Question

Air is streaming past a horizontal aeroplane wing such that its speed is $120m{s}^{-1}$ at the upper surface and $90m{s}^{-1}$ at the lower surface. If the wing is $10m$ long and $2m$ wide and density of air is $1.3kg{m}^{-3}$, then the net lift on it will be : ( in Newton)

• A. $81.9$
  
• B. $8.19$
  
• C. $4.095\times {10}^4$
• D. $8.19\times {10}^4$

Answer 1

The correct option is D $8.19\times {10}^4$

Applying Bernoulli's theorem above and below the wings.
Let 1 denote the upper side and 2 denote the lower side
$P_1+\frac{1}{2}\rho v_1^2=P_2+\frac{1}{2}\rho v_2^2$
$\Rightarrow P_1-P_2=\frac{1}{2}\times 1.3\times ({120}^2-{90}^2)$
$\Rightarrow P_1-P_2=\frac{1}{2}\times 1.3\times \left(6300\right)$
$\Rightarrow P_1-P_2=4095N/m^2$

So, the lift $=$ pressure difference $\times$ area
$=4095$ $\times$ $10$ $\times$ $2N$
$=81900N$
$=$$8.19\times {10}^{4}N$