Question A$3$: A pitot$-$static tube is introduced in a supersonic flow. Determine the speed of the flowing $($free$)$ stream if the tube reads a stagnation pressure of $130$ kPa $,$ a static pressure of $110$ kPa and a static temperature of $519$ K $($in the proximity of the tube$),$ for: $($a$)$ the gas is air $(R=287\frac{J}{k}g-K,=1\mathrm{.}4)$; $($b$)$ the gas is Helium $(R=2077\frac{J}{k}g-K,=\frac{5}{3}.$