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Applications of Bernoulli’s Principle
faster speedslower 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 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.