Answer to Question #238128 in Molecular Physics | Thermodynamics for Unknown346307

Question

In aircraft flying at an altitude where the pressure was 35 kPa and

temperature – 38°C, stagnation pressure measured was 65.4 kPa. Calculate the speed of the

aircraft. Take molecular weight of air as 28

Answer 1

The relation between a stagnation pressure and static pressure is the following:

$\frac{P_{t}}{P}=(1+\frac{\gamma-1}{2}M^2)^{\frac{\gamma}{\gamma-1}}$;

Using the given data and the air $\gamma$ coefficient we could rewrite the equation as:

$(1+0.2M^2)^{3.5}=1.869$;

Now we could extract the Mach number M:

$M=\sqrt{5\cdot(1.869^{\frac{2}{7}}-1)}=0.989$;

Finally, we could calculate the velocity of the aircraft:

$v=M\cdot c=0.989\cdot 343 m\cdot s^{-1}=339 m\cdot s^{-1}$;

Thus, the aircraft is flying at 339 meters per second.