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).

Question

Philoid · Accepted Answer

Given,

Area of the two wings, A = 2 × 25 = 50 m²

Air Velocity over wings, v₁ = 234 km/h = 65 m/s

Air Velocity below wings, v₂ = 180 km/h = 50 m/s

Density of the air, ρ = 1 kg/m³

Bernoulli’s equation,

(∵ neglecting potential energy)

Let, P₁ = pressure over wings

P₂ = pressure below wings

⇒

= 862.5 pa

We have,

Where,

ΔP = change in pressure = P₂ – P₁

A = area

∴ F = 862.5 pa × 50 m²

= 43125 N

As per Newton’s second law,

F = mg

Where,

F = force

g = acceleration due to gravity

⇒ mass of the plane,

Thus,

Mass of the plane, m ≈ 4400 kg

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).