Question

A Pitot-static probe is used to measure the speed of an aircraft flying at 3000 m. If the differential pressure reading is 3300 N/m2, determine the speed of the aircraft in m/s. The density of air at an altitude of 3000 m is 0.909 kg/m3
The speed of the aircraft is ____ km/h.

Answer 1

Answer:

   v = 306.76 Km/h

Explanation:

given,

height of the aircraft = 3000 m

differential pressure reading = 3300 N/m²

density of air = 0.909 Kg/m³

speed of aircraft = ?

Assuming the air flowing above air craft is in-compressible, irrotational and steady so, we can use Bernoulli's equation to solve the problem.

using Bernoulli's equation

          $\dfrac{v^2}{2} = \dfrac{\Delta P}{\rho}$

where ρ is the density of the air at 3000 m

          $v= \sqrt{\dfrac{2 \times \Delta P}{\rho}}$

          $v= \sqrt{\dfrac{2 \times 3300}{0.909}}$

          $v = \sqrt{7260.726}$

                 v = 85.21 m/s

          $v= 85.21 \times \dfrac{3600}{1000}$

                 v = 306.76 Km/h