Modern airplane design calls for a lift, due to the net force of the moving air on the wing, of about 2000 N per square meter of wing area. Assume the air flows past the wing of an aircraft with streamline flow. If the speed of flow past the lower wing surface is 120m/s, what is the required speed over the upper surface to give a lift of 2000 N/m^2? The density of air is 1.20 kg/m^3

To calculate the required speed over the upper surface of the wing to give a lift of 2000 N/m^2, we can use Bernoulli's equation, which relates the pressure, velocity, and height of a fluid.

The equation is as follows:

P + 0.5 * ρ * v^2 + ρ * g * h = constant

Where:
P is the pressure
ρ (rho) is the density of the fluid (in this case, air)
v is the velocity of the fluid
g is the acceleration due to gravity
h is the height above some reference point (often taken as zero)

In this case, we can assume that the height and pressure remain constant, so the equation simplifies to:

0.5 * ρ * v^2 = constant

Since the lift is proportional to the net force on the wing, and the net force is directly related to the change in pressure, we can also say that:

0.5 * ρ * v_lower^2 = 0.5 * ρ * v_upper^2 + 2000 N/m^2

Where:
v_lower is the speed of flow past the lower wing surface (given as 120 m/s)
v_upper is the speed of flow over the upper surface (what we want to find)

Now, we can set up the equation to solve for v_upper:

0.5 * 1.20 kg/m^3 * (120 m/s)^2 = 0.5 * 1.20 kg/m^3 * v_upper^2 + 2000 N/m^2

Simplifying this equation, we get:

8640 = 0.60 * v_upper^2 + 2000

Subtracting 2000 from both sides:

6640 = 0.60 * v_upper^2

And then dividing both sides by 0.60:

v_upper^2 = 11066.67

Finally, taking the square root of both sides:

v_upper ≈ 105.23 m/s

Therefore, the required speed over the upper surface of the wing to give a lift of 2000 N/m^2 is approximately 105.23 m/s.