Question

An airplane has wings, each with area A, designed so that air flows over the top of the wing at 265 m/s and underneath the wing at 234 m/s. If the mass of the airplane is 7.2×10^3 kg then what is the area of each wing needed to produce enough lift? (air = 1.29 kg/m^3 )

Answer 1

Answer

given,

Pressure on the top wing = 265 m/s

speed of underneath wings = 234 m/s

mass of the airplane =  7.2 × 10³ kg

density of air =  1.29 kg/m³

using Bernoulli's equation

 $P_1 + \dfrac{1}{2}\rho v_1^2 = P_2 + \dfrac{1}{2}\rho v_2^2$

 $\Delta P =\dfrac{1}{2}\rho (v_2^2-v_1^2)$

 $\Delta P =\dfrac{1}{2}\times 1.29\times (265^2-234^2)$

 $\Delta P =9977.5 Pa$

Applying newtons second law

2 Δ P x A - mg = 0

$A =\dfrac{mg}{2\Delta P}$

$A =\dfrac{7.2\times 10^3 \times 9.8}{2\times 9977.5}$

    A = 3.53 m²