What is the net upward force on an airplane wing of area 22.0 m2 if the speed of air flow is 315 m/s across the top of the wing and 270 m/s across the bottom?
To find the net upward force on an airplane wing, we need to calculate the difference in pressure between the top and bottom surfaces of the wing. This difference in pressure creates the lift force that allows the plane to stay in the air.
To calculate the net upward force, we can use Bernoulli's principle, which states that the total pressure of a fluid (or air) is constant along a streamline.
The equation for Bernoulli's principle can be written as:
P + 0.5 * ρ * v^2 = constant
where P is the pressure, ρ is the density of the air, and v is the velocity.
Let's consider two points on the wing, one on the top (Point 1) and one on the bottom (Point 2). The constant in Bernoulli's equation is the same for both points.
At Point 1 (top of the wing):
P1 + 0.5 * ρ * v1^2 = constant
At Point 2 (bottom of the wing):
P2 + 0.5 * ρ * v2^2 = constant
Since the wing is stationary, the static pressure at Points 1 and 2 is the same, which means P1 = P2.
Now, we need to find the difference in dynamic pressure between the top and bottom surfaces, which is given by the equation:
ΔP = 0.5 * ρ * (v2^2 - v1^2)
where ΔP is the pressure difference.
Given that the speed of air flow across the top of the wing (v1) is 315 m/s, and across the bottom (v2) is 270 m/s, we can substitute these values into the equation to find the pressure difference:
ΔP = 0.5 * ρ * (270^2 - 315^2)
Next, we need to find the value of ρ, the density of air. This value depends on temperature, pressure, and humidity. We'll assume standard conditions with a density of approximately 1.2 kg/m³.
Substituting the value of ρ into the equation, we get:
ΔP ≈ 0.5 * 1.2 * (270^2 - 315^2)
Finally, to calculate the net upward force on the wing, we can use the equation:
F = ΔP * A
where F is the force, ΔP is the pressure difference, and A is the area of the wing.
Given that the area of the wing is 22.0 m², we can substitute the values into the equation:
F ≈ (0.5 * 1.2 * (270^2 - 315^2)) * 22.0
Now, all that's left is to solve for F to find the net upward force on the airplane wing.