A plane is in level flight at constant speed and each of its two wings has an area of 20 m². If the speed of the air is 198 km/h over the lower wing and 270 km/h over the upper wing. Determine the plane's mass? (Take air density = 1 kg/m³)

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This question was previously asked in

AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 1)

Answer 1

Concept:

Using Bernoulli's Equation:

Also, ΔP = F /A, F = mg

Where, A is the total area of the two wings of the plane,
Calculation:

Given: A = 40m²,since the plane is two wings, v = 198 km/h = 55m/s, v = 270 km/h = 75m/s, ρ = 1kg/m³

Now since the plane is in a horizontal plane therefore there is no change in h i.e. Δh = 0

We can apply Bernoulli's theorem between any two points of the flow region as the flow is irrotational.

Applying Bernoulli's Equation between the upper and lower sides of the plane

Now ΔP × A = F = mg

⇒ 1300 × (2 × 20) = mg

Note, that we have to take the total area ie the area of the two wings.

⇒ mg = 52000

⇒ m = 52000/9.8 = 5306.1 kg

Hence the correct option is m = 5306.1 kg

Additional InformationBernoulli's equation in terms of head