What Factors Influence the Development of Static Pressure in Fluids?

[umair20]

In many books & articles that I have read; static pressure has been defined as pressure of a fluid at rest. In some articles, it is said to be the pressure which is applied against frictional forces in a fluid. But I want to know how a fluid develops static pressure & what is basic force in this pressure ? ...just like dynamic pressure is due to velocity & hydro-static due to height!

 

[russ_watters]

It is typically due to the fluid being constricted in a container.

 

[Chestermiller]

Terms like static pressure and dynamic pressure give me a real pain, particularly since they imply that there are different kinds of pressure that can exist. Pressure is pressure, period, and, at least for an incompressible fluid, corresponds to the isotropic part of the stress tensor.

Chet

 

[russ_watters]

Terms like static pressure and dynamic pressure give me a real pain, particularly since they imply that there are different kinds of pressure that can exist. Pressure is pressure, period, and, at least for an incompressible fluid, corresponds to the isotropic part of the stress tensor.

Those terms just describe how the pressure is created. In Bernoulli's principle scenarios, you need a way to keep them separated. Otherwise, people often mistakenly think that "pressure" drops in a moving fluid.

 

[Chestermiller]

Those terms just describe how the pressure is created. In Bernoulli's principle scenarios, you need a way to keep them separated. Otherwise, people often mistakenly think that "pressure" drops in a moving fluid.

Can you please elaborate. I still don't see why you have to keep them separated. To me, it would only confuse things. I have seen many posts on PF in which the OP thinks that two "kinds of pressure" can exist simultaneously, whatever that means.

Chet

 

[russ_watters]

Can you please elaborate. I still don't see why you have to keep them separated. To me, it would only confuse things. I have seen many posts on PF in which the OP thinks that two "kinds of pressure" can exist simultaneously, whatever that means.

Chet

Consider the question: "Why does pressure drop in a moving fluid? Doesn't that violate conservation of energy?" We get questions like that a lot. It is a wrong question because pressure doesn't drop in a moving fluid. The three forms (or causes, if you prefer) of pressure are always equal to each other. The question arises from an explanation of Bernoulli's principle that labels static pressure as "pressure" but doesn't adequatly describe velocity pressure or head pressure, leading people to believe they aren't pressure.

A related reason why I prefer treating them separately is that if I am measuring it with a pressure gauge and it is different from another orientation of a similar probe, it is tough to say the two "pressures" are measuring the same thing.

 

[Chestermiller]

I don't think I'm going to be able to figure this out. After all these years of experience with fluid mechanics, I still fail to see what the issue is, and why the pressure has to be thought of in terms of separate contributions. I'm sure this is not the way I learned the Bernoulli equation. I'll try to pay more attention to other posts in this area and see if I can get a better understanding of what the issue is.

Chet

 

[boneh3ad]

It's really just nomenclature. Static pressure is the only "real pressure" in terms of figuring out the force on a surface. Dynamic pressure is so called because it has units of pressure but that's about it. You can't feel it. It's really just kinetic energy per unit volume. In the context of energy, static pressure is akin to spring potential energy per unit volume. The two combined (or three if you care about Gravity) are total (or stagnation) pressure, which is the total energy of the system and is the conserved quantity in a conservative system.

But like I said, static pressure is the only "real" pressure that you can feel.

 

[Chestermiller]

But like I said, static pressure is the only "real" pressure that you can feel.

This is what I simply call "pressure." But why add the adjective "static?" I contend that this is just a source of confusion to students. Thoughts?

Chet

 

[boneh3ad]

This is what I simply call "pressure." But why add the adjective "static?" I contend that this is just a source of confusion to students. Thoughts?

Chet

Well I think it serves a couple of purposes. First, it helps differentiate the terms in Bernoulli's equation, which is obviously an important equation even if a lot of people don't seem to understand its limitations.

More importantly, there are a number of parameters that scale with dynamic pressure (such as drag), so having a name for it is useful. It has units of pressure and a definite relationship to the static pressure, so calling it a pressure seems reasonable to me.

Also, total/stagnation pressure is, in a sense, an actual pressure in that it physically represents the static pressure at a reference condition (that being isentropically slowing a given flow down to zero velocity).

So I think calling them all pressure is fine. I think the shortcoming is in how this is taught in some sources. For example, saying "dynamic pressure is pressure that arises from the velocity" doesn't really make any sense and seems to indicate a lack of understanding of what it really is.

I suppose that having originally learned these things as a mechanical engineer as an undergrad and then seeing it from the aerodynamics perspective as a graduate student, the nomenclature makes more sense from an aerodynamics perspective than it does from a piping or chemical process perspective.

 

[russ_watters]

This is what I simply call "pressure." But why add the adjective "static?" I contend that this is just a source of confusion to students. Thoughts?

I really don't understand. How can you explain Bernoulli's principle without the adjectives? For example:

I put a pressure probe into an air duct and measure 1" w.g. of pressure. What is the speed of the flow?

Here's a hint: no matter what you answer, I'll tell you that you are wrong.

