For an aircraft of mass $3.3 imes 10^5 ext{ kg}$ and wing area $500 ext{ m}^2$ flying at $960 e

Question

For an aircraft of mass $3.3 	imes 10^5	ext{ kg}$ and wing area $500	ext{ m}^2$ flying at $960	ext{ km/h}$, estimate the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface. (Density of air = $1.2	ext{ kg/m}^3$, $g = 9.8	ext{ m/s}^2$)

Professor PC Thomas Classes · Answer

By Bernoulli's principle, $\Delta P = \frac{1}{2} ho (v_{upper}^2 - v_{lower}^2) \approx ho v_{avg} \Delta v$. Fractional increase is $\frac{\Delta v}{v_{avg}} = \frac{\Delta P}{ho v_{avg}^2}$. $v_{avg} = 960	ext{ km/h} = 267	ext{ m/s}$. $\frac{\Delta v}{v_{avg}} = \frac{6468}{1.2 	imes (267)^2} \approx 0.08$.