Pressure Difference Across Airplane Wings

In summary, the conversation is about a person struggling to solve a problem related to the weight and airspeed of an airplane with a pressure difference of 545 Pa between the upper and lower surfaces of the wings. They have calculated the weight of the plane to be approximately 150420 N using the equation F = PA, but are unsure how to find the airspeed above the wings (part b). They mention the possibility of using Bernoulli's equation to solve this part.
  • #1
Ike
8
1
I've been at this one for hours and can't get a handle on it... Can anyone give me a little help here?


An airplane flies on a level flight path. There is a pressure difference of 545 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about 138 m^2. The air moves below the wings at a speed of 81.3 m/s. Estimate (a) the weight of the plane and (b) the airspeed above the wings.

The answer to (a) can be found by the quantity: F = P A. (Force = Pressure times Area) The sum of forces can be found to be:

(Weight of Plane) - (P + 545 Pa)(276 m^2) - (P)(276 m^2) = 0

(Weight of Plane) = (545 Pa)(276 m^2) = 150420 N​


I've gotten this far... now how do I do part (b)?
 
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  • #2
Ike said:
...I've gotten this far... now how do I do part (b)?
I imagine you would use Bernoulli's equation.
 
  • #3


To calculate the airspeed above the wings, we can use Bernoulli's principle, which states that in an ideal fluid (such as air), the sum of the static pressure and dynamic pressure (due to the motion of the fluid) remains constant. In this case, we can use the pressure difference across the wings and the known airspeed below the wings to calculate the airspeed above the wings.

We can set up the equation as follows:

(P + 545 Pa) + (1/2)ρv^2 = P + (1/2)ρv^2

Where P is the static pressure, ρ is the density of air, and v is the airspeed.

Simplifying the equation, we get:

545 Pa + (1/2)ρv^2 = (1/2)ρv^2

Rearranging for v, we get:

v = √(2 x 545 Pa/ρ)

To solve for ρ, we can use the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Assuming standard atmospheric conditions (1 atm and 273 K), we can calculate ρ as follows:

ρ = (P/RT) = (545 Pa)/(0.0821 L atm/mol K x 273 K) = 0.024 kg/m^3

Plugging this back into our equation for v, we get:

v = √(2 x 545 Pa/0.024 kg/m^3) = 81.3 m/s

Therefore, the airspeed above the wings is also 81.3 m/s.
 

What is the definition of pressure difference across airplane wings?

The pressure difference across airplane wings refers to the difference in air pressure above and below the wings of an aircraft. This difference in pressure creates lift, allowing the plane to stay in the air.

How is pressure difference created on airplane wings?

Pressure difference is created on airplane wings through the shape and design of the wing. The curved shape of the wing causes air to flow faster over the top of the wing, creating lower pressure, while the flat bottom of the wing creates higher pressure. This difference in pressure results in lift.

How does airspeed affect the pressure difference across airplane wings?

Airspeed plays a crucial role in the pressure difference across airplane wings. As the speed of the aircraft increases, the pressure difference also increases, resulting in more lift. This is why planes need to accelerate to a certain speed before takeoff.

What factors can affect the pressure difference across airplane wings?

The pressure difference across airplane wings can be affected by various factors such as the angle of attack, air density, and airfoil shape. Any changes in these factors can alter the pressure difference and affect the lift and stability of the aircraft.

Why is it important to maintain a proper pressure difference across airplane wings?

Maintaining a proper pressure difference across airplane wings is crucial for safe and efficient flight. Without enough pressure difference, the plane may not generate enough lift to stay in the air. On the other hand, too much pressure difference can cause the plane to become unstable or even stall. Proper maintenance and adjustments of pressure difference are essential for a successful flight.

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