Consider a Pitot static tube mounted on the nose of an experimental airplane. A Pitot tube measures the total pressure at the tip of the probe (hence, sometimes called the Pitot pressure), and a Pitot static tube combines this with a simultaneous measurement of the free-stream static pressure. The Pitot and free-stream static measurements are given below for three different flight conditions. Calculate the free-stream Mach number at which the airplane is flying for each of the three different conditions:

a. Pitot pressure \(=1.22 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\), static pressure \(=1.01 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\)

b. Pitot pressure \(=7222 \mathrm{lb} / \mathrm{ft}^{2}\), static pressure \(=2116 \mathrm{lb} / \mathrm{ft}^{2}\)

c. Pitot pressure \(=13107 \mathrm{lb} / \mathrm{ft}^{2}\), static pressure \(=1020 \mathrm{lb} / \mathrm{ft}^{2}\)