# Is circulation real?

Discussion in 'Hydrodynamics and Aerodynamics' started by Mikko Brummer, Jan 25, 2013.

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### BarrySenior Member

Interesting to know that Nasa with their PHD physicists and PHD engineers have got it wrong.

Your reference to Charles Law appears also to incorrect. Charles Law pertains to volume and temperature without a pressure component. V/T=k The only time PV=RT is at high temperatures and low pressures.
The Ideal Gas law contains PV and RT but only as PV=nRT

Your comment "It's the movement of the sail relative to the air that generates the pressure change" That is like saying when the wind blows there is pressure in on the sail.
So if a sail is not moving, the wind acting upon the sail does not generate thrust??? Sure it does

So rather the comment needs to be "It is the mass of the wind being redirected (ie change of velocity, acceleration, resulting force) that creates windward pressure on the sail. If you are interested I can probably dig out the formulas that can determine resultant forces. Again, this is the windward side that I am focusing on for this post. These formulae are the basis for vane and stator design in in turbines, pumps, jet engines, and the list goes on

Certainly, any change in volume or pressure will involve a temperature change but would the temp even have a 1% influence on the pressure? If you disagree that it is negligible, perhaps you could provide the mathematics to
produce the temperature change that the leading edge of a mast might see from the resulting hot air that is being produced at 15 knots.

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### Sailor AlSenior Member

Encyclopedia Britannica:
"Charles’s law, a statement that the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature, if the pressure remains constant."
No, I didn't say that.
 If, from the boat's frame of reference there's wind blowing on the sail, then, from the air's frame of reference, the the sail is moving through the air.
It's not the temperature change causing the pressure difference. It's the compression of the air that's causing the increase in pressure and the temperature change.
This is high-school physics.
 I think you may have missed the full explanation in Swept Volume Theory

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### Sailor AlSenior Member

Can you please explain why Mach 0.3 is the point at which air changes from incompressible to compressible?

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### Sailor AlSenior Member

But that's exactly what the are saying, over and over again. Here's one
"As the velocity of the airstream increases, air starts to be compressed as it flows around the aerofoil. This has a noticeable influence once the flow Mach number reaches 0.3 or above."
The literature abounds with it, including the Alan Cattelliot (above)

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### Sailor AlSenior Member

I think I'm on to a source of the mysterious Mach 0.3. It's to do with the solution to a complex algorithm described by NASA:
They make a claim:
"For subsonic flow (M<1), density is relatively constant"
and then
"1. For low speed, or subsonic conditions, the Mach number is less than one, M < 1 and the square of the Mach number is very small. Then the left hand side of the equation is very small, and the change in density is very small. For the low subsonic conditions, compressibility can be ignored."
But I think there is a fault in that algorithm because it relies on "rho is the fluid density" .
The significant feature of a gas is that, in accordance with the Gas Laws, its density (Mass/Volume) depends on its Mass and its Volume, and while, for a given quantity of air, its mass is a constant, its volume depends on its pressure and temperature: PV=RT, so from the outset the equations are using a variable as a constant!
So isn't the argument circular? Air is incompressible since its fluid density can be a constant therefore air is compressible! What?
Help me here!

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### DCockeySenior Member

Two statements which are fundamentally different:

1) The compressibility effects of air can be ignored below Mach 0.3. Therefore air can be treated in analysis and testing as if it is incompressible below Mach 0.3.

2) Air is incompressible below Mach 0.3 and compressible above Mach 0.3. ​

The first is true for typical aircraft, wings, sails, boat superstructures, road vehicles and similar, though the speed at which compressibility effects need to be considered depends on the details of the shape of the object and the accuracy needed. Mach 0.3 is nothing special. It is just a nice round number which is generally true for most configurations and uses of analysis and test results. It is important to keep in mid that nothing dramatic occurs at such a Mach number. The aerodynamic characteristics change smoothly at that speed as they do over the entire speed range. (One possible exception is at low Reynolds number with certain configurations there can be an abrupt change due to separation.)

The second is not literally true as written. Variations of it can be found in many discussions of aerodynamics as a short version of the first statement. Apparently this is causing confusion for some.

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### DCockeySenior Member

Not a complex algorithm but a brief summary of a portion of standard aerodynamics. Multi-variable differential calculus is used which can be confusing without appropriate knowledge. It is more complicated than basic differential calculus.

It is unfortunate that the introduction in the link includes an almost but not quite correct statement:
If the aircraft passes at a low speed, typically less than 250 mph, it is observed that the density of the air remains constant.​
What should have been said is:
If the aircraft passes at a low speed, typically less than 250 mph, it is observed that the density of the air remains essentially constant.​

The conclusion in the link is correct (emphasis added):
1. For low speed, or subsonic conditions, the Mach number is less than one, M < 1 and the square of the Mach number is very small. Then the left hand side of the equation is very small, and the change in density is very small. For the low subsonic conditions, compressibility can be ignored.

