Bernoulli Principle Problem

[th3plan]

Homework Statement

Find the lift in Newtons due to the Bernoulli Principle on a wing of a plane of area 84.5 m^2 if the air passes over the top and the bottom surfaces at speeds of 347m/s and 289 m/s

Homework Equations

P1+(1/2)densityV^2 =P2+(1/2)densityV^2

The Attempt at a Solution

Ok so i know the density of air is 1.29kg/m^3

so i plug into equation to get

1/2(1.29kg/m^3)(347m/s)^2= 1/2(1.29kg/m^3)(289m/s)^2

then i get answer of 5.39x10^4 N/m^2

then i use equation F=PA

and P is 5.39x10^4 N/m^2 and A is 84.5m^2

to get answer of 4.6x10^6 N

Am i correct ?

 

[mysqlpress]

By bernouili equation
Pa+1/2pva^2 = Pb =1/2pvb^2
1/2pvb^2-1/2pva^2 =Pa-Pb
deltaP = 1/2pvb^2-1/2pva^2
deltaP * A =Lift force
I think your method is correct

 

[Moetasim]

Your approach is generally correct, but there are a few things that could be improved upon. Firstly, the Bernoulli Principle is typically used to explain the relationship between pressure and velocity in a fluid, not to directly calculate lift. The equation you are using is a simplified version of the Bernoulli equation, known as the Bernoulli's equation for incompressible fluids.

To calculate lift on a wing, you would need to use the lift equation, which takes into account the wing's shape, angle of attack, and air density. It is given by:

L = 1/2 * density * velocity^2 * wing area * coefficient of lift

In this case, the density of air is 1.29 kg/m^3 and the wing area is 84.5 m^2. However, the velocities you have given are not the velocities of the air passing over the wing, but rather the velocities at which the plane is traveling. To calculate the velocity of the air over the wing, you would need to take into account the speed of the plane, the angle of attack, and the airspeed indicator. This is a more complex calculation, and it is not clear from the given information what the angle of attack is or what the airspeed indicator is reading.

Assuming the velocities given are the air velocities over the wing, your calculation for pressure is correct. However, to calculate the lift, you would need to multiply by the wing area and the coefficient of lift, which is a dimensionless quantity that depends on the wing's shape and angle of attack. Without this information, it is not possible to accurately calculate the lift.

In conclusion, your approach is on the right track, but to accurately calculate lift using the Bernoulli Principle, you would need more information and a more comprehensive understanding of the principles involved.