Why do I run out of breath when playing the flute?
You could simply not be breathing correctly, or deeply enough. That is something about learning the flute that people don't think about most of the time. It does take a LOT of air to produce the sounds you want.
How do flutists breathe?
SIMULTANEOUSLY, the flutist plays for a very short time by squeezing the air out of the mouth and the cheek (and sometimes tongue) muscles AND inhales a small bit of air through the nose. The back of the tongue returns to the normal position, restoring airflow from the lungs to the flute.