Blowing machine

[Terry McGee]

Oh damn! Oh well, while we keep thinking on how to calculate it, I reckon we can at least estimate it from just one manometer reading. More in a moment on that.

Here's the run as requested going up to 40L/Min (and remembering to measure both columns!). Note I've revised some of the earlier lower figures a smidge.
40 L/min (both flow meters) required 252mm of water pressure
30 L/min required 136mm of water pressure
20 L/min (back to one flow meter) required 64mm of water pressure
15L/Min required 33mm
10L/Min required 14mm.

Plot the square roots of those pressures against the flows and we get the classic straight line passing through zero. No sign of flattening off at the top end, so I think we can discount turbulence. I'd imagine you'd also hear audible artefacts from turbulent air? I am up in the fourth regime of xxx xxx though. And with hearing protection and the door shut to avoid terrifying the neighbours. (People around here are still a bit twitchy about things that sound like sirens, in the wake of the 2019 bushfires that came right up to our back fence! 2448 homes lost all up, 33 people killed. We came off unscathed, but did we ever go through some water that day!)

A trend line identifies the main slope factor as 0.3972etc. Taking just the 40L/Min and square root of 252mm pressure figures gives you a factor of 0.3969etc. I'd call that near enough! We can probably call it the "Feadog Mk1 Windway Resistance Factor" from now on. And use the same single point measurement to calibrate the resistance factors of any other whistles. I'll get to measuring the ones I have here as time permits. This should prove very interesting.

In other news, I've also made a useful improvement in useability by incorporating a gate valve (lever operated tap) in the path of the second flow meter. So I don't have to muck around with their needle valves any more. And I've made up a good-sized knob for the flow regulator (it originally had just a screwdriver slot, making it awkward to set.) Bit by bit, we're getting a bit more elegant. And I'm getting more confident that we can use the set-up and get reliable results.

And I just got around to comparing my U-tube manometer with a digital manometer I bought years back. They pretty much agree, apart from a bit of zero error. But it's a bit aggravating having 0.7cm (7mm) showing when nothing is happening. If I switch to Dif mode, that disappears, but then the rest of the readings slip a bit. I think maybe First Principles has a lot to offer!

[trill]

. . .Sorry, I'm being too cryptic. . .

Not cryptic at all ! Thank you for elaborating. What I meant by "understanding the "comment" was "understanding why it happens". To me, the wafties are a totally new animal.

[trill]

. . . but is it of practical relevance to us? . . . I still struggle to explore any of it by mouth. . .

Totally agree. I don't see myself trying to make a tune around them. Also, I cou'dn't replicate with mouth-blowing either. I certainly wonder why, though. . . . damping in the human-anatomy-cavities ?

[trill]

. . . This is getting out of my depth. . .

Well, my head is feeling pressurized . . .

In the interest of simplicity, I'm going to try the following, and see how it compares with Terry's measurements : Q=Cd*A*sqrt(2*g*delta-P)

Yes, Cd is "discharge coefficient", one of those "mysterious" coefficients which get used to account for the difference between theory + actuals.

I would agree: the windway will introduce it's own (length-dependent) losses. Those losses would rob energy from the flow. The question is, how much. I simply don't know. Intuitively ? Don't know yet. That's what the "Cd" is for.

I'm curious, in computing Reynolds number, which windway dimension does the model use ? length ? width ?

Edited 2/16/23
Ooopsie: that formula should be : Q=Cd*A*sqrt(2*delta-P/rho)

[trill]

. . . ditch the manometer . . . ditch the flow meters . . .

My vote is that both are used. More data + info for modelers.

Each gives a "view" into the "head-flow" process, which, after all, is a little fuzzy at this point. Two blurry lenses are better than one.

Also, from your prior description, is this what your flow meters look like ?

[stringbed]

The digital dream machine is the Fluke 922.

[trill]

. . . Permission to go off and make some flutes, Sir?

Granted !

Sir, you have given us a great gift: a *pile* of data to work with !

I haven't processed it all yet, but it is on my list of things to do.

I have 2 areas of interest here: curiousity + musicality.

