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

Total area of wings, A = 2 × 25 = 50m²

speed of air lover the longer wing,

V₁ = 180 km/h = 50 m/s

speed of air over the upper wings,

V₂ = 243 km/h = 65 m/s

Density of air, ρ =1kg/m³

Let P₁ and P₂ be the pressure of air over the lower wing and upper wing respectively.

From Bimoull’s equation,

∴ pressure difference, ∆P

The upward force on the plane, F = (∆P) A 

= 862.5 × 50

= 43125 N

We know that the upward force balances the weight of the plane

∴ F = mg

43125 = m × 9.8

⇒ m = 4400.51 kg.