Fluid mechanics, why does the air flow faster over the wing?

[Stan Butchart]

There is no frame of reference where the speed is 1V along the entire surface.

One last shot.
we have a fluid that is moving relative to the remote air. We have a body that is moving relative to the remote air. The body and moving air are moving relative to each other.

I mark the lip of a glass and place it upside down on the table and rotate it. (I should accelerate and decclerate it but that is a detaile.) Now as i rotate it as I move it across the table. What has the mark traced on the table?

I have resolved it from the source/sink pattern. I have resolved it from the tangental velocity relative tothe surface and i have resolved it from the cylinder surface velocity equation.
I have graphed its path as described in http://svbutchart.com
I have never ever suggested that the constant 1V was relative to the cylinder.

 

[boneh3ad]

One last shot.
we have a fluid that is moving relative to the remote air. We have a body that is moving relative to the remote air. The body and moving air are moving relative to each other.

I mark the lip of a glass and place it upside down on the table and rotate it. (I should accelerate and decclerate it but that is a detaile.) Now as i rotate it as I move it across the table. What has the mark traced on the table?

I have resolved it from the source/sink pattern. I have resolved it from the tangental velocity relative tothe surface and i have resolved it from the cylinder surface velocity equation.
I have graphed its path as described in http://svbutchart.com
I have never ever suggested that the constant 1V was relative to the cylinder.

You have to be careful with your choice of words. Velocity and speed are not the same thing. Going through the math, in the frame you are describing, the speed of a parcel of fluid is, in fact, going to be U_{\infty} along the circumference. The velocity isn't, and is a vector quantity. Additionally, your site is quote difficult to follow. For anyone else on here that has been reading along and thought Stan's explanations were somewhat opaque, I go through the math showing this below.

Earlier, I talked about potentials. The equation Stan keeps quoting is the same equation as mine for v_{\theta}, only you have the angle defined differently. My angle was defined in a typical coordinate system with 0 being on the right at the x-axis and increasing counter-clockwise. Otherwise, the two are identical. I am starting from my equation since it will make things easier to change to a Cartesian coordinate system and change frames.

Now, if we want to switch into a Cartesian system, we take my results for v_{\theta} and v_{r} and plug them into
u = v_r\cos\theta - v_{\theta}\sin\theta
u = v_r\sin\theta + v_{\theta}\cos\theta

Since we already determined that on the surface, v_{r}=0, this simplifies to
u = 2U_{\infty}\sin^2\theta
v = -2U_{\infty}\sin\theta\cos\theta

This defines the vector field on the surface of the cylinder in Cartesian coordinates in the frame where we are riding along with the moving cylinder (so it has no velocity and the free stream is moving). Now to change reference frames such that we are viewing the cylinder moving through the stagnant fluid, we just have to add the following:
(-U_{\infty},0)

Leaving us with
u = 2U_{\infty}\sin^2\theta-U_{\infty}
v = -2U_{\infty}\sin\theta\cos\theta

This is the velocity vector along the surface in a Cartesian coordinate system in the inertial frame. The cylinder is moving through stagnant air. We can transform this back into cylindrical coordinates for simplicity using
v_r = u\cos\theta + v\sin\theta
v_{\theta} = -u\sin\theta + v\cos\theta

This leaves us with (and you can do the algebra if you want)
v_r = -U_{\infty}\cos\theta
v_{\theta} = -U_{\infty}\sin\theta

Taking the magnitude of this, it is easy to then show that
|\bar{V}|=U_{\infty}

So yes, indeed, the fluid parcel is moving with a constant speed of U_{\infty} in an inertial frame. The problem is, this doesn't tell us a lot about the forces on the cylinder. The important quantity is the speed with respect to the cylinder.

 

[Stan Butchart]

So yes, indeed, the fluid parcel is moving with a constant speed of U_{\infty} in an inertial frame. The problem is, this doesn't tell us a lot about the forces on the cylinder. The important quantity is the speed with respect to the cylinder.

The only point here was that the Bernoulli Principle was not at work along the surface but that the Bernoulli Equation was, based on normal acceleration.

 

[boneh3ad]

The only point here was that the Bernoulli Principle was not at work along the surface but that the Bernoulli Equation was, based on normal acceleration.

That doesn't make any sense. Bernoulli's equation makes perfect sense in this situation, especially since we are doing this ideally. Just because the result of something is zero in a certain frame or reference doesn't mean it doesn't apply. Regardless, the important frame is that which follows the body.

 

[Stan Butchart]

Bernoulli's equation makes perfect sense in this situation,

In the long run you might be right.If we only want numbers the Bernoulli Equation dos just fine. However, most of the thousands that search the web and books are only looking to uderstand the lifting process.

The largest percentage of the hundreds of articles and sites firmly define the concept that pressure changes are created by linear variations in the flow tangent and relative to the surface. (in the sense of the venturi)

There is additional group that explains that the velocity changes are in response to the pressure variations.

The primary flow is from displacement. The source/sink pattern describes the motion effects throughout the entire flowfield. These instantaneous velocity vectors are relative to the remote (still) fluid. When we add the fwd motion of the cylinder we can find the tangent velocity relative to the surface. This tangent velocity, in combination with the surface radius produces the normal acceleration, v^2/R, creating a pressure gradient that must be integrated across the entire flowfield. It is almost luck that all of this can be reduced again to the Bernoulli Equation.

We find that we can still apply the Bernoulli Equation to the tangent velocity, relative to the surface. But is this the Bernoulli Principle??

 

[Stan Butchart]

Additionally, your site is quote difficult to follow.

boneh3ad --It appeares that I have a real problem here. If you (or anyone else) have any suggestions my "e" address is on the site. http://svbutchart.com