Question

Air streams horizontally past an air plane. The speed over the top surface is $60\text{m/s}$ and that under the bottom surface is $45\text{m/s}$. The density of air being $1.293{\text{kg/m}}^3$, calculate the difference in pressure across the wing.

• 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 $1018{\text{N/m}}^2$

Applying the bernoulli's equation for two points 1 and 2, just above the wing (top surface) and just below the wing (bottom surface ) of the aircraft.
$(\because$ wings of aircraft play role in aerodynamics or lifting of plane)


$v_1=60\text{m/s}$ (speed of air at top surface)
$v_2=45\text{m/s}$ (speed of air at bottom surface)
$(v_1>v_2),$ therefore $(P_2>P_1)$ from Bernoulli's principle of energy conservation.
$\Rightarrow P_1+\rho gh+\frac{1}{2}\rho v_1^2=P_2+\rho gh+\frac{1}{2}\rho v_2^2$
$\Rightarrow P_2-P_1=\frac{1}{2}\rho (v_1^2-v_2^2)$
or $\Delta P=\frac{1}{2}\times 1.293\times \left(\right(60{)}^2-\left(45{)}^2\right)$
$\therefore \Delta P=1018.23\approx 1018{\text{N/m}}^2$