Question #238128

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


1
Expert's answer
2021-09-17T09:31:16-0400

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


PtP=(1+γ12M2)γγ1\frac{P_{t}}{P}=(1+\frac{\gamma-1}{2}M^2)^{\frac{\gamma}{\gamma-1}};


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


(1+0.2M2)3.5=1.869(1+0.2M^2)^{3.5}=1.869;


Now we could extract the Mach number M:


M=5(1.869271)=0.989M=\sqrt{5\cdot(1.869^{\frac{2}{7}}-1)}=0.989;


Finally, we could calculate the velocity of the aircraft:


v=Mc=0.989343ms1=339ms1v=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.


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