Swept Volume Theory

Oh my dear, the completed expression has been around and accepted for a looong time now.

Bernoulli lived 1700-1782, that is about 50 to 100 years before the development of a scientifically consistent thermodynamic theory, so he might be excused for not incorporating all factors.

But there is no excuse for the neglect today........

 

Is that the same argument that Anderson uses to justify the "air is incompressible below Mach .3" claim?

 

What would that prove?

 

As you are stating unequivocally that Anderson claims that air is incompressible below Mach .3, please provide the quote. I believe he and others have suggested that below M .3 the compressibility of air is negligible wrt to calculating lift wrt to
wings.

This is what he says in his book ( I added this after when I found his passage)
We shall prove later that for gas velocities less than about 0.3 of the speed of sound, the associated pressure changes are small, and even though 7 is large for gases, dp in Eq. (1.6) may still be small enough to dictate a small dp. For this reason, the low-speed flow of gases can be assumed to be incompressible.

 

That shows a fundamental misunderstanding of physics. Any force applied over a surface area is, by definition, pressure. Whether it is a gas or not is irrelevant. You really need to study and comprehend the fundamentals. For example, the definition of pressure and force.

 

gonzo said: ↑
Where is the proof? If you agree water is "a bit compressible", then it is compressible. The difference between air and water is one of degree and not of behavior.

That is another instance of misunderstanding of basic principles.

 

He confuses negligible with absent or non-existent.

 

For once, why can't you just read what is presented to you and try to understand it, rather than asking some irrelevant thing!

 

If the lift is independent of Mach number, it's hard to argue that you need to consider Mach number effects.

 

There's also the tangential skin friction which contributes to the force - mainly to the drag component.

 

It’s just that I worked through Anderson’s argument and I was hoping I didn’t have to do it again. You keep presenting different texts and it’s hard work keeping up. Why didn’t you quote Drela if that’s your foundation text?

 

But I’m not considering Mach number effects. It’s your texts that claim an effective difference in air compressibility at different Mach numbers. I claim air is equally compressible at all the Mach numbers that are relevant to this discussion!

 

Good grief! When you started posting, I was sure you must be a troll. Then you started sounding like you really did want to learn. Now I'm back to the idea that you must be a troll.

 

At low mach numbers the changes in density are so small that compressibility may be negletet. Sure you can take care of compressibility and use it in calculations but you could keep it simple and don't take care of it..
KISS principle

 

Why? What did I do?