Question

An aeroplanewing has an area 50m^​2the speed of air flowing above wing and below wing is 100ms^-1and 80ms^-1. Find the aerodynamic lifting force acting on the aeroplane wing if density of air is 1.3kgm^-3

Answer 1

Using the relation,
$$\begin{gathered} {\mathrm{P}}_{\mathrm{above}}+\left(\frac{{\mathrm{\rho }}_{\mathrm{air}}}{2}\right){{\mathrm{v}}^2}_{\mathrm{above}}={\mathrm{P}}_{\mathrm{below}}+\left(\frac{{\mathrm{\rho }}_{\mathrm{air}}}{2}\right){{\mathrm{v}}^2}_{\mathrm{below}} \\ \mathrm{The}\mathrm{difference}\mathrm{in}\mathrm{pressure}\mathrm{accounts}\mathrm{for}\mathrm{the}\mathrm{aerodynamic}\mathrm{lift}. \\ \mathrm{i}.\mathrm{e}.\mathrm{Difference}\mathrm{in}\mathrm{pressure}=\mathrm{Resultant}\mathrm{force}\mathrm{per}\mathrm{unit}\mathrm{area}\mathrm{on}\mathrm{the}\mathrm{wing} \\ \mathrm{So},\mathrm{aerodynamic}\mathrm{lift}={\mathrm{P}}_{\mathrm{below}}-{\mathrm{P}}_{\mathrm{above}}=\left(\frac{{\mathrm{\rho }}_{\mathrm{air}}}{2}\right){{\mathrm{v}}^2}_{\mathrm{above}}-\left(\frac{{\mathrm{\rho }}_{\mathrm{air}}}{2}\right){{\mathrm{v}}^2}_{\mathrm{below}} \\ =\frac{1.3}{2}[{100}^2-{80}^2] \\ =\frac{1.3}{2}(100+80)(100-80) \\ =\frac{1.3}{2}\times 180\times 20=2340\mathrm{Pa} \end{gathered}$$