A fully loaded Boeing aircraft has a mass of 3.3×105 kg, its total wing area is 500 m2. It is in level flight with speed of 960 km/h. (a) Estimate the pressure difference between the lower and upper surfaces of the wings. (b) Estimate the fractional increase in the speed of the air on the upper surface of the wing relative to lower surface. (The density of air is ρ=1.2 kg m−3)
(a) the weight of boeing aircraft is balanced by upward force due to the pressure difference.
ΔP×A=3.3×105×g
where, g=9.8m/s2
ΔP=3.3×105×9.8500
ΔP=6.46×103 N/m2
(b) The pressure difference between the lower and upper surface of the wing is
ΔP=ρ2(v22−v21)
v2−v1=2ΔPρ(v2+v1)
vaverage=(v2+v1)2=960 kmph
or, vaverage=(v2+v1)2=266.67 m/s
v2−v1=ΔPρ×vaverage
v2−v1vaverage=ΔPρ×(vaverage)2v2−v1vaverage=6.46×1031.2×(266.67)2
v2−v1vaverage=0.075