Curiosity: the data you have given allows a check of understanding. My hunch for a long time has been that pressure+flow in a whistle would be roughly approximated by Bernoulli's equation using a simple discharge coefficient. The mix of agreement + small-percentage-differences listed by Tunburough make me optimistic.

Curiosity: the "wafty" tones you discovered at low flows, immune to tone-hole coverage. I found them too ! With my little Susato+oxygen setup ! Honestly, someday (in my spare time !) I'd like to understand them. Also, quite surprising to me was that the flow-rates with give the "wafty" tones give *nothing* audible in the naked head. Definately *not* what I was expecting !

Musicality I have two interests: backpressure+sound.

Backpressure: my thinking now is that windway area will be the primary driver. Yes, windway length + taper will contribute, but my hunch (side-bets later!) is that they will be small. As a player, backpressure is a *huge* factor in whistle playability.

Sound: I'm interested in both volume + timbre. Volume is easy. Honestly, with the approach used in all this testing, you could devise a power-rating for any whistle : [energy-out (dBa)]/[energy-in (watts)] . My ears tell me there are *vast* differences !

Timbre is harder. Have to look at PSDs + head designs (protrusions, chamfers, etc..). One thing I learned from a very flute-like whistle: all those freggin' high harmonics matter !

[trill]

The digital dream machine is the Fluke 992

Specs looks lovely ! Good toys ain't cheap !

[Terry McGee]

. . . ditch the manometer . . . ditch the flow meters . . .

My vote is that both are used. More data + info for modelers.

Each gives a "view" into the "head-flow" process, which, after all, is a little fuzzy at this point. Two blurry lenses are better than one.

Yes, but consider all the extra work needed to take and record that info, if it really is just repeating the flow info in a different form.

Also, from your prior description, is this what your flow meters look like ?

Exactly right.

The knob at the bottom is a needle valve. Turned fully clockwise it cuts off the flow. I haven't counted but it probably has 20 or more turns counterclockwise to fully open. You could probably use the needle valve as a "good enough" flow controller. I haven't tested this, but I could if anyone wants me to.

Just above the knob you can see a little blob. That's the flow indicator, in the rest position. It's trapped in a vertical tapered cavity in the perspex block. As the flow rate increases, the flow pushes it up the cavity until enough air leaks around it and it reaches equilibrium. You then read off the flow rate from the scale printed on the front of the block.

[Terry McGee]

Backpressure: my thinking now is that windway area will be the primary driver. Yes, windway length + taper will contribute, but my hunch (side-bets later!) is that they will be small. As a player, backpressure is a *huge* factor in whistle playability.

Indeed, I look forward to testing the backpressure of other whistles I have. One imagines one could rule a line at Minimum backpressure (below which it's hard to not overblow), and Maximum backpressure (above which it's hard to achieve and sustain). A good controllable whistle would lie between those lines. But is it quite that simple?

Sound: I'm interested in both volume + timbre. Volume is easy. Honestly, with the approach used in all this testing, you could devise a power-rating for any whistle : [energy-out (dBa)]/[energy-in (watts)] . My ears tell me there are *vast* differences !

So we're getting into efficiency here (energy out vs energy in). But we're also getting into being able to measure sound levels accurately, which gets us into acoustic treatment of the listening space.

Timbre is harder. Have to look at PSDs + head designs (protrusions, chamfers, etc..). One thing I learned from a very flute-like whistle: all those freggin' high harmonics matter !

Indeed, and again we are getting into the need for acoustic treatment. Now what's your acronym PSD? Not "Phase Sensitive Detector" I imagine?

[stringbed]

I can predict your height from the length of your shadow if I know the angle of the sun. Predicting your height from your weight is possible, but much less certain.

You cannot know how accurate the more reliable of those predicted values is, or the magnitude of the discrepancy between them, without comparing them with my height as measured directly. Since the latter quantity can easily be determined it is pointless to use a predicted or derived value in its stead.

[david_h]

. . . ditch the manometer . . . ditch the flow meters . . .

My vote is that both are used. More data + info for modelers.

