Bernoulli’s Equation

faster speed

slower speed

more pressure

less pressure

If no change in height:

P + ½ρv² = constant

P+ ρgy + ½ ρv² = constant

As the speed of a fluid increases,

the pressure in the fluid decreases.

P α 1/v

Motion of fluid

energy

kinetic

Pressure in fluid

energy

potential

KE + PE is constant

d

d/4

v

If incompressible fluid (density = ρ),

change in pressure?

Bernoulli & Flight

• Bernoulli’s Principle is what allows birds and planes to fly.
• The secret behind flight is ‘under the wings.’

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AIRFOIL

On top: greater air speed and

less air pressure

On bottom: less air speed and

more air pressure

DRAG

THRUST

LIFT

GRAVITY

v₁

v₂

Net force on wing?

½ Aρ(v₂² – v₁²)

ρ_air = 1.29 kg/m³

Spoiler – airfoil reversed

greater air speed

less pressure

less air speed

more pressure

net force: downward

Racecar

Spoiler provides better traction

and avoids lift

Wind over a roof

v

v = 0

p_atm

p_roof

P_atm = P_roof + ½ ρv²

slow air speed

fast air speed

Curve Ball

Golf ball dimples

Winds over a mountain

Shower Curtain

Atomizer – As air passes at top of tube,

the pressure decreases and fluid is drawn up

the tube.