 

[Chestermiller]

I really don't understand. How can you explain Bernoulli's principle without the adjectives? For example:

I put a pressure probe into an air duct and measure 1" w.g. of pressure. What is the speed of the flow?

Here's a hint: no matter what you answer, I'll tell you that you are wrong.

What's w.g.? Water gage pressure?

 

[russ_watters]

What's w.g.?

Water Gauge. It's what a manometer measures directly (well -- any unit of distance will do) and is used in my industry as a convenient unit for airflow since the numbers are low but not too low.
http://en.wikipedia.org/wiki/Pressure_measurement#Units.

[edit]
Let's make it multiple choice:

A. 4000 feet/sec
B. 0
C. 100 feet/sec
D. Not enough information provided

[edit2] I don't want to make this too hard because it is just an example for discussion of my point. So if you aren't comfortable with the English Units math, here's a chart that may or may not be helpful: http://www.airmonitor.com/pdfs/industrial_public/brochures/BRO_Conversion_Chart.pdf

 

[Chestermiller]

What direction is the gage facing? Of course, if it's facing the flow, its very presence changes the pressure at the location of the gage. In this case, it is measuring the stagnation pressure. So you need the pressure from a gage that doesn't disturb the flow (say upstream, or by rotating your gage perpendicular to the flow) and you need the stagnation pressure. This combination will tell you the velocity of the undisturbed stream. I'm sure I'm not telling you anything that you don't already know. OK, so I had to use the adjective stagnation; but that is just what specifies how this particular kind of gage is applied, or what happens when a flow velocity is forced to zero. I don't know. To me stagnation pressure has more physical significance than "static pressure" or "dynamic pressure." Maybe I'm just biased by my training.

Chet

 

[russ_watters]

What direction is the gage facing? Of course, if it's facing the flow, its very presence changes the pressure at the location of the gage. In this case, it is measuring the stagnation pressure. So you need the pressure from a gage that doesn't disturb the flow (say upstream, or by rotating your gage perpendicular to the flow) and you need the stagnation pressure. This combination will tell you the velocity of the undisturbed stream. I'm sure I'm not telling you anything that you don't already know. OK, so I had to use the adjective stagnation; but that is just what specifies how this particular kind of gage is applied, or what happens when a flow velocity is forced to zero. I don't know. To me stagnation pressure has more physical significance than "static pressure" or "dynamic pressure."

So you get my point. Adding one word to the problem statement changes it completely and you recognize the value of adding such a word (also, from my link you can see it is a convention in my industry in the US). I'm a bit confused by the last sentence though: since stagnation pressure is dynamic pressure plus static pressure, I can't see how it could be said that stagnation pressure has more significance than static or dynamic. Either all of them should have significance or none should.

Also, the "pressure probe" could be a pito-static probe. So it could get you dynamic pressure on its own, without another probe.

 

[Chestermiller]

Russ,

Until today, I didn't even know what the terms "static pressure" and "dynamic pressure" referred to. Stagnation pressure, I did know. I thought that when the term "static pressure" was used in Physics Forums, it referred to hydrostatic pressure. No wonder I was confused. Anyway, I was unfamiliar with the terminology that was being used.

Chet

 

[russ_watters]

It's really just nomenclature. Static pressure is the only "real pressure" in terms of figuring out the force on a surface. Dynamic pressure is so called because it has units of pressure but that's about it. You can't feel it...

But like I said, static pressure is the only "real" pressure that you can feel.

This will be slightly argumentative, but I disagree. I think total pressure is the only "real pressure". Why? Because a fluid imparts pressure against something else by hitting it -- whether the motion is random or organized. Without motion, there is no pressure.

Anyway, I recognize that in a manometer or other pressure gauge the tubes are filled with a non-moving (in bulk) fluid so you measure only static pressure even if it is created by a moving fluid stagnating at the opening of the pito-tube. But that's not the only scenario where you might "feel" it: if someone hits you with a fire hose, you will feel the dynamic pressure directly as the water achieves stagnation against your skin.

 

[russ_watters]

Russ,

Until today, I didn't even know what the terms "static pressure" and "dynamic pressure" referred to. Stagnation pressure, I did know. I thought that when the term "static pressure" was used in Physics Forums, it referred to hydrostatic pressure. No wonder I was confused. Anyway, I was unfamiliar with the terminology that was being used.

Chet

Fair enough -- I'm still confused though. What would you call the terms in an equation that finds stagnation pressure? In the previous post you described how to find them without giving them names, which is fine, but in an equation, the terms kinda need names.

 

[Chestermiller]

Fair enough -- I'm still confused though. What would you call the terms in an equation that finds stagnation pressure?

Do you mean the following equation:
p_{stag}=p+\frac{1}{2}\rho v^2

Chet

 

[russ_watters]

Do you mean the following equation:
p_{stag}=p+\frac{1}{2}\rho v^2

Chet

Yes -- or better yet:
p_{?}=\frac{1}{2}\rho v^2

I know you would just call the "p" term in your equation "pressure", but what would you call the last term (if anything)? Or in my equation? In this case, I'm really not trying to be argumentative. The reading you get from a pressure gauge is "pressure" and I would think that in order to insert that reading into an equation you would need to have a convenient name for it. Or, for convenience, if the pressure reading needs to be displayed on a control panel, it would be cumbersome to have a sentence describing it instead just a two-word name.

