A fully loaded Boeing air craft has a mass of \(3.3 \times 10^5 \mathrm{~kg}\). Its total wing area is \(500…
A fully loaded Boeing air craft has a mass of \(3.3 \times 10^5 \mathrm{~kg}\). Its total wing area is \(500 \mathrm{~m}^2\). It is in level flight with a speed of \(960 \mathrm{~km} / \mathrm{h}\). Estimate the pressure difference between the lower and upper surfaces of the wings.
\(4.5 \times 10^3 \mathrm{Nm}^{-2}\)
\(5.5 \times 10^3 \mathrm{Nm}^{-2}\)
\(6.5 \times 10^3 \mathrm{Nm}^{-2}\)
\(7.5 \times 10^3 \mathrm{Nm}^{-2}\)
Solution
Mass of boeing air craft,
\(M=3.3 \times 10^5 \mathrm{~kg}\)
Wing's area, \(A=500 \mathrm{~m}^2\)
The weight of boeing aircraft is balanced by upward force due to the pressure difference.
Hence, \(\Delta p \times A=m g\)
\(\begin{aligned}
\Rightarrow \quad \Delta p & =\frac{m g}{A}=\frac{3.3 \times 10^5 \times 9.8}{500} \\
& =6.47 \times 10^3 \mathrm{~N} / \mathrm{m}^2 \simeq 6.5 \times 10^3 \mathrm{~N} / \mathrm{m}^2
\end{aligned}\)