Question

Air streams horizontally past an airplane. The speed of air over the top surface of the wings is $60\text{m/s}$ and that under the bottom surface is $45\text{m/s}$. The density of air is $1.293{\text{kg/m}}^3$. Then, the difference in pressure between the top and bottom surface of the wings is:
(Consider airplane to be flying at a constant altitude)

• A. $1018{\text{N/m}}^2$
• B. $516{\text{N/m}}^2$
• C. $1140{\text{N/m}}^2$
• D. $2250{\text{N/m}}^2$

Answer 1

The correct option is A $1018{\text{N/m}}^2$

Apply Bernoulli's equation for the top and bottom surface of the airplane,
$P_1+\rho gh+\frac{1}{2}\rho v_1^2=P_2+\rho gh+\frac{1}{2}\rho v_2^2$
Here, $h=\text{constant}$ [considering the thickness of the wings to be negligible]
$v_1=60\text{m/s},v_2=45\text{m/s}$
$\Rightarrow P_2-P_1=\frac{1}{2}\times \rho [v_1^2-v_2^2]$
$\Rightarrow \Delta P=\frac{1}{2}\times 1.293\left[\right(60{)}^2-\left(45{)}^2\right]$
$\Rightarrow \Delta P\simeq 1018{\text{N/m}}^2$