Question

The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are $v$ and $\sqrt{2}v$ respectively. The density of air is $\rho$ and surface area of wing is $A$. The dynamic lift on the wing is:

• A. $\rho v^{2}A$
• B. $\sqrt{2}\rho v^{2}A$
• C. $\left(\frac{1}{2}\right)\rho v^{2}A$
• D. $2\rho v^{2}A$

Answer 1

The correct option is C $\left(\frac{1}{2}\right)\rho v^{2}A$

Dynamic lift = Pressure difference $\times$ Area
$=(P_{\text{lower}}-P_{\text{upper}})A$
According to Bernoulli's Theorem
$=(\frac{1}{2}\rho v_{\text{upper}}^2-\frac{1}{2}\rho v_{\text{lower}}^2)A$
$=\frac{1}{2}\rho A\left[\right(\sqrt{2}v{)}^2-v^2]=\frac{1}{2}\rho A{v}^2$