Linearly elastic balloon discharge
= Linearly elastic balloon discharge
{title2=$\Omega^2=K\pi a^2/(\rho L)$}
An inviscid uniform tube plug driven by entrance excess pressure $KV$ obeys $\rho L\dot u=KV$ and $\dot V=-\pi a^2u$. From rest, the first zero of $V$ occurs after a quarter harmonic period, independent of its initial volume. The maximum speed is proportional to that initial volume. Entrance losses, a reservoir kinetic head or independently prescribed initial flow change this ideal model.