Airplane Wing Pressure and Net Force Calculation

  • Thread starter iseidthat
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In summary, we can use Bernoulli's equation to find the pressure difference on an airplane wing with given air velocities and density. If the height of the wing is assumed to be negligible, the pressure difference can be calculated as (1/2)pv2^2-(1/2)pv1^2. Using this pressure difference and the wing's area, we can calculate the net upward force exerted on the wing as F=P/A. Checking our answer for reasonableness is always a good practice.
  • #1
iseidthat
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Homework Statement



(a) Find the pressure difference on an airplane wing where air flows over the upper surface with a speed of 117 m/s, and along the bottom surface with a speed of 104 m/s.

(b) If the area of the wing is 38 m2, what is the net upward force exerted on the wing?

Homework Equations



i have no clue.

The Attempt at a Solution



I think my teacher might have left off a part. I don't know how you could find a change in pressure without maybe the height of the wing. I guess you can assume the density of air is about 1.29 kg/m^3 and g=9.81 m/s^2. Is there a way to find it with just the 2 velocities?
 
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  • #2
do you know bernoulli's equation?
 
  • #3
the height of the wing could be required, but often assumed negligible, especially in such a general question.
 
  • #4
redargon said:
do you know bernoulli's equation?

P1+(1/2)pv1^2+pgy1=P2+(1/2)pv2^2+pgy2

what would you put as the y's?
if you ignored it, would the pgy's cancel?

i guess you could do P1-P2=(1/2)pv2^2-(1/2)pv1^2+pgy2-pgy1
 
  • #5
iseidthat said:
P1+(1/2)pv1^2+pgy1=P2+(1/2)pv2^2+pgy2

what would you put as the y's?
if you ignored it, would the pgy's cancel?

i guess you could do P1-P2=(1/2)pv2^2-(1/2)pv1^2+pgy2-pgy1

exactly! if we assume the height of the wing to be small then y1 = y2 and the pgy's cancel.

now you have the pressure difference in terms of velocity and density. you have those values so, what is your pressure difference?
 
  • #6
P1-P2=(1/2)(1.29)(104^2)-(1/2)(1.29)(117^2)
P1-P2=-1853.09 pa

well a change would be possitive. that seems kinda large for having only a difference of 13 m/s.
 
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  • #7
So that's telling us that the air pressure on top of the wing is 1853.09Pa less than the pressure at the bottom of the wing (P1=P2-1853.09), ie. the pressure difference. If it was positive then we would see that pressure at the bottom would be less than the top, which is not the case here. Kinda large is relative, 1853Pa is about 1.85kPa. The air pressure can change due to the weather between 900mbar and 1100mbar (approximately) which is a change of 200mbar or 20 000Pa. And that is just due to weather and you can't even feel it. So, 1853Pa is not really that much.

So, for the second part of the question, how do we calculate a force from a pressure difference and an area?
 
  • #8
P=F/A
so 1.85(38)=F=70.014 kN

Thanks!
 
  • #9
No problem.

Always remember to check your answer to see if it makes sense. For example, 70kN of lift, how much could I lift with that? using F=mg, I see that I can lift about 7000kg, that sounds about right for a medium sized plane. As long as I didn't get 7grams or 700000000kg, then I know my answer could be reasonable.
 

What is an airplane wing?

An airplane wing is a structure attached to the fuselage of an aircraft that produces lift, enabling the aircraft to fly. It is designed to create a pressure difference between the upper and lower surfaces, creating an upward force that counters the weight of the aircraft.

How does an airplane wing create lift?

An airplane wing creates lift through a phenomenon called Bernoulli's principle. As air flows over the curved surface of the wing, it travels faster over the top of the wing, creating a lower pressure area above the wing. This lower pressure area creates an upward force, lifting the wing and the aircraft attached to it.

What are the different types of airplane wings?

There are several types of airplane wings, including straight, swept, delta, and variable-sweep wings. Straight wings are the most common and are typically used for slower speed aircraft. Swept and delta wings are designed for higher speeds and are often used in jet aircraft. Variable-sweep wings can adjust their shape during flight to optimize performance at different speeds.

How are airplane wings tested for safety?

Airplane wings undergo extensive testing before they are deemed safe for flight. This includes wind tunnel testing to study the aerodynamics of the wing, as well as structural testing to ensure the wing can withstand the stresses of flight. Additionally, computer simulations and flight testing are also used to assess the safety of airplane wings.

What factors affect the design of airplane wings?

The design of airplane wings is influenced by several factors, including the desired flight characteristics, the weight and size of the aircraft, and the speed and altitude it will be flying at. Other factors that may affect wing design include the type of engine and fuel efficiency goals. Ultimately, the wing design must balance lift, drag, and stability to achieve safe and efficient flight.

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