Fluid Mechanics

JEE Main level, numerical answer, medium

6 of 192

Question 6 of 192

A plane is in level flight at constant speed and each of its two wings has an area of 40m2.40{m}^{2}. If the speed of the air is 180kmh−1180km{h}^{-1} over the lower wing surface and 252kmh−1252km{h}^{-1} over the upper wing surface, the mass of the plane is ________kg.kg. (Take air density to be 1kgm–31kg{m}^{–3} and g=10ms–2g=10m{s}^{–2})

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Answer: 9600

Total wing span area, A=2×40=80m2A=2\times 40=80{m}^{2}
Using Bernoulli's equation, we get uplift force as
A(P2−P1)=12ρ(V12−V22)AA\left({P}_{2}-{P}_{1}\right)=\dfrac{1}{2}\rho \left({V}_{1}^{2}-{V}_{2}^{2}\right)A
⇒mg=12×1(702−502)×80\Rightarrow mg=\dfrac{1}{2}\times 1\left({70}^{2}-{50}^{2}\right)\times 80
⇒mg=2400×40\Rightarrow mg=2400\times 40
⇒m=9600kg\Rightarrow m=9600kg

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