Punctured aorta! $(2$ pt$).$ During open$-$heart surgery, a surgeon accidentally tears a circular hole $(2$ mm diameter$)$ in the aorta. The speed of blood flow in the aorta is about $0\mathrm{.}33\frac{m}{s},$ at a pressure of roughly $100$ torr above atmospheric pressure.

$($a$)$ If that blood squirts straight up into the air, how high will it squirt? $($Hint: You can't use the continuity equation because not all of the blood from the aorta comes out of the hole $-$ thankfully!$)$

$($b$)$ If we had assumed the blood in the aorta were static, would this affect the result?