Applications of Bernoulli’s Principle

Chapter 8

faster speedslower speed

more pressure less pressure

If no change in height: P + ½ρv2 = constant

P + ρgy + ½ ρv2 = constant

P + ρgy + ½ ρv2 = constant

P = Pressureρ = densityg = gravity, y = height v = velocity

As the speed of a fluid increases, the pressure in the fluid decreases.

P α 1/v

Motion of fluid energykinetic

Pressure in fluid energypotential

KE + PE is constant

d d/4v

If incompressible fluid (density = ρ),change in pressure?

Bernoulli & FlightBernoulli & Flight• Bernoulli’s Bernoulli’s

Principle is what Principle is what allows birds and allows birds and planes to fly.planes to fly.

• The secret The secret behind flight is behind flight is ‘under the wings.’‘under the wings.’

AIRFOIL

On top: greater air speed and less air pressure

On bottom: less air speed and more air pressure

DRAGDRAGTHRUSTTHRUST

LIFTLIFT

GRAVITYGRAVITY

v1

v2

Net force on wing?

½ Aρ(v22 – v1

2)

ρair = 1.29 kg/m3

Spoiler – airfoil reversed

greater air speedless pressure

less air speedmore pressure

net force: downward

Racecar

Spoiler provides better tractionand avoids lift

Wind over a roof

v

v = 0patm

proof

Patm = Proof + 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 upthe tube.