Bernoulli’s Principle states that within a steady, incompressible, and frictionless flow, the total energy per unit volume remains constant along a streamline. That energy comprises:
Pressure energy (static pressure, p)
Kinetic energy (½ ρ v², where ρ is density, v is fluid speed)
Potential energy (ρ g h, associated with elevation h)
In equation form:
p + ½ρv² + ρgh = constant
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🌀 Simplified Form (Horizontal Flow)
For flows where elevation doesn’t change (i.e., horizontal flow), the equation reduces to:
p + ½ρv² = constant
This means: when fluid speed increases, pressure decreases, and vice versa .
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⚡ How It Works: Energy Conservation
Bernoulli’s Principle is a direct consequence of energy conservation: as fluid accelerates (increasing kinetic energy), pressure energy must drop if elevation remains fixed.
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✈️ Real‑World Applications
1. Airplanes: Faster airflow over the wing’s top surface lowers pressure, creating lift .
2. Venturi effect: Narrow sections of a pipe speed up flow and reduce pressure—used in carburetors, Venturi meters, and atomizers .
3. Everyday phenomena: High-speed air between moving vehicles creates low pressure, pulling them toward each other .
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⚠️ Important Caveats & Misconceptions
Only valid for steady, incompressible, non-viscous (frictionless) flows .
Common myths (e.g., “air over top and bottom of wing must reach simultaneously”) are false—Bernoulli’s principle does not require equal transit times .
It applies along a streamline—not between completely separate flow regions.
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🔍 Example: Hose Nozzle
If water flows from a large hose into a thinner nozzle, its velocity increases, so pressure in the nozzle drops. Bernoulli’s equation lets us calculate the pressure difference based on speed change .
✅ Summary
Bernoulli’s Principle balances pressure, velocity, and elevation in flowing fluids.
Core idea: Faster flow → lower pressure; slower flow → higher pressure.
Applications: Aviation, fluid flow measurement, fuel mixing, everyday airflow effects.
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