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A fully loaded boeing aircraft has a mass of  5.4 \times 10^5 \mathrm{~kg}. Its total wing area is 500 \mathrm{~m}^2. It is in level flight with a speed of 1080 \mathrm{~km} / \mathrm{h}. If the density of air \rho  is 1.2 \mathrm{~kg} \mathrm{~m}^{-3}, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. \left(g=10 \mathrm{~m} / \mathrm{s}^2\right)

Option: 1

16


Option: 2

10


Option: 3

8


Option: 4

6


Answers (1)

best_answer

\begin{aligned} & P_2 A-P_1 A=5.4 \times 10^5 \times g \\ & P_2-P_1=\frac{5.4 \times 10^6}{500}=10.8 \times 10^3 \\ & P_2+0+\frac{1}{2} \rho v_2^2=P_1+0+\frac{1}{2} \rho v_1^2 \\ & P_2-P_1=\frac{1}{2} \rho\left(v_1^2-v_2^2\right)=\frac{1}{2} \rho\left(v_1+v_2\right)\left(v_1-v_2\right) \\ & 10.8 \times 10^3=\frac{1}{2} \times 1.2 \times\left(v_1-v_2\right) \times 2 \times 3 \times 10^2 \\ & \mathrm{v}_1-v_2=30 \\ & \frac{v_1-v_2}{v_0} \times 100=\frac{30}{300} \times 100=10 \% \end{aligned}

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