What is the net upward force on an airplane wing of area 20 m^2 . if the speed of airflow is 300 m/s across the top of the wing and 280 m/s across the bottom? assume the Density of air is 1.29 kgm^-3 .
a. 3.5*10^4
b. 5.5*10^7
c.4.5*10^8
d.1.5*10^5
To calculate the net upward force on an airplane wing, we need to use the Bernoulli's principle, which relates the pressure difference due to the difference in airflow speed across the top and bottom of the wing.
Bernoulli's principle states that the pressure of a fluid decreases as its speed increases, and the pressure increases as the speed decreases.
The formula we can use to calculate the net upward force is:
Net upward force = pressure difference × wing area
First, let's calculate the pressure difference between the top and bottom of the wing using Bernoulli's principle.
For the top side of the wing:
P(top) + (1/2)ρv(top)^2 = constant
where P(top) represents the pressure on the top side of the wing, ρ is the density of air, and v(top) is the speed of airflow across the top of the wing.
For the bottom side of the wing:
P(bottom) + (1/2)ρv(bottom)^2 = constant
where P(bottom) represents the pressure on the bottom side of the wing, and v(bottom) is the speed of airflow across the bottom of the wing.
Since the wing is in equilibrium, the pressure on the top side of the wing is equal to the pressure on the bottom side of the wing (P(top) = P(bottom)).
Therefore, we can rewrite the equations as:
P + (1/2)ρv(top)^2 = constant
P + (1/2)ρv(bottom)^2 = constant
Subtracting the second equation from the first equation, we get:
(1/2)ρ(v(top)^2 - v(bottom)^2) = 0
Rearranging the equation, we have:
v(top)^2 - v(bottom)^2 = 0
Now, let's substitute the given values into the equation:
v(top)^2 - v(bottom)^2 = (300 m/s)^2 - (280 m/s)^2
= 90000 m^2/s^2 - 78400 m^2/s^2
= 11600 m^2/s^2
Next, we need to calculate the pressure difference:
Pressure difference = (1/2)ρ(v(top)^2 - v(bottom)^2)
= (1/2)(1.29 kg/m^3)(11600 m^2/s^2)
= 7494 kg/m⋅s^2
Finally, we can calculate the net upward force:
Net upward force = pressure difference × wing area
= 7494 kg/m⋅s^2 × 20 m^2
= 149880 kg⋅m/s^2
= 1.4988 × 10^5 N
The closest answer option is d. 1.5 × 10^5.