Each gives a "view" into the "head-flow" process, which, after all, is a little fuzzy at this point. Two blurry lenses are better than one.

Yes, but consider all the extra work needed to take and record that info, if it really is just repeating the flow info in a different form.

Indeed, I look forward to testing the backpressure of other whistles I have.

Am reading with interest, but I must be missing something. Doesn't the relationship between pressure and flow (e.g. the constant in Bernoulli's equation) vary with overall windway geometry as well as final exit area? Unless we are only interested in (and wanting to model) Terry's Feadog don't you have to measure both pressure and flow? Consider the extra work needed to do it all again.

[Tunborough]

Doesn't the relationship between pressure and flow (e.g. the constant in Bernoulli's equation) vary with overall windway geometry as well as final exit area? Unless we are only interested in (and wanting to model) Terry's Feadog don't you have to measure both pressure and flow?

Yes, but if we can find a formula that incorporates the windway geometry, then we just have to measure the windway geometry to know what the relationship will be. And with a careful statement of the problem, and some algebra, I think I have that formula...

Let h be the height of the windway exit in mm,
w be the width of the windway exit in mm,
L be the length of the windway (the windway, not the whole whistle) in mm,
rho be the density of air in kg/m^3,
Q be the air flow in L/min,
P be the mouth pressure in mm H2O.

Assuming the cross-sectional area of the mouth is quite a bit larger than that of the windway exit (there's a more elaborate definition if it isn't):

Let K = 1 + fd * L * (h + w)/(2 * h * w)

The first term is from Bernoulli, the second is from Darcy-Weisbach. fd is the Darcy friction factor. This is a bitch to calculate, but it turns out to be close enough to 0.04 for pretty much everything we're interested in.

If we know the flow rate, we can calculate the air speed in m/s as:

v = Q / (0.060 * h * w)

(The 0.060 is to convert from L/min to mL/sec.)

If we know the mouth pressure, we can calculate the air speed in m/s as:

v = sqrt(2 * 9.807 * P / (rho * K))

(The 9.807 is to convert from mm H20 to Pascals.)

For Terry's measurements on the Feadog Mk 1, those two formulas agree within 0.5%. An interesting aspect of the second formula is it is much less sensitive to measuring errors in h.

My thanks to Terry and to stringbed for their contributions in getting here.

Now we need measurements on a couple of other whistles, preferably with very different windway geometries.

[david_h]

Yes, but if we can find a formula that incorporates the windway geometry, then we just have to measure the windway geometry to know what the relationship will be. And with a careful statement of the problem, and some algebra, I think I have that formula...

I don't see how that formula covers Terry's qualitative observations of tapered windways in this post: https://forums.chiffandfipple.com/viewt ... 7#p1258847 I had thought, from the numerous discussions on this forum, that a wider or higher windway entrance was one way that makers reduced the required blowing pressure for the same length windway.

I guess it would only need one set of measurement over the pressure-flow range for each windway.

[Terry McGee]

So, we can now work out a Resistance figure for any of the whistles we've measure Flow and Pressure for, eg the three I gave data for before. I'll add my suggested Resistance figure to each here, based on Resistance = SqRt(Pressure)/Flow:

(Note that I had measured these at the 30L/Min flow rate to avoid repainting the lab ceiling with the manometer liquid with the Killarney!)

Killarney: 340mm H20, Resistance = 0.615
Tweaked Mellow D: 170mm H20, Resistance = 0.435
Feadog Mk 1: 134mm H20, Resistance = 0.388
and adding the 1/2" bore whistle I made recently, Resistance = 0.408

So, note the bottom three are all withing a few percent of each other, but the Killarney is about 50% higher.

Given a known Resistance figure, we can easily calculate Pressure if we know Flow from Pressure = (Resistance x Flow)^2,
Or given the Pressure, we can find Flow = SqRt(Pressure)/Resistance.

Seem plausible?

(Note I've given figures to three decimal places, which is a bit laughable when you remember I'm reading off a manometer rule (and then doubling it) and a floating bead flow meter!)

It would be interesting to add calculated values for these resistances....