, which is the sum of static and dynamic pressure. You'd have to measure total and static pressure and subtract static from total in order to calculate the dynamic pressure (and velocity). This is how a Pitot static tube works.

 

[thetexan]

Then this is what I need to understand.

On a wing the static pressure is measured as psi on a unit of area normal to the surface. That’s what we care about...the difference of the psi on top of the wing compared to the psi on the bottom of the wing.

To me that represents a force of pressure pressing against the wing. That’s easy to for me to understand. So what exactly is dynamic pressure AS A PRESSURE and how is it related to static pressure so that when it increases the pressure measured against the wing decreases. Why does increasing one reduce the other. I guess what I’m trying to understand is the mechanism of that relationship.

Tex

 

[russ_watters]

Why does increasing one reduce the other. I guess what I’m trying to understand is the mechanism of that relationship.

The mechanism is energy conversion between static and kinetic (dynamic). If you think about what happens when air is released from a balloon, the static pressure pushes the air out of the balloon, trading static pressure (potential energy) for kinetic/dynamic.

 

[thetexan]

Maybe if I ask it this way...

Let’s start with zero velocity.

There will be no dynamic pressure. So all of the pressure in the fluid is static which to me means that all of the pressure is acting in all directions. For example, an aircraft sitting on the ramp...the static pressure against every square inch of the wing is about 14.7 psi. But if we move that wing thru the air and introduce velocity to the fluid dynamic pressure begins to increase (and, by the way, I don’t quite understand how velocity is related to dynamic pressure) and the 14.7 begins to decrease. So somehow by increasing the kenetic energy of the flow parallel to the surface reduces the pressure normal to the surface.

Let me try this...

Is it this way...

14.7 at zero velocity represents the total kenetic energy available at the wing surface, which exerts pressure in all directions at that point on the surface. Then when you add velocity some of that total energy is used in the moving of the fluid which subtracts from that available to press against the wing.

Is that how it works?

Tex

 

[jbriggs444]

Maybe if I ask it this way...

Let’s start with zero velocity.

There will be no dynamic pressure. So all of the pressure in the fluid is static which to me means that all of the pressure is acting in all directions. For example, an aircraft sitting on the ramp...the static pressure against every square inch of the wing is about 14.7 psi. But if we move that wing thru the air and introduce velocity to the fluid dynamic pressure begins to increase (and, by the way, I don’t quite understand how velocity is related to dynamic pressure) and the 14.7 begins to decrease. So somehow by increasing the kenetic energy of the flow parallel to the surface reduces the pressure normal to the surface.

If you are considering Bernoulli, the relevant difference is between the flow velocity upstream and downstream from the wing compared with the flow velocity above and below the wing. The flow velocity is high above the wing and low in front and behind. This must be so in order for the flow to have accelerated in front and to have decelerated behind.

14.7 at zero velocity represents the total kenetic energy available at the wing surface, which exerts pressure in all directions at that point on the surface. Then when you add velocity some of that total energy is used in the moving of the fluid which subtracts from that available to press against the wing.

Speeding up a box containing a parcel of air does nothing to change the pressure of that parcel of air. Speeding up a parcel of air by having it rush from an area of high pressure to an area of low pressure... results in the air being at a lower pressure. (obviously!)

 

[thetexan]

I’m still in the dark.

Most pilot students including myself 40 years ago learned it this way...fast velocity over the top of the wing than below the wing results in lower pressure above the wing than below so the wing is either sucked up due to lower pressure or pushed up due to higher pressure below. We learned that it’s the difference in pressure above and below the wing that does the trick. We learned that velocity, being faster above the wing due to camber, means a difference in velocity above and below the wing, with a resulting difference in pressure above and below the wing...and all due to something called Bernullis principle. We even learned the basics of B’s principle, that is, tha velocity reduces pressure as in a Venturi tube. This is the usual extent of their knowledge.

Then...here comes an aerodynamics class where they ask “why should it be so?”

So I’m struggling in explaining why, when we increase velocity over a surface, even a flat surface, the pressure against the surface reduces because of something called dynamic pressure! Not velocity but dynamic pressure!

So, I have to be able to explain how and increase in velocity increases this thing called dynamic pressure and how increasing dynamic pressure decreases the pressure acting against the surface of the wing (static pressure) and what is this thing called dynamic pressure. Static pressure is easy to understand and visuallize, it is simply the pressure acting perpendicular against the surface of the wing. But how to visuallize dynamic pressure?

tex

 

[russ_watters]

Let’s start with zero velocity.

There will be no dynamic pressure. So all of the pressure in the fluid is static which to me means that all of the pressure is acting in all directions. For example, an aircraft sitting on the ramp...the static pressure against every square inch of the wing is about 14.7 psi.

