(a) Find the pressure difference on an airplane wing where air flows over the upper surface with a speed of 126 m/s, and along the bottom surface with a speed of 101 m/s.(kPa)

(b) If the area of the wing is 30 m2, what is the net upward force exerted on the wing? (kN)

pressure difference= 1/2 densityair(V1^2-V2^2)

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To find the pressure difference on the airplane wing, we can use Bernoulli's principle, which states that the sum of the pressure, kinetic energy, and potential energy per unit volume remains constant along a streamline.

(a) First, let's calculate the pressure difference on the airplane wing:

Given:
- Speed of air over the upper surface (V1) = 126 m/s
- Speed of air along the bottom surface (V2) = 101 m/s

Using Bernoulli's principle, the equation can be written as:

P1 + (1/2)*ρ*V1^2 + ρ*g*h1 = P2 + (1/2)*ρ*V2^2 + ρ*g*h2

Assuming the height difference (h1 - h2) is negligible, we can ignore the potential energy terms. Also, since the air density (ρ) is the same on both surfaces, it cancels out:

P1 + (1/2)*V1^2 = P2 + (1/2)*V2^2

P1 - P2 = (1/2)*V2^2 - (1/2)*V1^2

Now, substituting the given values:

P1 - P2 = (1/2)*(101^2 - 126^2) m^2/s^2

P1 - P2 = (1/2)*(10201 - 15876) m^2/s^2

P1 - P2 = (1/2)*(-5665) m^2/s^2

P1 - P2 = -2832.5 m^2/s^2

To convert the pressure difference from m^2/s^2 to kPa, we multiply by a conversion factor of 1 kPa / 1000 N/m^2:

P1 - P2 = -2832.5 m^2/s^2 * (1 kPa / 1000 N/m^2)

P1 - P2 = -2.8325 kPa

Therefore, the pressure difference on the airplane wing is approximately -2.8325 kPa.

(b) To calculate the net upward force exerted on the wing, we can use the equation:

Force = Pressure difference * Area

Given:
- Area of the wing (A) = 30 m^2

Using the pressure difference we found in part (a):

Force = -2.8325 kPa * 30 m^2

To convert kPa to kN, we multiply by a conversion factor of 1 kN / 1000 N:

Force = -2.8325 kPa * 30 m^2 * (1 kN / 1000 N)

Force = -2.8325 kPa * 0.03 kN

Force = -0.084975 kN

Therefore, the net upward force exerted on the wing is approximately -0.084975 kN.

To find the pressure difference on an airplane wing, we can use Bernoulli's equation, which relates the pressure, velocity, and height of a fluid.

(a) Firstly, let's calculate the pressure difference on the airplane wing:
According to Bernoulli's equation, we have:

P1 + ρgh1 + 1/2 * ρv1^2 = P2 + ρgh2 + 1/2 * ρv2^2

Where:
P1 and P2 are the pressures at points 1 (bottom surface) and 2 (upper surface) respectively.
ρ (rho) is the density of the air.
g is the acceleration due to gravity (approximately 9.8 m/s^2).
h1 and h2 are the heights at points 1 and 2 respectively (but let's assume that they are equal and cancel out of the equation).
v1 and v2 are the velocities at points 1 and 2 respectively.

Since we want to find the pressure difference, we can simplify the equation by canceling out the height terms:

P1 + 1/2 * ρv1^2 = P2 + 1/2 * ρv2^2

Rearranging the equation, we get:

P1 - P2 = 1/2 * ρ(v2^2 - v1^2)

To find the pressure difference, we need to know the density of the air. Let's assume it's 1.2 kg/m^3.

Now, substituting the given values into the equation:

P1 - P2 = 1/2 * 1.2 kg/m^3 * ((101 m/s)^2 - (126 m/s)^2)

Calculating the pressure difference:

P1 - P2 = 1/2 * 1.2 kg/m^3 * (-2505 m^2/s^2)

Finally, converting the pressure difference to kilopascals (kPa):

P1 - P2 = -1503 kPa (note: the negative sign indicates that the pressure on the upper surface is lower than the pressure on the bottom surface)

Therefore, the pressure difference on the airplane wing is -1503 kPa.

(b) To find the net upward force exerted on the wing, we can use the equation:

F = P * A

Where:
F is the force.
P is the pressure difference.
A is the area of the wing.

Substituting the given values:

F = -1503 kPa * (30 m^2)

Calculating the force:

F = -45,090 kPa*m^2

Finally, converting the force to kilonewtons (kN):

F = -45.09 kN

Therefore, the net upward force exerted on the wing is approximately -45.09 kN. Note that the negative sign indicates that the force is acting upward.