An airplane wing is designed so that the speed of the air across the top of the wing is 255 m/s when the speed of the air below the wing is 199 m/s. The density of the air is 1.29 kg/m3. What is the lifting force on a wing of area 27.0 m2?

Respuesta :

Answer:442758.96N

Explanation:

This problem is solved using Bernoulli's equation.

Let [tex]P[/tex] be the pressure at a point.

Let [tex]p[/tex] be the density fluid at a point.

Let [tex]v[/tex] be the velocity of fluid at a point.

Bernoulli's equation states that [tex]P+\frac{1}{2}pv^{2}+pgh=constant[/tex] for all points.

Lets apply the equation of a point just above the wing and to point just below the wing.

Let [tex]p_{up}[/tex] be the pressure of a point just above the wing.

Let [tex]p_{do}[/tex] be the pressure of a point just below the wing.

Since the aeroplane wing is flat,the heights of both the points are same.

[tex]\frac{1}{2}(1.29)(255)^{2}+p_{up}= \frac{1}{2}(1.29)(199)^{2}+p_{do}[/tex]

So,[tex]p_{up}-p_{do}=\frac{1}{2}\times 1.29\times (25424)=16398.48Pa[/tex]

Force is given by the product of pressure difference and area.

Given that area is [tex]27ms^{2}[/tex].

So,lifting force is [tex]16398.48\times 27=442758.96N[/tex]