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Bernoulli’s Principle

Bernoulli’s Principle. By: Alexandra Jaureguizar . Basics . Created by Dutch-Swiss mathematician Daniel Bernoulli – Hydrodynamica: 1738 As the speed of a moving fluid increases, the pressure within the fluid decreases. . Bernoulli’s .

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Bernoulli’s Principle

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  1. Bernoulli’s Principle By: Alexandra Jaureguizar

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

  3. Bernoulli’s • Basically considered to be a method of conservation of energy • Describes the inverse relationship between velocity and pressure. • Is based on Newton’s first law, or the law of fluid dynamics. • http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html

  4. Bernoulli’s

  5. Bernoulli’s • 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)

  6. 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.

  7. 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

  8. 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?v=WDGNcmEOjs4

  9. Bernoulli’s 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 it’s relation to pressure by using known laws (Newton’s 1st and 2nd , law of fluid dynamics)

  10. Venturi’s effect • Giovanni Battista Venturi – Italian Physicist that proved Bernoulli’s priciple with his pipe experiment • Lab: http://home.earthlink.net/~mmc1919/venturi.html

  11. Venturi’s effect • Can be used to solve for volumetric flow rate= • Can be used to mix liquids and gases and for analyzing differential pressure.

  12. Problem 1 • A liquid (ρ = 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

  13. Problem 2 • Water (p=1000 kg/m^3) 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 10^5 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.

  14. Problem 3 • A horizontal pipe has a cross sectional area 40.0cm^2 at the wider portion and 10.0cm^2 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/cm^3.

  15. 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-Principle-How-it-works.html • http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html

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