It is blindingly obvious that the flow is moving with the belt. This is because the belt powers the "wind", whereas a road does not power the real wind, and even then, it is going the wrong way, because without air flow to represent the wind, it cannot stay on the belt, let alone travel.
It is fundamentally flawed. This boundary example is rock-solid proof of that claim. No more games.
Hard to figure out what that means, because although it follows the rules of English syntax, beyond that it's just muddle. (What does power the real wind, by the way?)
Let's simplify the question of the "a-h" windspeeds. Forget the speed, just tell us the direction at each level. Finding this to be misleading because of the perspective that it's viewed from? Fine, pick any perspective you like, tell us what it is, and tell us the direction of the airflow at each level. This is a question. If you feel that we have the wrong answer, then you have to tell us what the right answer is, not just claim that the question is wrong.
That is another fine plan, jjcote, just getting the directions from humber, with a single and unchanging frame of reference.
Humber wrote:
Let me solve this tricky syntactical conundrum for you .
Even a layman should appreciate that the boundary layer is viscously attached to the belt, so will flow with the belt.
Agreed
The boundary layer is associated with the belt, because the belt is the only source of power for the treadmill "winds". However, it is not the case that roads power the wind or boundary layer in the external world ( a.k.a nature, the environment).
Agreed, as far as makes no odds.
The belt-generated boundary layer, is in the opposite direction to that found in the external world ( a.k.a nature, the environment).
Agreed, at least in the sense of "I understand what you're trying to say."
In the external world, the boundary layer flows in the direction of what is often called 'the wind', whereas on the treadmill it flows opposite to that expected direction.
Agreed.
This suggests that the cart is actually traveling the wrong way and should be traveling with the belt, in which case, the boundary layer would be in the appropriate direction.
No, because if it travelled with the belt, it would be travelling into a belt-generated headwind, and it is a d
DWfttw vehicle. For Christ's sake, please try to understand that for the treadmill situation NOTHING is going the wrong way. EVERYTHING is shifted 10 m/s. It is as simple as that. That statement is virtually the whole explanation of the velocities. Where once a cart would have been going 10 m/s to the right to match the 10 m/s tailwind, it is now at 0 or around there (a shift of 10 leftwise). Where the ground was still, it is now going 10 to the left (a shift of 10 leftwise). Where a person was standing measuring the windspeeds at different heights at 0, he is now doing so at 10 m/s to the left (a shift of 10 leftwise). Where once he measured a windspeed of 10 m/s to the right as he stood still, he now measures a windspeed of 10 m/s to the right - what? no change, no shift of 10 leftwise? No. Why? Because the wind has shifted 10 leftwise, but he has also (along with the belt) undergone a shift 10 leftwise.
Now, if you can understand still air (w.r.t. the room) as a 10 m/s "belt-generated wind" that is "going to" the right, which you grudgingly do (a shift of 10 rightwise), it is only one small step further to recognise a boundary layer flow of 1 m/s to the left (w.r.t. the room) as a 9 m/s "belt-generated wind" that is "going to" the right (a shift of 10 rightwise). That is...and this is the crucial bit...if you have got to the stage in your mechanical and physical knowledge to understand relative motion and frames of reference (and you have enough links to follow).
Similarly, a 10 m/s wind to the left at belt level (w.r.t. the room) is, by switching frames, motionless (a shift of 10 rightwise). What is the new frame in all these second cases? It is that of the belt. That is why I wanted you to say what you thought were the windspeeds recorded by our person going back with the belt, because they are identical to those in the land-based situation where the ground actually is still. Person and wind have both had a shift of the same amount, so the anemometer will read the same values.
However, this would result in the cart simply traveling with the belt as expected of a can of beans, perhaps. (Not very noteworthy.)
Without airflow to represent a tailwind, the cart cannot travel with that belt beyond that limited manner. It is therefore a matter of necessity to the windspeed claim, that the cart be set against the travel of the belt.
(It looks more impressive, but that is all.)
No. You know that if the cart is pushed backwards by the belt into the air behind it, that is a tailwind. The even funnier thing is that if you had a clue how the cart worked, you'd realise that it is impossible to run it that way [ETA: the way you suggested, with the belt], and if you turn it round, it still goes left to right.
Is that not clear? You want maths for that? Walk before running.
What we wanted was a simple number, or set of numbers, or a direction. Your maths was not very helpful, because you were trying to measure different speeds and make your new-fangled paddle spin with them, and because, as always, your frame of ref was all over the shop.
(1)In nature, the boundary layer flows in the direction of the wind, but slower.
YES, you don't need to repeat things we all have agreed.
(2)On the treadmill, the tailwind is said to flow up the belt, to drive the rear ofthe cart. The boundary layer, moves with the belt, and so in the opposite direction of the tailwind.
There you go again, shifting frames. That statement is so monumentally stupid, young children are probably coming here from bebo just to laugh at it.
Look at it this way. You say the b.l. moves with the belt and so is going the opposite way to the tailwind. But the tailwind is at 0 (you said so yourself), so the b.l. can't be opposite to that. What wind is opposite to stationary air? The tailwind you talk of only exists once whateveritis that is your frame of reference is moving to the left, and as your frame moves to the left, miraculously the value of the b.l. changes too, since all motion is relative, and is shifted right by that same amount. Like if you are on a train, and another train seems to be going backwards, but in fact is only going forwards slower than you. You're overtaking it, so it's going backwards from your frame. Jesusss, how long do we have to explain relative motion?
However, you have been precise enough, I think, for my purposes. You do actually seem to have said that when a surface is driven through a fluid, there will be two opposite flows created. The one near the surface is 'reversed' so as to go faster than the surface. Lovely. Let's phone NASA.
(3) It is not possible to reconcile this situation in a manner that makes them equivalent.
(4) The "layers" do not matter, because of that eclipsing error.
The 'two directions of flow at once" error. Yeah, I'd say that was pretty eclipsing.
Patently obvious. 10 seconds though for me, if not immediate.
Less haste, more speed, or just try to go in the right direction.