Question

A pitot tube, mounted on an airplane flying at 8000 m standard altitude, reads a stagnation pressure of 52.2 kPa. Estimate (a) the velocity in mi/h and (b) the Mach number.

Answer 1

Answer:

$524.31\ \text{mi/h}$

$0.761$

Explanation:

$p_0$ = Stagnation pressure = 52.2 kPa

$p$ = Atmospheric pressure at 8000 m = 35.581 kPa (from chart)

M = Mach number

$v_s$ = Velocity of sound at 8000 m = 308 m/s

v = Velocity of airplane

We have the following equation

$\dfrac{p_0}{p}=(1+0.2M^2)^{3.5}\\\Rightarrow M=\sqrt{\dfrac{1}{0.2}[(\dfrac{p_0}{p})^{\frac{1}{3.5}}-1]}\\\Rightarrow M=\sqrt{\dfrac{1}{0.2}[(\dfrac{52.2}{35.581})^{\frac{1}{3.5}}-1]}\\\Rightarrow M=0.761$

Mach number is given by

$M=\dfrac{v}{v_s}\\\Rightarrow v=Mv_s\\\Rightarrow v=0.761\times 308\\\Rightarrow v=234.388\ \text{m/s}\times \dfrac{3600}{1609.34}=524.31\ \text{mi/h}$

The velocity of the airplance is $524.31\ \text{mi/h}$ and has a mach number of $0.761$.