Answer to Question #237509 in Molecular Physics | Thermodynamics for Unknown346307

Question

The pressure leads from Pitot-static tube mounted on an aircraft were

connected to a pressure gauge in the cockpit. The dial of the pressure gauge is calibrated to read

the aircraft speed in m/s. The calibration is done on the ground by applying a known pressure

across the gauge and calculating the equivalent velocity using incompressible Bernoulli’s equa￾tion and assuming that the density is 1.224 kg/m3.

The gauge having been calibrated in this way the aircraft is flown at 9200 m, where the

density is 0.454 kg/m3 and ambient pressure is 30 kN/m2. The gauge indicates a velocity of

152 m/s. What is the true speed of the aircraft ?

Answer 1

$p+\frac{\rho v^2}2=const,$

$v_s=v_0\sqrt{\frac{\rho_0}{\rho_s}}=249.57~\frac ms,$

$c_0=\sqrt{\gamma\frac{p_0}{\rho_0}}=304.16~\frac ms,$

$M=\frac{v_0}{c_0}=0.82,$

$cf=1+\frac{M^2}4=1.168,$

$v=\frac{v_s}{\sqrt{cf}}=230.9~\frac ms.$