Calculate the mass of aero plane with the wings of area 55m2 flying horizontally. The velocity of air above and below the wings is 155m/s and 140 m/s respectively.

Solution:
 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 Aero plane

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

   Here g = 10 (approximately)

                    m = 243375/10

                    m = 24337.5 kgs

   Hence, Mass of the Aero plane m = 24337.5 kgs