Bernoullis Principle

1
Bernoullis Principle Fluid Continuity
2
Principles of Fluid Flow

• The speed of a fluid depends on the cross
  sectional area
• This is because the same volume of fluid must
  pass through the given object per unit of time.
• Fluid Continuity
• A1v1 A2v2
• When you put your finger over the end of the
  hose, what happens?
• Animation

3
Bernoullis Principle

• Pressure also changes with velocity.
• Bernoullis Principle
• When the speed of a fluid increases, the pressure
  within the fluid decreases.
• This has to do with conservation of energy.
• If the velocity increases, the KE increases.
• In order to keep the total energy constant, a
  quantity must decrease.
• Since PE is constant, work must be done.
• W Fd and P F/A ? W PAd PV
• The volume stays the same, therefore the pressure
  decreases.

4
Applications of Bernoulli

• Why during storm might a roof blow off?
• There is fast moving air above (bunched up
  streamlines) the roof. Faster moving air means
  less pressure above than inside.

5
Applications of Bernoulli

• A small jeep has a soft, ragtop roof. When the
  jeep is at rest the roof is flat. When the jeep
  is cruising at highway speeds with its windows
  rolled up, does the roof
• Bow upward
• Remain flat
• Bow downward
• A. The roof bows upward
• When the jeep is in motion air flows over the top
  of the roof, while the air inside the jeep is at
  restsince the windows are closed. Thus, there
  is less pressure over the roof than under it. As
  a result the roof bows upward.