Flutists are an airy bunch: we lose more of the air we put out than other wind instruments. Other wind players blow into their instruments, but we create our notes by bouncing the air across an into the instrument. In fact, part of the skill of playing flute is to direct the air into it as well as across the hole.
As a flutist air capacity has been one of my problems from the very beginning. My teacher would stand there and say "more air, out more air into it!" and I would push,but there was nothing to work with. I have improved, but putting enough air behind a note is still an issue. I am forever running out of air in the middle of a phrase.
My teacher has a new exercise for me: pick an easy note, play it very softly, for as long as you can, until the air is fully exhausted from your lungs...goal: 1 minute. Sounded easy until I tried it. I thought I was blowing for at least 30 seconds....nope. Only 17. Sigh.
I just had a partial knee replacement (second knee, now both are fixed!), and part of my time in the hospital was breathing into a bottle. The bottle is called an "incentive spirometer." It's purpose is to expand and oxygenate your lungs. Your goal with this little tool is to breathe in through the tube and keep the markers in the right place. It is surprising how difficult it is! I thought I had good deep breathing technique, but not so good as I thought. As I used this tool, I also focused on making a flute embouchure and blowing the air out as long as possible.
I haven't picked up the flute since my surgery, and all my breathing in the bottle (10 breaths very hour!) but I am eager to see if it is any better.
There are other ways to work on air, so check back to see what I come up with!