A fully loaded Boeing aircraft has a mass of 5.4 × 10⁵ kg. Its total wing area is 500 m². It is in level flight with a speed of 1080 km/h. If the density of air ρ is 1.2 kg m⁻³, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be: [g = 10 m s⁻²]
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Question

A fully loaded Boeing aircraft has a mass of 5.4 × 10⁵ kg. Its total wing area is 500 m². It is in level flight with a speed of 1080 km/h. If the density of air ρ is 1.2 kg m⁻³, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be: [g = 10 m s⁻²]

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G1 Physics · Accepted Answer

Lift equals weight, so pressure difference ΔP = mg/A = (5.4 × 10⁵ × 10)/500 = 1.08 × 10⁴ Pa. By Bernoulli, ΔP = (1/2)ρ(V₁²−V₂²) = (1/2)ρ(V₁−V₂)(V₁+V₂). The aircraft speed is 1080 km/h = 300 m s⁻¹, so take V₁+V₂ ≈ 600 m s⁻¹. This gives V₁−V₂ ≈ 30 m s⁻¹. Percentage increase ≈ (30/300)×100 = 10%.