The diaphragm is a muscle at the base of your rib cage, essentially underneath your lungs. To play the flute with full, clear tone, you need to use this muscle effectively.
With a full breath, your lungs will expand in such a way that your diaphragm expands downward, causing your abdominal area to expand. Your rib cage will normally expand somewhat while breathing, but many people have been culturally conditioned to take a breath with only the chest and shoulder area expanding, which inhibits power in flute playing. Essentially, there’s no muscle power to support your playing.
For flutist, vocalists, other wind players, speakers, etc, we need to not only allow the air to also expand the diaphragm downward, we need to take advantage of the diaphragm’s power. When you take a breath, imagine that you’re a glass, filling from the bottom up. This is sometimes easiest to feel if you first empty out any existing air, then just allow the vacuum created to refill. You can also get the feeling of where you want the air to go by lying on your back (effectively immobilizing the upper ribs/chest area) – the air will have no choice but to go lower down.
Place your hands on your waist, just high enough to feel the base of your rib cage. Take a full breath (from the bottom of the glass up – feel it start way down in your lower abdomen and work it’s way up – then feel your lower ribs expand. For now, try to keep your shoulders and upper rib cage pretty much out of the picture – very little movement there, if any. (In the long run, you’ll have times you want to fill up as much as possible for long stretches without a breath, but for learning to use the diaphragm as a power source right now, keep the expansion mostly in the belly area into the lower rib cage). Take a few breaths to get the feeling.
Now, put your fingers in your upper abdomen – feel just below the place where your ribs come together in an upside-down V. Take a full belly-breath as described above. Then try saying one or more of the following as emphatically as you can: “hissssssssss” or “HoHoHo” – yes the big fat Santa Claus variety, no small elves here; or perhaps try to bark like a dog. Feel your diaphragm engage – in the spot described above – with these sounds. If you don’t feel a pronounced movement and hardening of your diaphragm muscle you’re probably either not quite putting your hand in the right spot, or you need to enunciate your “H” more strongly, hiss with more air behind it, or something along those lines, so give it another go. Or try to get a genuine belly laugh going – this really gives your diaphragm a work-out!
Once you’ve got the feel of breathing in to the diaphragm area, a good exercise is to practice scales or your music with diaphragm starts: First, identify a small section of music you’d like to work on – maybe just a few notes, or even just a single note, or perhaps a whole scale, a phrase, etc. Then begin each note in that section with no tongue – just a strong “hoo” breath start – with awareness of the muscle you used in the “hisssss” or “hohoho.” Once you’re able to play the note(s) strongly and clearly, noticing a clean beginning and full middle of the note, then (and only then) add the tongue back in. Be aware to keep the power that you had in the breath start, and just add a bit more definition to the beginning of the note with your tongue. This should not substantially change the quality of the sound. It should just lend a small bit of extra clarity to the beginning of the note.
The following YouTube videos might be helpful to further your understanding of the use of the diaphragm:
Voice Lessons – “Diaphragm Breathing” (3:43) (start 30 seconds in)