But if we move that wing thru the air and introduce velocity to the fluid dynamic pressure begins to increase (and, by the way, I don’t quite understand how velocity is related to dynamic pressure) and the 14.7 begins to decrease. So somehow by increasing the kenetic energy of the flow parallel to the surface reduces the pressure normal to the surface...

14.7 at zero velocity represents the total kenetic energy available at the wing surface, which exerts pressure in all directions at that point on the surface. Then when you add velocity some of that total energy is used in the moving of the fluid which subtracts from that available to press against the wing.

Is that how it works?
[emphasis added]

To start with, you have to be a little careful with the airplane example because switching reference frames can be confusing. The air is stationary with respect to itself, so its dynamic pressure is zero in that frame. But by the airplane moving, using the airplane's reference frame, the air is now declared to be moving, with a non-zero dynamic pressure and increased total pressure.

...now, that highlighted bit you said isn't really accurate as stated. For the pito-static tube attached to the airplane, the static pressure of the air has not changed, but the dynamic and therefore total pressure has.

For air flowing over the wing, though, there is an additional increase in velocity (above the airspeed of the plane) in some places and the pressure does drop below ambient.

(and, by the way, I don't quite understand how velocity is related to dynamic pressure)

Can you elaborate on what is confusing you? You know the equation, right? I feel like, though, by jumping right to flow around a wing you are making the issue more complicated instead of ensuring you understand the simple versions first (a balloon, a Venturi tube, etc) and applying the solidly understood principles to the more complicated case.

 

[russ_watters]

Then...here comes an aerodynamics class where they ask “why should it be so?”

So I’m struggling in explaining why, when we increase velocity over a surface, even a flat surface, the pressure against the surface reduces because of something called dynamic pressure! Not velocity but dynamic pressure!
[emphasis added]

For emphais: the static pressure does not drop just by a flat, parallel surface gaining speed in air.

 

[thetexan]

Here's my understanding and explanation...

At zero velocity on the ramp let's say the pressure against every square inch of wing surface above and below the wing is 14.7 psi. If we are going to take advantage of Bernouli and reduce the pressure above the wing compared to below the wing we have to somehow make the velocity above the wing faster than below the wing. So we create a cambered airfoil. When we move this through the air thus increasing velocity both above and below the wing we reduce the 14.7 both above and below the wing...only we reduce it more above the wing because of the relatively increased velocity above the wing compared to below because of the camber.

So, for example, at 100 kts we may have a pressure of 13.9 above the wing and 14.5 below the wing. The pressure against both surfaces have reduced...the top surface has reduced more due to the faster velocity. There is still a greater pressure below thus giving us the upward force due to differential pressure. So far so good. The question then is why does an increase in velocity compared to some other velocity reduce the resulting static pressure to 13.9 psi against the wing? What is actually happening that causes the static pressure of 14.7 psi to be reduced to 13.9 just because the air moved at an increased velocity across the surface? The answer is dynamic pressure. Increasing velocity increased this thing called dynamic pressure which in turn reduced the static pressure from 14.7 to 13.9.

So I have struggled to understand the relationship of velocity to dynamic pressure and...how dynamic pressure is related to static pressure in that there is something about the increase in dynamic pressure the reduces the 14.7 to 13.9. The answer, I believe is in the idea of the constant total pressure...so when one is reduced the other increases. I understand that it is so, but I don't understand WHY it is so.

I know I am making a mess of the explanation and I am sorry I am not explaining myself better.

tex

 

[jbriggs444]

The question then is why does an increase in velocity compared to some other velocity reduce the resulting static pressure

Exactly what velocity do you imagine is being increased in comparison to exactly what other velocity? i.e. as @russ_watters suggested, are you frame-jumping?

 

[cjl]

Here's my understanding and explanation...

At zero velocity on the ramp let's say the pressure against every square inch of wing surface above and below the wing is 14.7 psi. If we are going to take advantage of Bernouli and reduce the pressure above the wing compared to below the wing we have to somehow make the velocity above the wing faster than below the wing. So we create a cambered airfoil. When we move this through the air thus increasing velocity both above and below the wing we reduce the 14.7 both above and below the wing...only we reduce it more above the wing because of the relatively increased velocity above the wing compared to below because of the camber.