 

[Chestermiller]

Yes -- or better yet:
p_{?}=\frac{1}{2}\rho v^2

I know you would just call the "p" term in your equation "pressure", but what would you call the last term (if anything)? Or in my equation? In this case, I'm really not trying to be argumentative. The reading you get from a pressure gauge is "pressure" and I would think that in order to insert that reading into an equation you would need to have a convenient name for it. Or, for convenience, if the pressure reading needs to be displayed on a control panel, it would be cumbersome to have a sentence describing it instead just a two-word name.

I would call the second term "the kinetic energy term," or, more precisely, "the kinetic energy per unit volume." But, I can see where, for convenience, it could be called the "dynamic pressure." But, until now, I was unfamiliar with that term. I guess we ChE's didn't learn to call it that. I'm going to check out BSL and see whether they ever use such terminology.

Chet

 

[boneh3ad]

This will be slightly argumentative, but I disagree. I think total pressure is the only "real pressure". Why? Because a fluid imparts pressure against something else by hitting it -- whether the motion is random or organized. Without motion, there is no pressure.

Anyway, I recognize that in a manometer or other pressure gauge the tubes are filled with a non-moving (in bulk) fluid so you measure only static pressure even if it is created by a moving fluid stagnating at the opening of the pito-tube. But that's not the only scenario where you might "feel" it: if someone hits you with a fire hose, you will feel the dynamic pressure directly as the water achieves stagnation against your skin.

That's not true, though. Consider flow in a pipe. If you put a pressure port in the pipe that does not intrude at all, that measures static pressure directly. If you put a Pitot tube in the flow, yes, that measures the stagnation pressure, but why? It does so because it is a physical obstruction that isentropically slows the air at the tip to zero velocity, so at that point, the stagnation pressure and the static pressure are the same thing. It is still sensing the static pressure directly. You can't directly sense the dynamic pressure, either. It simple is a measure of how much static pressure could be gained by stagnating the flow, so the air hitting the tip of the Pitot probe is now experiencing a static pressure that has risen by exactly the dynamic pressure in the mean flow, but it is still the static pressure at that point that it is sensing.

Stagnation (total) pressure is simply the measure of what the static pressure would be in a fluid if all of it's flow kinetic energy was converted into potential energy in the form of static pressure. It is a reference condition. The only way to measure it is to actually change the flow so that the static pressure rises to the stagnation pressure by bringing its velocity to zero. I suppose it is semantics, in some sense, but it's important to understand. You don't directly feel stagnation pressure except in the regions where the flow stagnates, and you never directly feel dynamic pressure.

 

[russ_watters]

boneh3ad, you didn't directly address the scenarios I presented. I'll be more succinct for one: the way air pressure is imparted on a surface is by air molecules bouncing off of the surface.

 

[Chestermiller]

Guys, I think we are beating a dead horse. We all realize that we are using different terminology (i.e., Chet) and that there are well-defined interpretations to the terms, but the important thing is not the terminology; it's getting a problem correct when we encounter one in practice. I think that all three of us can do that competently, without much trouble. Through our interaction, I've learned something new about the terminology that is apparently widely used, and will be alert to that when I see it in future PF threads. But, I propose that, at this point, we let the discussion drop,

Chet

 

[rcgldr]

getting back to the original post:

In many books & articles that I have read; static pressure has been defined as pressure of a fluid at rest.

or from a frame of reference that moves at the same speed as the fluid.

$p + \frac{1}{2} \ \rho \ v^2$

This is an approximation for stagnation pressure which doesn't take compressibility into account. It's not accurate enough for commercial airliners which cruise at well above mach 0.3.

 

[boneh3ad]

This is an approximation for stagnation pressure which doesn't take compressibility into account. It's not accurate enough for commercial airliners which cruise at well above mach 0.3.

What you quoted was not stagnation pressure. Did you misquote?

 

[rcgldr]

What you quoted was not stagnation pressure. Did you misquote?

See post #19.

Wiki articles:

http://en.wikipedia.org/wiki/Stagnation_pressure

http://en.wikipedia.org/wiki/Impact_pressure

 

[boneh3ad]

See post #19.

Wiki articles:

http://en.wikipedia.org/wiki/Stagnation_pressure

http://en.wikipedia.org/wiki/Impact_pressure

I am aware of the concept of stagnation pressure, but what you quoted was the dynamic pressure, not stagnation pressure.

 

[rcgldr]

I am aware of the concept of stagnation pressure, but what you quoted was the dynamic pressure, not stagnation pressure.

It was called stagnation pressure in post #19. Quotes from post #18 and #19:

What would you call the terms in an equation that finds stagnation pressure?

p_{stag}=p+\frac{1}{2}\rho v^2

 

[boneh3ad]

It was called stagnation pressure in post #19. Quotes from post #18 and #19:

Right, so he was asking what he would call the two terms on the right hand side that add up to stagnation pressure. You only quoted the one term, and the term you quoted was the dynamic pressure term.