Question

calculate the mass of aeroplane with the wings of area 55m2 flying horizontally. The velocity of air above and below the wings is 155m/s and 140 m/s​

Answer 1

Answer:

Mass = Velocity ÷ time

in this case,

155 - 140 = 15 m/s

15 * 55 m²

825 kg

Answer 2

Answer:

Mass of the Aeroplane m = 24337.5 kgs

Explanation:

  Let v₁ and v₂ be the velocities of air above and below surface of wings.

   and P₁ and P₂ be the pressure of the wings.

According to Bernoulli's theorem,

  P₁+(1/2)ρ(v₁)² = P₂+(1/2)ρ(v₂)²

   P₁ - P₂ = (1/2)ρ(v₂²-v₁²)

 Here,  v₁ = 140 m/s and v₂ = 155 m/s

  ρ is the density of air = 1 kg/m³

     Area of wings A = 2 × 55 = 110m²

   So,  P₁ - P₂ = (1/2)×1×(155²-140²)

                     = (1/2)×(24025-19600)

                     = (1/2)×(4425)

                     = 2212.5

 Upward force on the plane = (P₁ - P₂)×A

                                               = 2212.5×110

                                               = 243375

As the plane is in the level flight, therefore upward force balances the weight of the plane.

                mg =  (P₁ - P₂)×A  where m is the mass of Aeroplane

                    m = [(P₁ - P₂)×A]/g

   Here g = 10 (approximately)

                    m = 243375/10

                    m = 24337.5 kgs

   Hence, Mass of the Aeroplane m = 24337.5 kgs

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