Question

As an aircraft flies 500 miles, from a region of higher pressure into a region of lower pressure, with the aircraft’s pressure altimeter indicating a constant altitude of 700 feet, is the aircraft’s ACTUAL altitude changing? If so, is it gaining or losing altitude? Explain your answer. (Assume constant temperature air and no corrections made to the altimeter along the flight path.)

Answer 1

Answer:

Aircraft is losing altitude

Explanation:

$\rho$ = Density of air

P = Pressure

g = Acceleration due to gravity = 9.81 m/s²

h = Altitude

1 denotes initial

2 denotes final

From Bernoulli's theorem we have

$P_1+\dfrac{1}{2}\rho v^2+\rho gh_1=P_2+\dfrac{1}{2}\rho v^2+\rho gh_2$

Velocity v is constant

$P_1+\rho gh_1=P_2+\rho gh_2\\\Rightarrow P_1-P_2=\rho gh_2-\rho gh_1$

From the question

$P_2>P_1$

so in the equation

$h_1>h_2$

So, the aircraft is losing altitude