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Applications of Bernoulli’s Principle. P+ ρ gy + ½ ρ v 2 = constant. If no change in height: P + ½ ρ v 2 = constant. slower speed. faster speed. more pressure. less pressure. As the speed of a fluid increases , the pressure in the fluid decreases . P α 1/v. kinetic.
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P+ ρgy + ½ ρv2 = constant If no change in height: P + ½ρv2 = constant slower speed faster speed more pressure less pressure
As the speed of a fluid increases, the pressure in the fluid decreases. P α 1/v
kinetic energy Motion of fluid Pressure in fluid energy potential KE + PE is constant
v d/4 d 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.’
AIRFOIL On top: greater air speed and less air pressure On bottom: less air speed and more air pressure
LIFT THRUST DRAG GRAVITY
v2 v1 Net force on wing? ½ Aρ(v22 – v12) ρair = 1.29 kg/m3
Spoiler – airfoil reversed less air speed more pressure greater air speed less pressure net force: downward
Racecar Spoiler provides better traction and avoids lift
Wind over a roof Patm = Proof + ½ ρv2 v proof v = 0 patm
slow air speed fast air speed
Atomizer – As air passes at top of tube, the pressure decreases and fluid is drawn up the tube.