When playing the flute, does lip-hole aperture size affect air pressure in the mouth?

Question

I apologize if this is too basic of a question for this forum, but when having arm-chair discussions about the fluid dynamics of flute playing, a friend has said:

The lip-hole area together with the lung pressure is the cause of the pressure built in the mouth.

When measuring the mouth pressure you are already taking into account the lip-hole area and the lungs pressure.

My intuition is that this is incorrect--mouth pressure is caused by the "upstream" pressure in the lungs, and not any "downstream" container/flow size changes.

But intuition is often wrong in these situations--can anyone clarify the situation for us?

Answer 1

Unless the air moving through the lips goes sonic, the downstream does influence the pressure in the chamber.

So long as the fluid, any fluid, is moving less than the speed of sound, the downstream influences the upstream because pressure waves can move against the flow direction.

The smaller the opening in your lips, the higher the pressure in your mouth (and the harder you have to push with your lungs to make the air leave). This is a simple test to validate -- make a tiny opening with your lips and push as hard as you can. You'll notice your cheeks have to work hard to hold the air in your mouth and you have to push quite hard. Open your mouth all the way and repeat, you'll notice the pressure in your mouth is much lower and you don't have to push as hard.

Answer 2

Downstream effects can certainly affect what happens upstream. A good analogy is a traffic jam. Suppose a busy highway which starts with four lanes, going to three some kilometers down. The traffic jam (increased pressures), will occur upstream of the narrowing. For fluid flow, you have the same arguments, but less intuitive.