Use Bernoulli's equation to estimate the upward force on an airplane's wing if the average flow speed of air is 195 m/s above the wing and 162 m/s below the wing.

You need the wind area for the force. The Bernoulli equation will only give you the pressure difference between the top and bottom of the wing.

You also need the air density, which varies with altitude.

To use Bernoulli's equation to estimate the upward force on an airplane's wing, we need to understand the principle behind it. Bernoulli's equation states that the total pressure in a fluid stream remains constant when there is no external energy input or output. It relates the pressure, velocity, and elevation of a fluid at any two points along a streamline.

To estimate the upward force on an airplane's wing, we can use Bernoulli's equation as follows:

1. Identify the points above and below the wing where we have the average flow speeds of air. Let's call the point above the wing Point A and the point below the wing Point B.

2. Bernoulli's equation is given by:
P₁ + (1/2)ρv₁² + ρgh₁ = P₂ + (1/2)ρv₂² + ρgh₂

Where:
P₁ and P₂ are the pressures at Points A and B, respectively.
ρ is the density of the air.
v₁ and v₂ are the average flow speeds at Points A and B, respectively.
g is the acceleration due to gravity.
h₁ and h₂ are the elevations of Points A and B, respectively.

3. Since the airplane is in steady flight, the elevation at both points can be considered the same. Therefore, the h₁ and h₂ terms cancel out.

4. The upward force on the wing is equal to the pressure difference times the wing area. Mathematically, we have:
Force = (P₁ - P₂) * Wing Area

5. Rearrange Bernoulli's equation to solve for the pressure difference:
(P₁ - P₂) = (1/2)ρ(v₂² - v₁²)

6. Substitute the given average flow speeds of air above and below the wing into the equation.

7. Calculate the pressure difference by substituting the density of air for ρ.

8. Finally, multiply the pressure difference by the wing area to find the upward force on the wing.

Note: Keep in mind that this estimation is a simplified approach and does not consider all factors that affect the actual lift force on an airplane's wing.