Please help
A fully loaded aircraft has a mass of 3.3×10^5 kg.its total wing area is 500m2 . It is in level flight with a speed of 960km/h.
Calculate the pressure difference between the lower and upper surface of the wings.
Thank you!
Pressure*areawings=weightaircraft
Pressure*500=3.3E6 kg* 9.8N/kg
solve for pressure difference in Newtons
To calculate the pressure difference between the lower and upper surfaces of the wings, you can use Bernoulli's principle. Bernoulli's principle states that in a flowing fluid, an increase in speed is accompanied by a decrease in pressure.
First, let's convert the speed of the aircraft from km/h to m/s. We can do this by dividing the speed by 3.6:
Speed = 960 km/h ÷ 3.6 = 266.67 m/s
Next, we'll calculate the dynamic pressure using the formula:
Dynamic Pressure = 0.5 * ρ * V^2
In this equation:
- ρ (rho) represents the air density (which we can assume to be approximately 1.2 kg/m^3)
- V represents the velocity of the aircraft
Dynamic Pressure = 0.5 * 1.2 kg/m^3 * (266.67 m/s)^2 = 0.5 * 1.2 kg/m^3 * 71,111.11 m^2/s^2 = 42,666.67 Pa
Now, let's calculate the lift force, which is equal to the pressure difference between the lower and upper surfaces of the wings multiplied by the wing area:
Lift Force = Pressure Difference * Wing Area
Since the lift force and the weight of the aircraft are equal in level flight, we can calculate the pressure difference:
Pressure Difference = Lift Force / Wing Area
The weight of the aircraft is given as the mass multiplied by the acceleration due to gravity (g = 9.8 m/s^2):
Weight = Mass * g = 3.3 * 10^5 kg * 9.8 m/s^2 = 3.234 * 10^6 N
Pressure Difference = Weight / Wing Area
Pressure Difference = (3.234 * 10^6 N) / 500 m^2 = 6468 Pa or 6.468 kPa
Therefore, the pressure difference between the lower and upper surface of the wings is approximately 6.468 kPa.