Question

A pitot tube on a high altitude aircraft measures a differential pressure of 180 Pa. What is the aircraft's airspeed if the density of the air is $0.031kg/{{m}^{3}}$?

Answer 1

Hint:As a very first step, one could read the question well and hence note down the given values. Then one could directly recall the expression for airspeed or maybe derive the same from Bernoulli’s equation and then carry out the substitutions accordingly to find the answer.

Formula used:
Airspeed,
$v=\sqrt{\dfrac{2\Delta P}{\rho }}$

Complete step-by-step solution:
In the question, we are given that a pitot tube on certain high altitude aircraft measures a differential pressure of 180 Pa. We are supposed to find the aircraft’s airspeed when the air density is found to be $0.031kg/{{m}^{3}}$.
One should know that the indicated airspeed would be the airspeed reading that the pilot would see on her airspeed indicator and this is driven by a pitot-static system.
This system basically works on the principle of Bernoulli’s equation which says,
${{P}_{static}}+{{P}_{dynamic}}={{P}_{total}}$
Since, change in height along the streamline is negligible, $\rho gh$could excluded to get,
$\Rightarrow {{P}_{static}}+\dfrac{1}{2}\rho {{v}^{2}}={{P}_{total}}$
Therefore, airspeed could be calculated from the following expression,
$v=\sqrt{\dfrac{2\Delta P}{\rho }}$
Substituting the given values,
$v=\sqrt{\dfrac{2\left( 180Pa \right)}{0.031kg/{{m}^{3}}}}$
$\therefore v=1.1\times {{10}^{2}}m/s$
Therefore, we found the airspeed of the given aircraft to be $v=1.1\times {{10}^{2}}m/s$.

Note: The pitot static system basically uses the difference between the total pressure and the static pressure in order to determine the dynamic pressure which is then converted into airspeed reading. The total pressure or the pitot pressure or the stagnation pressure is measured by the pitot probe.