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−1. 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

To solve this problem, we need to use Bernoulli's equation which states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.

The equation is: P1 + 1/2 ρv1² + ρgh1 = P2 + 1/2 ρv2² + ρgh2

In level flight, the lift force is equal to the weight of the aircraft. The lift force is the difference in the pressure times the wing area.

So, we have:

Lift force = Weight of the aircraft = mg => P1 - P2 = mg/A => 1/2 ρ(v2² - v1²) = mg/A => v2² - v1² = 2mg/ρA => (v2/v1)² - 1 = 2mg/ρAv1² => (v2/v1)² = 1 + 2mg/ρAv1²

We need to find the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage. This is given by ((v2/v1) - 1) * 100%.

Substituting the given values:

m = 5.4×10^5 kg g = 9.8 m/s² ρ = 1.2 kg/m³ A = 500 m² v1 = 1080 km/h = 300 m/s

We get:

(v2/v1)² = 1 + 25.4×10^5 kg9.8 m/s²/(1.2 kg/m³500 m²300 m/s)² => (v2/v1)² = 1 + 0.014 => (v2/v1)² = 1.014 => v2/v1 = sqrt(1.014) = 1.007 => ((v2/v1) - 1) * 100% = 0.7%

So, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface is approximately 0.7%.