They may soon be able to quantify the advantage of bore roughness in reducing friction loss in the wall of flutes. The kind of changes in playing characteristics observed by Doug Tipple in his PVC pipes with rough interior walls. I ran into this article while searching for the consiquence of a really smooth bore: http://www.star-board.com/forum/starbulletin/read.asp?ID=4338&t=2005313115310 .
They say that the important thing is the amount and randomness of the roughness. I have not looked into the details.
I think that the flow rate down a flute would be very low, so low in fact to be insignificant with respect to drag. If you put your hand near the end of a friends flute while they play a low D, can you feel much air coming out?
For dimples to have an effect on the flow, the speed (more precisely the Reynolds number) has to be quite high (high enough for the dimples to make any laminar flow become turbulent). The effects of this, at least the benefiial ones, are limited to certain shapes, such as bluff bodies (golf balls!), or pipes (where if the laminar boundary layer meets at the center of the pipe, the flow rate is impaired), etc.
I would imagine that the internal roughness affects the internal reflection of the standing waves, perhaps adding some ‘colour’ to the sound produced.
Molecules in a flute do travel back and forth at, say A is 440 Hz, 440 times a second. A standing wave being the superposition of two oppositely traveling waves at the speed of sound, the molecular velocity would be about mach 1. This gives a Reylnolds number of,
R=ρ c d / ν
The density is about 1.2 Kg/M^3 ; the speed is about 600 M/s ; the distance is about 2 cm; and the viscosity is about 1.7 x 10 – 4 . This gives a Reynolds number of about 10000. Maybe the distance is only the thickness of the surface layer, which is 0.05 mm. I do not know, but to feel the air coming out of the end of the flute is bogus.
To quote from “Acustical Aspects of Woodwind Instruments”, C.J.Nederveen, page 19, “for a flute tube with radius 9.5 mm, resonating at 600 Hz, … this implies that the real part of the impedance…is solely dependent on the boundry layer effect at the wall.” So what ever the case, there is turbulant flow close to the wall and wall roughness has everything to the Q of the resonator.
Nelson
I was falling into the “bulk air flow through the flute” thinking, too, and was about to show that the Reynolds number was probably too low for turbulent flow even with dimples. Thinking of it in terms of the acoustic wave does change things significantly! Thanks for the enlightenment. Looks like I should just stick to heat transfer.
The molecular displacement corresponding to a frequency of 440 Hz is
5.062E-5 inch, or 0.0013 mm.
d = 9.8/(f^2)
That has nothing to do with anything – I was just curious.
Looking back through my fluids text, I’m reminded that calculating boundary layer thickness is pretty complicated. I’m far, far too rusty on this stuff!
My wife asked me what I was so intent on, writing this, I said, “Drag”. She said, “Well, don’t use my lip stick”. I said, “No, drag racing, I’m going to trade you in on a new model.”
I looked up how fast the molecules are going inside the flute and it is from one-tenth to one-hundredth mach 1, depending on the loudness. In any case the Reynolds number is lible to be more than 30 which puts the molecules along 0.1 and 0.5 mm from the wall into turbulent flow. Riding on one of them, you get a hell of a ride conpaired with riding a molecule in the middle of the flute. One little demond said to the other, “You ought to got on one of these molecules down (or up) by the wall. Besides going back-and-forth, you would think you are on a white-water raft; fliping and turning all over the place.”
We need to take two 16 feet long Doug Tipole tubes, (8 footers hooked together) or even 24 feet. One smooth walled and one rough walled. Put a sound at one end and an ear at the other and turn the volume down, down, down, until you don’t hear it anymore, like they do in a hearing test. See the difference in the sound level in the two. There are other ways to measure the wall loss difference, but that is the straight forward way.
A less quantative way is to take two flutes in half. Cover the ends with something like a film can lid. Play the fundamental and 3rd octive (a closed end pipe only plays odd harmonics). What size pin hole makes them play the same loudness? The ratio of the size of the pin hole to the size of the tube gives the difference in loss. That tells the wall effect also. Probably an easier experiment.
I can’t profess to be an expert on vibrating air in pipes, my knowledge only extending to a Kundt’s dust tube experiment I did at school about a quarter of a century ago! However, aren’t longitudinal waves just pressure variations, and if so then surely there is very little motion of air, as one molecule just bumps into the next, etc. until this pressure wave reaches an anti-node and reflects back, ad infinitum? In other words, this pressure wave travels at the speed of sound, but are the air molecules merely a medium through which it can travel, without themselves having to travel (beyond the small amount of motion required to bump into each other of course)?
Also, Nelson, surely the Reynolds number based on 2cm displacement is 1.2293430.02/1.73e-5 = 487,300? According to Daryl’s calculation of molecular displacement being 0.0013mm, then the Re is 31.7? Though, I don’t know how either of these displacements were arrived at.
As I said, I’m no expert on this (though I know a lot more about wing design), so I’m quite open to ideas/explanations.
Oh, well, since I’m already off-topic, I might as well take the plunge. I couldn’t resist trying to find that story I just mentioned.
It’s called “Abandon All Heat, Ye Who Enter Here,” by Phil Bertoni. According to http://www.logan.com/loganberry/stump.html it was published in the September 1976 issue of Galaxy magazine.
Now I’ve not only gone off-topic, I’ve just revealed my age AND set up a quest for myself to get ahold of a copy of that old Galaxy mag!