Density is treated as a variable, not a constant in the derivation in the link. Isentropic flow is explicitly assumed, and in isentropic flow density is not constant. With the assumption of isentropic flow the gas properties can be calculated using only pressure and density (or only temperature and density or only temperature and density). That is why temperature does not appear in the derivation.
From the derivation in the link:

From our derivation of the conditions for isentropic flow, we know that:

dp/p = gamma * drho/rho

dp = gamma * p / rho * drho​

Aerodynamics is complicated, and can easily be confusing.

Barry likes this.
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### Sailor AlSenior Member

"Argument by assertion is the logical fallacy where someone tries to argue a point by merely asserting that it is true, regardless of contradiction. While this may seem stupid, it's actually an easy trap to fall into and is very common."
In the quoted paper, rho is provided as a constant. Density is defined in the paper as being "relatively constant" (whatever relatively constant means!)
The whole development of the Bernoulli equation relies on the density of the fluid being constant (and thus independent of pressure).
Let's not get too condescending, some of us have degrees in mathematical physics, and a brain that's still quite active.

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### Sailor AlSenior Member

Let me remind the forum of some long established principles of classical mechanics.
1. Matter exists in three states: solid, liquid and gas. (plasma is more recent than classical mechanics and is clearly not relevant to the current discussion)
2. Air, in the environment of sails and aircraft wings, is a gas.
3. A gas differs from solids and liquids in that their density is constant whereas the density of a gas is directly proportional to its pressure and inversely proportional to its absolute temperature.
4. Newton's laws apply to "bodies", which are a) solids of constant density and b) do not flow like liquids and gases.
5. Bernoulli's principle applies to fluids of constant density.
Anyone, including NASA who claims that, in the operating environment of sails or aircraft wings, the density of air is constant, is flying in the face of 250 years of classical mechanics.

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### Alan CattelliotSenior Member

Anderson, J.D., Fundamentals of Aerodynamics, 4th Ed., McGraw–Hill, 2007 ....

Where the MACH 0.3 is cited. These definitions may vary from one author to another. For instance, flows above mach 10 were qualified as hypersonic flows by my masters and professors, without them introducing another higher interval.

Last edited: Aug 18, 2022
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### Alan CattelliotSenior Member

1. It exists, for purpose of explaining phenomenon, more states of matter than those cited here.
2. Basically, I agree, although airplane wings can also be equipped to cope with water, and ice.
3 . The difference between a gaz, a liquid, and a solid is the arrangement of their molecules. Pressure, density, temperature, internal energy are physical properties being used inside principle to help use describe phenomenon and reproduce them. No more... No less...
4. I don't agree, and I am very interested to know what reference that you have for such an assertion.
5. Yes.... and ? Do you want to say that, because air is compressible, we cannot apply Bernouilli ? It seems to me that you keep on and on circling around your main idea, which may be usefull if only it provides a good way to calculate the forces around a wing. Have you tried to apply your model, and compare it with some wind tunnel experiments? If so, can you show me your results ?

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### Sailor AlSenior Member

Yes, that is what scientific principles do.
No, they don't. Challenge issued.
Again, yes. That's what scientific principles do.
Only every school textbook ever written on the subject. The fact you don't agree puts you at odds with the millions of scientists who for the past 250+ years have used them in their day-to-day endeavours.
yes Yes YES! That is the whole point of the discussion.
No, you are missing the point. It is used to explain the existence of the pressure differences. Not the size. We know the pressure differences exist: 1) they have been measured, 2) Planes stay in the air, sailboats move. The apparent wind speed provides the aeronautical force. The only way a gas can exert a force on a body is via pressure. Bernoulli's Principle does not explain the existence of the pressure differences.

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### Sailor AlSenior Member

Let me expand my list:
Anyone, including NASA And Anderson who claim that, in the operating environment of sails or aircraft wings, the density of air is constant, is flying in the face of 250 years of classical mechanics.

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### Sailor AlSenior Member

I see you made this claim earlier in #291. I didn't chose to follow it up as it was not then pertinent.
Maybe I should have. What are the "more states sometimes"?

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### Sailor AlSenior Member

Mikko Brummer: Are you able to respond to my question please? My challenge is still open:
"If not, please provide a link to an algorithm which will take the geometry of an aerofoil, the dimensions of a wing, airspeed and altitude and, without a lookup table of L/D ratios, generate a value for the lift generated in Newtons."

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