Question

A plane is in level flight at constant speed and each of its two wings has an area of 25 m². If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane's mass. (Take air density to be 1 kg m^-3).

Answer 1

Area of each wing = 25 m²

Speed, v₁ = 234 km h^-1

= {234 x 1000}/{60 x 60} = 65 ms^-1

Speed, v₂ = 180 km h^-1 = 180 x 5/18 = 50 ms^-1

Let p₁ and p₂ be the pressure of air at the upper and lower wings of plane respectively, then

p₁/ρ + 1/2v²₁ = p₂/ρ + 1/2v²₂

or, p₁ - p₂ = 1/2ρ(v²₁ - v²₂)

or, p₁ - p₂ = 1/2 x 1 x (65² - 50²)(Air density, ρ = 1 kg m^-3)

= 1/2 x (4225 - 2500) = 1725/2 = 862.5

Pressure = Force/area

⇒ Pressure x area = Force

or, 862.5 x 25 = Force

Hence, Force = 21562.5 N

Mass = 21562.5/10 = 2156.25 kg

Mass of plane = 2156.25 x 25 x 2 = 4312 kg