Answer
given,
local velocity missile,v = 3000 ft/s
1 ft/s = 0.3048 m/s
3000 ft/s = 914.4 m/s
Temperature, T= 500°R
1°R = 0.5556 K
500°R = 277.8 K
now,
Sonic velocity calculation
[tex]c = \sqrt{\gamma RT}[/tex]
γ is adiabatic constant for air = 1.4
R is the gas constant = 287.14 J.kg/K
now,
[tex]c =\sqrt{1.4\times 287.14\times 277.8}[/tex]
c = 334.17 m/s
Mach no. =[tex]\dfrac{v}{c}[/tex]
M=[tex]\dfrac{914.4}{334.17}[/tex]
M= 2.74
Now, Relation between Characteristic Mach number M* and mach number M is given by.
[tex]M^2 = \dfrac{2}{\dfrac{\gamma + 1}{M*^2}-{\gamma-1}}[/tex]
[tex]2.74^2 = \dfrac{2}{\dfrac{1.4 + 1}{M*^2}-{1.4-1}}[/tex]
[tex]\dfrac{1.4 + 1}{M*^2} = 0.6664[/tex]
[tex]M*^2 =\dfrac{2.4}{0.6664}[/tex]
M* = 1.89
Hence, the characteristics Mach number is equal to 1.89.
