Bernoulli

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Bernoullis Principle

• By Alexandra Jaureguizar

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Basics

• Created by Dutch-Swiss mathematician Daniel
  Bernoulli Hydrodynamica 1738
• As the speed of a moving fluid increases, the
  pressure within the fluid decreases.

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Bernoullis

• Basically considered to be a method of
  conservation of energy
• Describes the inverse relationship between
  velocity and pressure.
• Is based on Newtons first law, or the law of
  fluid dynamics.
• http//hyperphysics.phy-astr.gsu.edu/hbase/pber.ht
  ml

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Bernoullis
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Bernoullis

• Used to describe an ideal situation in absence of
  other forces (e.g. viscosity)
• Has multiple aspects that contribute to the
  principle
• Laminar (Streamlined) Flow
• Turbulent (Uneven)

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Laminar (Streamlined) Flow

• Smooth/Regular
• Always has the same speed and direction
• Characterization
• All particles that pass a particular point follow
  a path identical to all particles that passed the
  point earlier.

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Laminar (Streamlined) Flow

• Occurs when viscosity is absent.
• Basic rules of BP (ideal)
• Flow smoothly
• No swirls or variations
• No flow separation
• Density is uniform

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Turbulent (Uneven/Ram) Flow

• May have differing speed, tend to go in the same
  direction
• Often occurs when a stream is divided by a
  barrier.
• Used in flight/ for aircraft.
• Ex. (demonstration)
• http//www.youtube.com/watch?vWDGNcmEOjs4

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Bernoullis Purpose

• To show us how much the pressure within a moving
  fluid increases or decreases as the speed of the
  fluid changes.
• It establishes the principle behind velocity and
  its relation to pressure by using known laws
  (Newtons 1st and 2nd , law of fluid dynamics)

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Venturis effect

• Giovanni Battista Venturi Italian Physicist
  that proved Bernoullis priciple with his pipe
  experiment
• Lab http//home.earthlink.net/mmc1919/venturi.ht
  ml

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Venturis effect

• Can be used to solve for volumetric flow rate
• Can be used to mix liquids and gases and for
  analyzing differential pressure.

                                               
                 
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Problem 1

• A liquid (? 1.65 g/cm3) flows through two
  horizontal sections of tubing joined end to end.
  In the first section the cross-sectional area is
  10.0 cm2, the flow speed is 265 cm/s, and the
  pressure is 1.20 x105 Pa. In the second section
  the cross-sectional area is 2.50 cm2.(a)
  Calculate the smaller section's flow speed. (b)
  Calculate the smaller section's pressure

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Problem 2

• Water (p1000 kg/m3) flows down a pipe of
  circular cross section from a height of 10m to
  the ground and out into the atmosphere. The gauge
  pressure inside the pipe at the elevated level is
  105 Pa. The pipe has a radius of 10 cm at the
  elevated level and a radius of 7.5 cm at the
  ground level. Determine the speed of the water
  flow as it exits at the ground level.

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Problem 3

• A horizontal pipe has a cross sectional area
  40.0cm2 at the wider portion and 10.0cm2 at the
  constriction. Water is flowing in the pipe, and
  the discharge from the pipe is 6.00 l/s,
• -A) Find the flow speeds in the wide and
  narrow portions. -B) Find the pressure
  difference between these portions. -C) Find the
  difference in height between the mercury columns
  in the U- shaped tube. Density of mercury is
  13.6 g/cm3.

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References

• http//library.thinkquest.org/27948/bernoulli.html
  
• http//www.ehow.com/how_2247750_explain-bernoullis
  -theorem-experiment-kids.html
• http//home.earthlink.net/mmc1919/venturi_discuss
  _math.html
• http//www.scienceclarified.com/everyday/Real-Life
  -Chemistry-Vol-3-Physics-Vol-1/Bernoulli-s-Princip
  le-How-it-works.html
• http//hyperphysics.phy-astr.gsu.edu/hbase/pber.ht
  ml