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68) The Pitot tube is commonly used to measure the air speed of an aircraft. Air flows into a small opening at the end of a tube that is closed at the other end, bringing the air to rest and allowing the measurement of the pressure difference between air at rest inside the tube and air moving rapidly just outside the tube. If the high-altitude air density is 0.364 kg/m3, and the pressure difference between inside and outside the tube is 9460 Pa, what is the airplane’s speed relative to the air?

Respuesta :

ANSWER:

224.32 m/s

STEP-BY-STEP EXPLANATION:

We can use Bernoilli's theorem:

[tex]P_1+\frac{1}{2}\rho(V_1)^2=P_2+\frac{1}{2}\rho(V_2)^2[/tex]

We replace and solve for V2, like this:

[tex]\begin{gathered} P_1-P_2=\frac{1}{2}\rho(V_2)^2-\frac{1}{2}\rho(V_1)^2 \\ 9460=\frac{1}{2}\cdot0.376\cdot(V_2)^2-\frac{1}{2}\cdot0.376\cdot(0)^2 \\ 9460=\frac{1}{2}\cdot0.376\cdot(V_2)^2 \\ (V_2)^2=50319 \\ V_2=\sqrt[]{50319}=224.32\text{ m/s} \end{gathered}[/tex]

The airplane’s speed relative to the air is 224.32 m/s

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