(a) Find the pressure difference on an airplane wing where air flows over the upper surface with a speed of 126 m/s, and along the bottom surface with a speed of 101 m/s.
kPa
(b) If the area of the wing is 30 m2, what is the net upward force exerted on the wing?
kN
To find the pressure difference on an airplane wing, we will use Bernoulli's equation, which states that the total pressure in a fluid system remains constant along a streamline.
(a) First, let's find the dynamic pressure on the upper and lower surfaces of the wing using the formula:
Dynamic Pressure (q) = 0.5 * density * velocity^2
The density of air is approximately 1.225 kg/m^3.
For the upper surface:
Velocity (V1) = 126 m/s
Dynamic Pressure (q1) = 0.5 * 1.225 kg/m^3 * (126 m/s)^2
For the lower surface:
Velocity (V2) = 101 m/s
Dynamic Pressure (q2) = 0.5 * 1.225 kg/m^3 * (101 m/s)^2
Next, let's find the pressure difference between the upper and lower surfaces. We can use the equation:
Pressure Difference (ΔP) = q2 - q1
Finally, let's convert the pressure difference into kilopascals (kPa) by dividing by 1000:
Pressure Difference (ΔP) in kPa = (q2 - q1) / 1000
(b) To find the net upward force exerted on the wing, we can use the equation:
Net Force (F) = Pressure Difference (ΔP) * Area (A)
Given that the area of the wing is 30 m^2, we can substitute the values to calculate the net upward force.
Net Force (F) in kN = (Pressure Difference (ΔP) in kPa) * (Area (A) in m^2) / 1000
Now, let's calculate the values for both (a) and (b).
(a) To find the pressure difference on an airplane wing, we can use Bernoulli's equation, which states that the total pressure at any point in a fluid flow system is the sum of the static pressure and the dynamic pressure.
The equation for dynamic pressure is given by:
Dynamic Pressure = (1/2) * ρ * v^2
Where:
ρ = density of the fluid (air in this case)
v = velocity of the air flow
Given that the air flows over the upper surface with a speed of 126 m/s and along the bottom surface with a speed of 101 m/s, we can calculate the dynamic pressure at each surface.
For the upper surface:
Dynamic Pressure (upper) = (1/2) * ρ * v^2
= (1/2) * ρ * (126)^2
For the bottom surface:
Dynamic Pressure (bottom) = (1/2) * ρ * v^2
= (1/2) * ρ * (101)^2
The pressure difference is then given by:
Pressure Difference = Dynamic Pressure (upper) - Dynamic Pressure (bottom)
(b) To calculate the net upward force exerted on the wing, we can use the pressure difference and the area of the wing.
The equation to calculate the force is given by:
Force = Pressure Difference * Area
Given that the area of the wing is 30 m^2 and the pressure difference is calculated in part (a), we can calculate the net upward force exerted on the wing.
Let's calculate part (a) first, and then we can proceed to part (b).
(a) (1/2)*(air density)*(V2^2 - V1^2)
Pressure is highest on the surface with lowest air velocity (the bottom of the wing)
(a) (Pressure difference) x (wing area)