You can’t beat a good reaming! 
There’s a whole genre of machine shop chat-up lines, I’m sure.
I’m an engineering lecturer, so mechanical jokes are quite familiar. But this takes some beating. My female colleague was lecturing on machine elements (nuts, bolts, etc) and wanted some class participation.
“So, how much do you think a washer costs?” she asks. The students mumble some guesses. She carries on enthusiastically: “Ok, and how much for a screw?” 
Thanks very much for these pictures and for your brief discussion of the embouchure hole. I am currently getting ready to start a flute using 3/4" CPVC. It will also have a CPVC lip plate. The holdup is finding correct info on the embouchure hole. I have heard it should be bored just above the axis of the pipe and at an angle so that the blown edge of the hole is an angle of approximtely 45 degrees. Yours appears to be at the center of the pipe and heading straight down. Is this correct?
I hope this newbie hasn’t hijacked this thread too far, but I would appreciate your comment.
Thanks.
RVC
I just wrestled with this same issue reworking an antique flute. In my case the hole was already drilled, and the question was how to under cut it slowly so I could try it as I went. Jon recommenced sandpaper on a 1/4 in dowel so I contact cemented some sandpaper to a dowel and chucked it in my drill press. I could then sand the embouchure from straight sided to more and more undercut and/or shape the hole as I went, keeping the sides straight (meaning not curved going in.)
Additional advice from Terry was to undercut all the way around the same amount. Which I did. And it came out quite nice. I recommend this approach.
That said, my first embouchure in a PVC flute was straight sided and round and made acceptable sound. But undercutting it per above did make it better.
PS - There is a Flutemaker’s Yahoo group where you can search the archives and find out a lot about this. http://launch.groups.yahoo.com/group/flutemakers/
Thanks, Carey. So apparently the 45 degree blown edge is not a factor. I appreciate the tip on undercutting. Thanks also for the link to the Flutemakers forum. I am aware of it and have spent some time searching through the messages there but was not aware they had an archive. The search continues.
Maybe the best thing to do is just make one and go from there. CPVC is not that expensive.
Thanks again.
RVC
Yeah, that’s pretty much always true. The sound production of whistles and flutes is real non-linear, bordering on chaotic. You can have a pretty good idea what you want to do but until you actually do it, don’t bet on the results. Holes too, to a lesser degree. Some of the stuff that really matters is very hard to measure, at least to the degree that matters, so eye it up, start on one side of where you want to be and sneak up on the right value.
It’s all good tho.
Amen to that!
Not just “bordering on” tho → turbulence phemomena are classic “chaos” math. By definition - anything that is capable of period 3 is chaotic. as you increase the air pressure - the frequency can go from the fundamental (1st octave) to the 1st harmonic (octave) to the second harmonic (Octave + 5) to the third harmonic (2 octaves) and beyond. In between each transition are a series of other notes expressing both higher harmonics and silence - all classic chaos graphs contain this stuff - including the “ghost-notes”.
The boundaries of chaotic systems are where all the magic happens - people are chaos detectors - we thrive in it. I pitty the whistle that has no chiff (or the person who plays it 
)
Sorry for slow response - others have at least partially answered your query before I could. Your general observation is correct - the embouchure holes on the school piccolos are drilled vertically or near as dammit and on the centre line of the bore, though not on the same centre line as the tone holes as these are one-piece instruments so one cannot adjust the embouchure angle - the embouchure centre line is about 2-3mm back from that of the tone holes. I do try to give a very slight angle to the embouchure drilling to achieve a small undercut on the working edge, but only slight, and it really doesn’t matter. 45 degrees would be FAR too much in any case, and on such small tubing (16mm OD) virtually impossible anyway! No properly made embouchure is undercut by more than about 15 degrees.
I opted for speed and ease of manufacture with a class of children doing their own - to keep things very simple. If I was making these to sell, as I may do, I would probably give the extra time to filing the embouchure out to an ellipse and undercutting it - not difficult or very time-consuming. Far easier than trying to drill at an angle on a curved surface too! I’d recommend drilling a 9mm vertical hole, then filing out by about 1mm each side along the long axis and 0.5mm on the near and working edges, with a moderate undercut all around, though less at the up- and down-tube sides. It will be far more responsive and richer sounding thus. Sand paper and then fine wet-&-dry wrapped around 6mm dowel (no need to glue it on unless you want to use it on a power drill as Carey suggests - it wears out too fast to bother - just cut a small rectangle of abrasive paper and roll it around the dowel and hold it on with your fingers) will do if you don’t have engineering files, but you can pick up sets of those quite cheaply - use the round and half-round ones and then finish with abrasive paper on dowel. A piece of 9mm dowel is useful for the late stages on larger flutes.
