Question 5.C-A.66: An aeroplane wing has an area 50 m^2.The speed of air flowin...
An aeroplane wing has an area 50 m^{2}.The speed of air flowing above the wing is 100 m s^{−1} and below the wing is 80 m s^{−1}. Find the aerodynamic lifting force acting on the aeroplane wing if density of air is 1.3 kg m^{−3}.
Given,
Velocity of air below the aeroplane wing
V_{1}=80 m s ^{-1}Velocity of air above the aeroplane wing
V_{2}=100 m s ^{-1}Area of aeroplane wing A =50 m ^{2}
Aerodynamic lifting force F = ?
Aerodynamic lifting force F=\left(P_{1}-P_{2}\right) A → (1)
Where P_{1} and P_{2} are pressures of air at the bottom and top of the wings respectively.
According to Bernoulli’s theorem,
\frac{P_{1}}{\rho}+\frac{1}{2} V_{1}^{2}=\frac{P_{2}}{\rho}+\frac{1}{2} V_{2}^{2}Or \left(P_{1}-P_{2}\right)=\frac{1}{2} \rho\left(V_{2}^{2}-V_{1}^{2}\right) (2)
Substituting (2) in (1)
\therefore F=\frac{1}{2} \rho\left(V_{2}^{2}-V_{1}^{2}\right) A[density of air \rho=1.3 kg m ^{-3} ]
F=\frac{1}{2} 3.1 \times=\left(100^{2}-80^{2}\right) \times 50We get F =117 \times 10^{3} N