[Leejohnston]

## Bernoulli’s Equation — Why Airplanes Fly

### 1. The Equation

P + ½ρv² + ρgh = constant

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### 2. What Each Symbol Means

- P = pressure
- ρ = fluid density
- v = fluid speed
- g = gravitational acceleration
- h = height

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### 3. What the Equation Is Telling Us

In a flowing fluid:
- higher speed → lower pressure
- lower speed → higher pressure

Energy is shared between pressure, motion, and height.

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### 4. Where It Comes From (Intuition)

A fluid has a fixed amount of energy along a streamline.

If it speeds up, pressure must drop to compensate.

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### 5. Worked Example

If air speeds up over a wing:
- pressure above drops
- pressure below remains higher

This pressure difference produces **lift**.

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### 6. Real-World Applications

- Aircraft wings
- Carburetors
- Venturi meters
- Weather systems

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### 7. Common Misconceptions

- Wings only work because of Bernoulli → false
- Faster air means stronger force automatically → incomplete
- Lift requires curved wings → false

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### Try It Yourself

Why does blowing between two hanging sheets pull them together?