Bernoulli's Principle

A moving fluid trades pressure for speed: wherever it flows faster, it pushes less hard sideways, so its pressure drops. This is why air rushing over a curved wing or water squeezing through a narrow pipe pulls at lower pressure than the slower fluid around it.

P + ½ · ρ · v² = constant

• P — pressure (Pa): the pushing force the fluid exerts per unit area
• ρ — density (kg/m³): how much mass is packed into each cubic meter of the fluid
• v — speed (m/s): how fast the fluid is flowing at that point

Water at 1000 kilograms per cubic meter flows at 2 meters per second through a wide pipe, then speeds up to 4 meters per second in a narrow section. How much does the pressure drop?

• ρ = 1000 kg/m³
• v₁ = 2 m/s
• v₂ = 4 m/s

1. ΔP = ½ · ρ · (v₂² − v₁²)
2. ΔP = ½ · 1000 kg/m³ · (16 − 4) m²/s²

ΔP = 6000 Pa

Water flows from a wide pipe into a narrow section, so its speed increases. What happens to its pressure in the narrow section?

• It increases
• It decreases
• It stays the same

Same water, still 1000 kilograms per cubic meter, still 1 meter per second in the wide pipe, but now it speeds up to 3 meters per second in the narrow part. What is the pressure drop?

• 4000 Pa
• 8000 Pa
• 1000 Pa