A fully loaded boeing aircraft has a mass of 5 . 4 × 10 5 kg . Its total wing area is 500 m 2 . 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 ( g = 10 m s - 2 )

Step-by-step solution

Required lift force, F = P 2 A - P 1 A = 5 . 4 × 10 5 × g ⇒ P 2 - P 1 = 5 . 4 × 10 6 500 = 5 . 4 × 2 × 10 3 = 10 . 8 × 10 3 Now applying Bernoulli's Theorem we get P 2 + 0 + 1 2 ρ V 2 2 = P 1 + 0 + 1 2 ρ V 1 2 ⇒ P 2 - P 1 = 1 2 ρ V 1 2 - V 2 2 = 1 2 ρ V 1 - V 2 V 1 + V 2 Since for small change ,   V 1 = V 2 = V = 1080   km   h - 1 = 300   m   s - 1 ⇒ 10 . 8 × 10 3 = 1 2 × 1 . 2 V 1 - V 2 ×