Some fellow flutists and I are pretending to be experts at fluid dynamics and reading Patricio Cuadra's thesis on the topic:
On page 17, it says:
The central speed of the jet $U_j$ at the channel exit can be estimated assuming atmospheric pressure outside the channel and using Bernoulli’s equation:
$$U_j = \sqrt{ \displaystyle\frac{2P_f}{\rho_1} }$$
Where $P_f$ = pressure in the cavity before the channel, and $\rho_1$ = gas density
Our question, why does this omit the channel size, how big the lip-hole is, which intuitively seems to have a large affect on speed (e.g. a hose with the nozzle half open vs. open).
What is "central velocity"? Is it what we are thinking of when we say, "jet velocity"?
Or maybe the key phrase is "at the channel exit" (e.g. after the constraints of the channel size no longer apply?)