As a fuel saving measure, commercial jets cruise at an altitude of about 10 km. While cruising at an altitude of 10 km, a small leak occurs in one of the window seals in the passenger compartment of an Airbus. Within the passenger compartment, the pressure and temperature are, respectively, 1.05 atm and 20°C and the pressure outside the craft is 0.274 atm. Model the air as an ideal fluid to find the speed (in m/s) of the stream of air flowing through the leak. (Assume the density of air to be 1.20 kg/m3.)

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valetta valetta · Answer 1 · 2019-08-06T09:15:38+02:00

Answer:

[tex]v_o[/tex] = 357.26 m/s

Explanation:

Given:

first convert both pressures to pascals

Outside pressure = 0.294 atm = 0.294 × 101300 = 29782.2 Pascals

Inside pressure = 1.05 atm = 1.05 × 101300 = 106365 Pascals

Now, using the Bernoulli's equation

, we have

[tex]P_i + \frac{1}{2} \rho v_i^2=P_o + \frac{1}{2} \rho v_o^2[/tex]

where

P is the pressure

v is the velocity

ρ is the density

i denotes the inside

o denotes the outside

the speed inside is approximately zero,thus

[tex]106365 + \frac{1}{2} \times1.20\times 0^2=29782.2 + \frac{1}{2} \times1.20\times v_o^2[/tex]

[tex]76582.8=\frac{1}{2} \times1.20\times v_o^2[/tex]

or

[tex]v_o[/tex] = 357.26 m/s