Question

A fully loaded Boeing aircraft has a mass of $3.3\times {10}^5$ kg, its total wing area is $500m^2$. 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 $\rho =1.2kg{m}^{-3}$)

Answer 1

(a) the weight of boeing aircraft is balanced by upward force due to the pressure difference.

$\Delta P\times A=3.3\times {10}^5\times g$

where, $g=9.8m/s^2$

$\Delta P=\frac{3.3\times {10}^5\times 9.8}{500}$

$\Delta P=6.46\times {10}^{3}N/m^2$

(b) The pressure difference between the lower and upper surface of the wing is

$\Delta P=\frac{\rho }{2}(v_2^2-v_1^2)$

$v_2-v_1=\frac{2\Delta P}{\rho (v_2+v_1)}$

$v_{average}=\frac{(v_2+v_1)}{2}=960kmph$

or, $v_{average}=\frac{(v_2+v_1)}{2}=266.67m/s$

$v_2-v_1=\frac{\Delta P}{\rho \times v_{average}}$

$\frac{v_2-v_1}{v_{average}}=\frac{\Delta P}{\rho \times (v_{average}{)}^2}$

$\frac{v_2-v_1}{v_{average}}=\frac{6.46\times {10}^3}{1.2\times (266.67{)}^2}$

$\frac{v_2-v_1}{v_{average}}=0.075$