Question

Let air be at rest at the front edge of a wing and air passing over the surface of wing at a fast speed v. If density of air is $\rho$, the highest value for v in streamline flow when atmospheric pressure is $P_{atmosphere}$ is:

• A. ${\left[\frac{P_{atmosphere}}{\rho }\right]}^{\frac{-1}{2}}$
• B. ${\left[\frac{P_{atmosphere}}{\rho }\right]}^2$
• C. ${\left[\frac{P_{atmosphere}}{\rho }\right]}^{\frac{1}{2}}$
• D. $\frac{P_{atmosphere}}{\rho }$

Answer 1

Answer: (C)

${\left[\frac{P_{atmosphere}}{\rho }\right]}^{\frac{1}{2}}$

As we know that pressure at some height $h$ is given by $P_{atmospheric}=\rho gh$----------(1)

so if air is passing through the wings of plane,then apply the equation of motion $V^2=U^2+2gh$

air is at rest so $U=0$ and heighest value of $V$ is at height $\frac{h}{2}$

$V^2=gh$---------(2)

equating equation (1) and (2) we find

$V={\left(\frac{P_{atmospheric}}{\rho }\right)}^{\frac{1}{2}}$