Question

Air is streaming past a horizontal aeroplane wing such that its speed is $120\text{m/s}$ over the upper surface and $90\text{m/s}$ at the lower surface. If the density of air is $1.3{\text{kg/m}}^3$ and wing is $10\text{m}$ long and has an average width $2\text{m}$, calculate the gross lift of the wing.

• A. $9.2\times {10}^8\text{N}$
• B. $8.2\times {10}^4\text{N}$
• C. $7.2\times {10}^4\text{N}$
• D. $6.2\times {10}^8\text{N}$

Answer 1

The correct option is B $8.2\times {10}^4\text{N}$

According to Bernoulli's equation for a horizontal plane, we have
$p_1+\frac{1}{2}\rho v_1^2=p_2+\frac{1}{2}\rho v_2^2$
i.e., $p_1-p_2=\frac{1}{2}\rho (v_2^2-v_1^2)$
So, $p_1-p_2=\frac{1}{2}\times 1.3\times ({120}^2-{90}^2)$
$=4.1\times {10}^{3}N/m^2$
Now as Gross lift $=\Delta p\times A$
So, Gross lift $=4.1\times {10}^3\times (10\times 2)=8.2\times {10}^4\text{N}$