So it's worth being careful here. When we move the airfoil through the air, it doesn't matter that above and below the wing, the velocity is higher than it was earlier when the wing was stationary. What matters is what the local velocities are relative to freestream. In the freestream, the static pressure is 14.7 psi and the velocity is some value V. Locally, around a cambered airfoil at a nonzero angle of attack, I'd tend to expect the lower surface local velocity to be slower than V, and the upper surface local velocity to be higher than V. This leads us to your next paragraph:

So, for example, at 100 kts we may have a pressure of 13.9 above the wing and 14.5 below the wing. The pressure against both surfaces have reduced...the top surface has reduced more due to the faster velocity. There is still a greater pressure below thus giving us the upward force due to differential pressure. So far so good. The question then is why does an increase in velocity compared to some other velocity reduce the resulting static pressure to 13.9 psi against the wing? What is actually happening that causes the static pressure of 14.7 psi to be reduced to 13.9 just because the air moved at an increased velocity across the surface? The answer is dynamic pressure. Increasing velocity increased this thing called dynamic pressure which in turn reduced the static pressure from 14.7 to 13.9.

As I said above, I'd actually expect a situation more along the lines of 13.9 above the wing and 15.1 below the wing, since the air on the underside of the wing will be moving slower than freestream. It is very important to remember that we're always comparing local velocity to freestream, and not velocity now to some other velocity at a different arbitrary point in time.

If you remember this, it starts to make a lot more sense why the pressure has to do what it does. Above the wing, the local airspeed is higher than freestream. As a result, the air must accelerate from far away to the point above the wing. The only way to cause the air to accelerate is for there to be a pressure gradient forcing each parcel of air to speed up. This means that where the local velocity is higher, the pressure *must* be lower than it is in the freestream, otherwise the air could not have accelerated to get to that point.

Similarly, below the wing, the airspeed is below freestream. To slow the air down, there must have been an adverse pressure gradient it was fighting against, implying the local pressure below the wing *must* be higher than out far from the wing. Trying to claim that the pressure mysteriously went to this thing called "dynamic pressure" is just increasing confusion and introducing something that isn't necessary to understand the basic principles here.

So I have struggled to understand the relationship of velocity to dynamic pressure and...how dynamic pressure is related to static pressure in that there is something about the increase in dynamic pressure the reduces the 14.7 to 13.9. The answer, I believe is in the idea of the constant total pressure...so when one is reduced the other increases. I understand that it is so, but I don't understand WHY it is so.

I know I am making a mess of the explanation and I am sorry I am not explaining myself better.

tex

Again, be very careful. Total pressure is not constant in the scenario you laid out. In the case of your static wing with no flow, total pressure is the same everywhere (and equal to the static pressure), and in the case of your moving wing, total pressure is also the same everywhere, but there's absolutely no reason why total pressure in the moving wing case needs to be equal to total pressure in the static wing case.

 

[russ_watters]

When we move this through the air thus increasing velocity both above and below the wing we reduce the 14.7 both above and below the wing...

No: the pressure on the bottom surface is generally higher than ambient, not lower.

You are indeed fame-jumping.

 

[jartsa]

It as if when velocity across the surface (wing) increases the fluid (air) doesn’t “have time” to spend exerting static pressure perpendicular to the surface. And the slower the velocity the more normal pressure that can be exerted.

A parcel of air next to the surface always pushes on the surface. Sometimes said parcel does work as it pushes, sometime it doesn't. Said work consists of the parcel pushing itself to a higher speed. (That is true in such frame where the kinetic energy of the parcel increases)

Actually parcel is not doing work, as its energy stays constant. Parcel's static pressure is doing work on parcel's dynamic pressure, maybe that's how it could be expressed.

 

[thetexan]

There is an increased flow velocity below the wing also isn't there. The flow across the lower surface of the wing is faster than before so why should it not also reduce the static pressure below...just not as much. Any fluid velocity across a surface reduces static pressure on that surface. I know enough about how wings work to know that. Every course I know of teaches that there is a reduction of pressure on all parts of the wing just more so along the top due to increased velocity due to camber. If static pressure is decreased won't it be below some starting point...namely...14.7?

How can increasing the flow along the bottom of the wing increase the pressure and not decrease the pressure?

 

[russ_watters]

There is an increased flow velocity below the wing also isn't there.

No, it's decreased.

The flow across the lower surface of the wing is faster than before...

Sure, but so what? Bernoulli's principle applies to steady flow. Is flow steady for an accelerating airplane?

Any fluid velocity across a surface reduces static pressure on that surface.

No. It. Does. Not.

 

[thetexan]

I don’t understand. You say flow along bottom of wing is decreased. Decreased from what?In the ramp the velocity across the bottom of the wing is zero...now it’s 100kts! How can you say that velocity s decreased?

 

[cjl]

Decreased from the flow velocity far away from the wing in the same scenario. You can't compare when the airplane is stationary to when it is flying because those are not the same frame of reference and are not the same flow field. You need to look at what the flow is doing in a single, steady moment in time.