Best of luck!
BTW, if you make a tuneable flute with a separate head-joint, if you screw up the embouchure, you don’t have to remake the whole darn thing…ditto with getting the tone-holes right on the body - so well worth working out how to do a simple tuning slide if your PVC tube is malleable when heated. And, I strongly recommend making a Tipple-Fajardo wedge for the head as no matter how much you fiddle, acceptable tuning between the 1st & 2nd 8ves of an all-cylinder flute just IS NOT POSSIBLE without some kind of bore correction. Save yourself the heartache and dissatisfaction!
Thanks very much, gentlemen, for your responses. They are quite enlightening and helpful, and most appreciated.
I have been under the impression that an undercut was a slight rounding or chamfer of the drilled edge on the inside of the pipe. Your comments indicate that it is more of a straight line from the outer edge of the hole. Is this correct? For my own education, in AutoCAD I drew a piece of 3/4" CPVC (0.695" ID, 0.875" OD) with a 0.090" lip plate and a 10mm hole through the center. The angle between the drilled edge and the outside edge of the pipe at the tangent came out to a little more than 71 degrees. So you’re right - that is considerably more than 45 degrees.
Great info here! Will do.
Yes. One of the good things about the 3/4" CPVC is there are copper couplers with an inside diamter just the right size for an interferance fit. My first attempt will be with a single tube the correct length (more or less, per Flutomat) for low D with the intent of actually making a sound with it. From there I’ll go to the tuning slide approach.
My main problem in all this is I have never played a flute and I cannot afford to buy one. Hence my desire and research toward getting everything as close as possible before I begin. Fortunately I know folk locally who do play and can tell me if I’m headed in the right direction.
Thanks again for your help.
It is most appreciated.
RVC
Sorry to you whistle only guys that this thread is being flute-jacked for now…
Ahhhh, I see - we’re talking at crossed purposes…
to do with familiarity with jargon usages…
References to the angle of the undercut (or the converse if the “funnel” profile of the embouchure is inverted - expanding outwards - as is very occasionally seen on cheaply made old flutes, but which has no technical name I know of…) of a flute embouchure are made with reference to deviation from the straight sides (which are of course parallel with each other) of a plain-drilled hole with it’s centreline being perpendicular to the long axis of the bore. The angle of the walls of the embouchure hole with the surface of the tube or the lip-plate is not relevant here, and though it may be significant to tone production is much less discussed and fussed about. “Undercut” is the inwards expansion of a hole through the thickness of the tube wall towards the bore. As Carey implies, it is desirable that the walls of the hole be a straight line (or “flat”) from outer to inner edge (across the tube-wall thickness), not vertically convex, though it is also desirable to have some rounding of the bottom “corner” at the junction with the bore as you describe for smoothness of airflow/reduction of turbulence and impedance (which, it should now be obvious, is not really what is meant by “undercut”). One usually ever-so-slightly takes the sharpness of a fresh cut off the outer edge also, especially on the near side, for reasons of lip comfort.
It may help to envisage the embouchure hole as being a lateral segment of a steep-sided elliptical conoid with its apex somewhere outside the flute tube. In high grade instruments, especially modern Boehm instruments, the angle of undercut is not uniform all around, but is less on the near side than on the far, playing side, while the side walls are near enough vertical. Boehm himself did empirical experiments to try to determine the optimums and there are diagrams in his Treatise. He advocated an undercut angle of 7 degrees, but Miller comments that examination of flutes produced by him actually mostly don’t bear it out as they are mostly near-enough parallel sided and perpendicular.
Thank you one more time for the information. As last time, it is very helpful.
We now return control of this thread to the whistle folk, of which I am one, to a minor degree.
RVC
Good luck! You will never be able to stop making them now, of course - I have been hooked since the first one I made! And you will look at all tubing with a very different eye!
Lesley
Great to see you back here devondancer!
Feadoggie
Yes, I fear the worst. I can’t go to Lowe’s without stopping by the PVC section, and I’m already aquiring quite a collection of it. At least it’s cheap.
Thanks for your note.
RVC
Question: would it be possible to make an E whistle using the materials I already have or would I need pvc pipe with a narrower bore?
I think you can make one from the same material. You said it has a 10.5mm inside diameter, right? Use your favorite calculator to determine the sounding length of the E whistle. Then do a length to bore ratio calculation. Just divide the length by the bore diameter. You want the ratio to be between 20 and 30. 25 would be a happy medium. My guess is that you’ll be around 26-27.
Feadoggie
Actually no, I was sick and confused at the time. The inside diameter is 13mm, nothing else 
Oops, I misread the calipers too!
13mm is a tad on the large side. Try it though. I would start with a smallish voicing window though.
Feadoggie