Mechanical Properties Of Fluids Question 1
Question 1 - 2024 (01 Feb Shift 1)
A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm{~m}^{2}$. If the speed of the air is $180 \mathrm{~km} / \mathrm{h}$ over the lower wing surface and $252 \mathrm{~km} / \mathrm{h}$ over the upper wing surface, the mass of the plane is kg. (Take air density to be $1 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
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Answer: (9600)
Solution:
$\mathrm{A}=80 \mathrm{~m}^{2}$
Using Bernonlli equation
$\mathrm{A}\left(\mathrm{P}{2}-\mathrm{P}{1}\right)=\frac{1}{2} \rho\left(\mathrm{V}{1}^{2}-\mathrm{V}{2}^{2}\right) \mathrm{A}$
$\mathrm{mg}=\frac{1}{2} \times 1\left(70^{2}-50^{2}\right) \times 80$
$\mathrm{mg}=40 \times 2400$
$\mathrm{m}=9600 \mathrm{~kg}$