It's completely valid to compare the flow next to the wing when it is on the ramp to the flow far from the wing also when it is on the ramp (though it'll be somewhat boring, since flow velocity is zero both next to the wing and far from it). It's also valid to compare the flow next to the wing and the flow far from the wing while the airplane is in flight. It's not valid, however, to compare the flow next to the wing with the wing in flight to the flow next to the wing with the plane on the ramp. There's no connection between these two flows, and no reason they would have any particular relationship to each other.

 

[thetexan]

Perhaps someone can explain how a wing reduces lift because some of these answers don’t make sense. Maybe we have different unferstandings.

Can someone Please explain how lift is generated on a wing using airstream velocity, free stream velocity, dynamic pressure and statiic pressure and Bernoulli’s principle in the definition. Somehow I think I don’t understand everything I have ever been taught.

 

[cjl]

A wing moving through air generates a flowfield in which the local velocity above the wing is higher than ambient (far from the wing), and the local velocity below the wing is lower than ambient. In steady flow, the only way for a local area to have a velocity higher than ambient is for the pressure to be lower than ambient. Similarly, the only way for a region to have a local velocity below the velocity far from the wing is for it to have a locally higher pressure. Because the pressure below the wing is higher than the pressure above the wing, upward force is generated.

Alternatively, you can say that a wing deflects airflow downwards. This creates a reaction force pushing the airfoil upwards. This is sometimes called the "Newtonian" explanation for lift, and both the above pressure-based explanation and the momentum based Newtonian explanation are correct and valid, though neither actually gets into the details of exactly why the airfoil creates the flowfield that it does with an overall downward deflection of the flow and higher velocity above it.

Note that in this explanation, I never once compare a moving airfoil to a static airfoil. The important thing to consider is the flow of air next to the airfoil vs the flow of air far from the airfoil. This is where you can apply Bernoulli.

 

[thetexan]

Well there is camber below the wing just like above just not as much. Bernouli is acting on the bottom just like the top. Just not as much since the velocity is greater on top due to greater camber above.

 

[russ_watters]

Well there is camber below the wing just like above just not as much. Bernouli is acting on the bottom just like the top. Just not as much since the velocity is greater on top due to greater camber above.

I'm not sure you realize that camber is the sum of the curvatures. There is only one camber.

And again: bernoulli deals with one flow scenario at a time. A stationary and a moving plane are different scenarios. This is your critical misunderstanding.

 

[russ_watters]

Can someone Please explain how lift is generated on a wing using airstream velocity, free stream velocity, dynamic pressure and statiic pressure and Bernoulli’s principle in the definition. Somehow I think I don’t understand everything I have ever been taught.

It's pretty simple once you fix your reference frame problem:

1. The reference velocity is freestream.
2. Velocity above the wing is higher, so pressure is lower.
3. Velocity below the wing is lower, so pressure is higher.
[in general for level flight]

That's it!

 

[rcgldr]

Well there is camber below the wing just like above just not as much. Bernouli is acting on the bottom just like the top. Just not as much since the velocity is greater on top due to greater camber above.

A flat wing can produce lift, it just needs an angle of attack. Using the wing as a frame of reference, the air is deflected off the bottom, increasing pressure, and the air above the wing is drawn into what would otherwise be a void swept out by the wing as it passes through a parcel of air, reducing pressure above the wing. The wing at an effective angle of attack causes the air to accelerate downwards, curving the relative flow, both below and above the wing. There is a pressure gradient perpendicular to the flow, higher above and lower below (the air is accelerated towards the center of radius of curvature of the flow). The higher and lower pressure zones also cause the air to accelerate in the direction of flow.

From a molecular perspective, static pressure is related to the momentum of random collisions between molecules of air. In the case of flow in a pipe, if the pipe narrows, then the velocity of the flow increases, and the flow becomes more organized, due to the change in the net velocity of the molecules, which reduces the momentum of collisions, since the amount of random movement between molecules decreases as the flow velocity increases and becomes less random. This is assuming that no external forces are involved, so the exchange of energy between pressure and kinetic doesn't involve any externally induced gains or losses in overall energy.

 

[boneh3ad]

https://www.physicsforums.com/insights/airplane-wing-work-primer-lift/

 

[thetexan]

Who said anything about an accelerating airplane? At a steady 100kt velocity there is no accelerating airplane.

I have studied many diagrams and now understand the dynamic/static relationship.

There is an acceleration then deceleration of the flow over the wings curved surface...and the same over the wings curves surface under the wing. A gentler curve but a curve none the less. If Bernouli applies above the wing it does so also under the wing and that IS a fact.

So, as I understand it the static pressure reduction is what we are interested in when considering the difference between upper and lower wing pressures that produce lift, is that right?

Tex