A fully loaded Boeing aircraft has a mass of $5.4 \times 10^{5} k g .$ Its total wing area level flight with a $500 m ² .$ It is in speed of 1080 km/h. If the density of air p is $1.2 k g / m ³,$ the fractional increase in the speed of the air on the surface upper of the wing relative to the lower surface in percentage will be $10^{n} % .$ Then the value of n is $(g = 10 m / s ²)$

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Detailed Solution

$P_{2} A - P_{1} A = 5.4 \times 10^{5} \times g P_{2} - P_{1} = \frac{5.4 \times 10^{6}}{500} = 5.4 \times 2 \times 10^{2} \times 10 = 10.8 \times 10^{3} P_{2} + 0 + \frac{1}{2} ρ V_{2}^{2} = P_{1} + 0 + \frac{1}{2} ρ V_{1}^{2} P_{2} - P_{1} = \frac{1}{2} ρ (V_{1}^{2} - V_{2}^{2}) = \frac{1}{2} ρ (V_{1} - V_{2}) (V_{1} + V_{2}) 10.8 \times 10 = 3.6 (V_{1} - V_{2}) V_{1} - V_{2} = 30 (\frac{V_{1} - V_{2}}{V}) \times 100 = \frac{30}{300} \times 100 = 10 %$

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