Question

Consider the Bell X-2 research aircraft, which was the first aircraft to achieve Mach 3 on September 27th , 1956. During this flight, the aircraft reached a velocity of 936 m/s at an altitude of 65,500 ft. Calculate the actual Mach number that the X-2 achieved during this flight. Now, consider two other conditions. Condition #1: Assuming the aircraft travels at the same velocity in Jupiter’s atmosphere at an altitude where the temperature is -145 °C. Also, assume that the atmosphere of Jupiter is made up of entirely hydrogen gas (H2) which has a molecular weight of 2.016 g/mol. Calculate the Mach number of the X-2 on Jupiter. Condition #2: Assuming the aircraft travels at the same velocity in Pluto’s atmosphere at an altitude where the temperature is -223 °C. Also, assume that the atmosphere of Pluto’s is made up of entirely nitrogen gas (N2) which has a molecular weight of 28.013 g/mol. Calculate the Mach number of the X-2 on Pluto.

Answer 1

Step-by-step explanation:

mach number is ratio of speed with respect to speed of sound .

speed of aircraft = 936 m /s

speed of sound at 65500 ft = 295 m /s

mach number = 936 / 295 = 3.17

velocity of sound at - 145 degree and in hydrogen gas .

velocity of sound

`V=\sqrt{(RT)/(M) }`

`V=\sqrt{(8.3*(273-145))/(2*10^(-3)) }`

= 729 m /s

mach number

= 936 / 729 = 1.28

velocity of sound at - 223 degree and in nitrogen gas .

velocity of sound

`V=\sqrt{(RT)/(M) }`

`V=\sqrt{(8.3*(273-223))/(28.013*10^(-3)) }`

= 122 m /s

mach number

= 936 / 122 = 7.67