an aeroplane has a mass of 15 tonnes. At cruising speed,air flows over the top of it's wing at 150 m/s and under the wing at 120m/s. Calculate the pressure in difference between the top and the bottom of the wing and the surface area underside the wing
To calculate the pressure difference between the top and bottom of the wing, we can use Bernoulli's principle, which states that as the velocity of a fluid (or air) increases, the pressure decreases.
First, let's determine the velocity difference between the top and bottom of the wing:
Velocity difference = Velocity on top of the wing - Velocity underneath the wing
= 150 m/s - 120 m/s
= 30 m/s
Next, we need to convert the mass of the airplane from tonnes to kilograms, as the SI unit for mass is kilograms.
1 tonne = 1000 kilograms
Mass of the airplane = 15 tonnes * 1000 kg/tonne
= 15000 kg
Now, we can calculate the pressure difference. We'll use the equation:
Pressure difference = (1/2) * (density of air) * (velocity difference)^2
The density of air is approximately 1.225 kg/m³.
Pressure difference = (1/2) * (1.225 kg/m³) * (30 m/s)^2
= 550.125 Pa
Therefore, the pressure difference between the top and bottom of the wing is approximately 550.125 Pascal (Pa).
Now, moving on to calculating the surface area underneath the wing. Unfortunately, we do not have enough information to directly calculate the surface area. The surface area of the wing depends on its shape, size, and wing design. Thus, we would need additional information or specifications about the wing to determine its surface area.
If you have access to the wing's specifications or any other relevant information, please provide it, and I will be able to help you calculate the surface area.