What is the net upward force on an airplane wing of area 20.1 m2 if the speed of air flow is 302 m/s across the top of the wing and 287 m/s across the bottom? (assume the density of air is 1.29 kg/m3)

Using Bernoulli equation:

P+(1/2)ρV²+ρgh=constant.
We get
P1+(1/2)ρV1²=P2+(1/2)ρV2²
ρgh being constant.

Thus
P2-P1=(1/2)ρ(V1²-V2²)
=(1.293*g)*(302²-287²)
=111,952 N/m²
The net upward lift
=111,952*20.1 N/m² m²
=2.25*106 N

Compare with the weight of a Boeing 747-8:
442,000 Kg= 4.33*106 N.

I need answer for this question

Why did the airplane go to therapy? Because it had an "uplift" complex! But let me do the math for you.

To calculate the net upward force on the airplane wing, we need to find the difference in pressure between the top and bottom surfaces of the wing. The difference in pressure creates the lift force.

First, we need to calculate the air pressure on the top and bottom surfaces of the wing. The pressure of the air can be determined using Bernoulli's equation.

Using Bernoulli's equation:

P + (1/2) * ρ * v^2 = constant

where P is the pressure, ρ is the density of air, and v is the speed of air flow.

The pressure on the top of the wing is given by:

P_top + (1/2) * ρ * v_top^2 = constant

And the pressure on the bottom of the wing is given by:

P_bottom + (1/2) * ρ * v_bottom^2 = constant

Since the constant is the same for both equations, we can subtract the equations to find the pressure difference:

P_top - P_bottom = (1/2) * ρ * (v_top^2 - v_bottom^2)

Now, let's plug in the given values:

P_top - P_bottom = (1/2) * 1.29 kg/m^3 * (302 m/s)^2 - (287 m/s)^2

Calculating this gives us the pressure difference.

To calculate the net upward force on the airplane wing, we need to use Bernoulli's equation, which relates the pressure and speed of a fluid in motion:

P + (1/2) * ρ * v^2 = constant

Where:
P is the pressure
ρ is the density of air
v is the velocity of air

Since the airplane is in equilibrium, the net upward force is equal to the difference in pressure between the top and the bottom surfaces of the wing.

Let's calculate the pressure difference step-by-step:

Step 1: Calculate the pressure at the top of the wing.
Using Bernoulli's equation at the top surface of the wing:

P_top + (1/2) * ρ * v_top^2 = constant

Since the airplane is at rest, the constant on both sides of the equation is the same. Rearranging the equation:

P_top = - (1/2) * ρ * v_top^2

Step 2: Calculate the pressure at the bottom of the wing.
Using Bernoulli's equation at the bottom surface of the wing:

P_bottom + (1/2) * ρ * v_bottom^2 = constant

Since the airplane is at rest, the constant on both sides of the equation is the same. Rearranging the equation:

P_bottom = - (1/2) * ρ * v_bottom^2

Step 3: Calculate the net upward force.
The net upward force is equal to the difference in pressure between the top and bottom surfaces of the wing:

Net Upward Force = P_bottom - P_top

Now, let's plug in the values and calculate the net upward force:

P_top = - (1/2) * ρ * v_top^2
P_top = - (1/2) * (1.29 kg/m^3) * (302 m/s)^2

P_bottom = - (1/2) * ρ * v_bottom^2
P_bottom = - (1/2) * (1.29 kg/m^3) * (287 m/s)^2

Net Upward Force = P_bottom - P_top

Substituting the calculated values, we get:

Net Upward Force = (- (1/2) * (1.29 kg/m^3) * (287 m/s)^2) - (- (1/2) * (1.29 kg/m^3) * (302 m/s)^2)

Simplifying, we find:

Net Upward Force = -11,772.36 - (- 11,599.26)

Net Upward Force ≈ -173.1 N

Therefore, the net upward force on the airplane wing is approximately 173.1 N.

To find the net upward force on an airplane wing, we can use the concept of Bernoulli's principle, which states that in a steady flow of fluid, the pressure decreases as the fluid's velocity increases.

The equation for Bernoulli's principle is given by:

P + (1/2)ρv^2 + ρgh = constant

Where:
P is the pressure
ρ is the density of the fluid
v is the velocity of the fluid
g is the acceleration due to gravity
h is the height of the fluid

In this case, let's assume that the height is constant, so we can ignore the last term.

Let's consider two points: one on the top surface of the wing and one on the bottom surface of the wing.

At both points, the pressure is the same, as they are both at the same height. We can cancel out the pressure from the equation.

So, we are left with:

(1/2)ρv_top^2 = (1/2)ρv_bottom^2

To find the net upward force, we need to calculate the difference in pressure between the top and bottom surfaces of the wing.

ΔP = P_top - P_bottom

Since we canceled out the pressure, ΔP = 0.

Therefore, the net upward force on the wing is zero.

This means that the weight of the airplane is balanced by the net downward force due to gravity.