1. Tardigrade
  2. Question
  3. Physics
  4. Air is streaming past a horizontal airplane's wing such that its speed is 120 ms -1 over the upper surface and 90 ms -1 at the lower surface. If the density of air is 1.3 kgm -3 and the wing is 10 m long and has an average width of 2 m, then the difference of the pressure on the two sides of the wing is

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Q. Air is streaming past a horizontal airplane's wing such that its speed is $120 \,ms ^{-1}$ over the upper surface and $90\, ms ^{-1}$ at the lower surface. If the density of air is $1.3\, kgm ^{-3}$ and the wing is $10 \,m$ long and has an average width of $2 \,m$, then the difference of the pressure on the two sides of the wing is

Mechanical Properties of Fluids

Solution:

From the Bernoulli's theorem,
$p_{1}-p_{2} =\frac{1}{2} \rho\left(v_{2}^{2}-v_{1}^{2}\right)$
Given, $ \rho =1.3\, kgm ^{-3} $
$v_{2} =120 \,ms ^{-1} $
$v_{1} =90 \,ms ^{-1} $
$\Rightarrow p_{1}-p_{2} =\frac{1}{2} \times 1.3 \times\left[(120)^{2}-\left(90^{2}\right)\right] $
$=4095 Nm ^{-2} $ or $ Pa$