What is the maximum weight of an aircraft with a wing of area 50m sq. flying horizontally, if the velocity of the air over the upper surface of the wing is 150m/s and that of lower surface is 140 m/s.
Upi meed aor density, density of air is 1.20 kg/m^3
The net lift per wing area, using the Bernoulli equation, is
(1/2)(air density)[(Vtop)^2-(Vbottom)^2]
= ......
So that is lift per m^2, and you have 50m^2
Ni
To find the maximum weight of the aircraft, we need to calculate the lift and drag forces acting on the wing.
Step 1: Calculate the lift force:
The lift force on an aircraft wing can be calculated using the formula:
Lift force (L) = 1/2 * ρ * V^2 * A * Cl
where:
ρ is the air density
V is the velocity of air
A is the wing area
Cl is the coefficient of lift
Step 2: Determine the coefficient of lift:
The coefficient of lift (Cl) is determined by the shape of the wing profile and the angle of attack. Since the angle of attack is not given in the question, we will assume a typical value of 1.0 for Cl.
Step 3: Find the air density:
The air density (ρ) is required for the lift force calculation. The typical value at sea level is approximately 1.225 kg/m^3.
Step 4: Calculate the lift force:
Using the given values, we can substitute them into the lift force formula to calculate the lift force acting on the wing.
Lift force (L) = 1/2 * 1.225 kg/m^3 * (150 m/s)^2 * 50 m^2 * 1.0
Step 5: Calculate the maximum weight:
The lift force that the wing generates is equal to the weight of the aircraft when it is flying level. Therefore, the maximum weight of the aircraft can be calculated by equating the lift force to the weight.
Weight = Lift force
You can now substitute the values into the formula to calculate the maximum weight of the aircraft.
To find the maximum weight of an aircraft with a given wing area and air velocities over the upper and lower surfaces of the wing, we need to use a principle of aerodynamics called Bernoulli's principle.
Bernoulli's principle states that for an incompressible, steady flow of fluid, the sum of the pressure energy, kinetic energy, and potential energy per unit volume is constant.
In the case of an aircraft wing, the lift generated by the wing is a result of differences in air pressure between the upper and lower surfaces. The faster airflow over the upper surface creates lower pressure, while the slower airflow under the lower surface creates higher pressure. This pressure difference generates lift.
Using Bernoulli's principle, we can calculate the lift force acting on the wing, and from there, determine the maximum weight the wing can support.
First, we need to calculate the lift force as follows:
Lift = (pressure on upper surface - pressure on lower surface) x wing area
To calculate the pressure on each surface, we use Bernoulli's equation:
P + 1/2 * ρ * v^2 = constant
Where:
P is the pressure
ρ is the air density
v is the velocity of the fluid (air)
For the upper surface:
P_upper + 1/2 * ρ * v_upper^2 = constant
For the lower surface:
P_lower + 1/2 * ρ * v_lower^2 = constant
Since the constant is the same for both equations because the fluid flow is incompressible, we can subtract the two equations to obtain:
P_upper - P_lower = 1/2 * ρ * (v_lower^2 - v_upper^2)
Now, we substitute this expression for the pressure difference into the lift equation:
Lift = 1/2 * ρ * (v_lower^2 - v_upper^2) * wing area
We also know that the lift force equals the weight of the aircraft:
Lift = Weight
So, we have:
Weight = 1/2 * ρ * (v_lower^2 - v_upper^2) * wing area
Now, we can plug in the given values to calculate the maximum weight of the aircraft:
Wing area (A) = 50 m^2
Velocity over the upper surface (v_upper) = 150 m/s
Velocity over the lower surface (v_lower) = 140 m/s
However, we still need the value for air density (ρ), which would depend on the altitude and temperature. Without this information, we cannot give a specific answer.
To find the air density, you would need to know the altitude and temperature at which the aircraft is flying. With these values, you can use the ideal gas law equation:
ρ = P / (R * T)
Where:
ρ is the air density
P is the atmospheric pressure at the given altitude
R is the specific gas constant for air (approximately 287 J/(kg·K))
T is the temperature in Kelvin
By substituting the values for pressure and temperature into this equation, you can calculate the air density (ρ). Then, you can use the equation mentioned above to find the maximum weight of the aircraft.