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PHYS16 – Lecture 33

PHYS16 – Lecture 33. Fluids: Bernoulli’s Principle. On a windy day in 1735, a new wig gives Bernoulli an idea. Fluids pre-question.

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PHYS16 – Lecture 33

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  1. PHYS16 – Lecture 33 Fluids: Bernoulli’s Principle On a windy day in 1735, a new wig gives Bernoulli an idea.

  2. Fluids pre-question • You are watering some flowers with a garden hose. You want to water some flowers in the very back of the garden. Assume that the flowers you want to water are at the same level as the hose. What do you have to do to the opening of the hose to increase the range by 4? A) Decrease the area by a factor of 16 B) Decrease the area by a factor of 4 C) Decrease the area by a factor of 2 D) Increase the area by a factor of 2 E) Increase the area by a factor of 4

  3. Outline for Fluids • Fluid Statics • Pressure and Pascal’s Principle • Buoyant Force and Archimedes’ Principle • Fluid Dynamics • Ideal Fluids • Equation of Continuity • Bernoulli’s Equation

  4. Buoyant Force and anchors… • If I have a boat in a pond and I toss out an anchor what happens to the water level in the pond?

  5. Fluid Dynamics: Ideal Fluids

  6. Ideal Fluids • Incompressible – density is a constant • Nonviscous – ignore frictional effects • Irrotational – doesn’t rotate • Laminar – no acceleration Streamlines represent fluid flow

  7. Ideal Fluids • Mass is conserved • Energy is conserved • Momentum is conserved • Continuum hypothesis is true – properties defined at infinitesimal points (density, pressure, temperature, etc.)

  8. Which fluids are ideal? • Water – can be turbulent (waterfall not ideal, ideal in a slow moving river) • Air – compressible (piston not ideal, ideal in a laminar wind) • Honey – viscous fluid such that drag forces can’t be neglected (Not usually ideal) • Blood – pulsatile flow, filled with proteins/cells (ideal in large arteries or veins, not capillaries) • Water • Air • Honey • Blood

  9. What happens if fluid is not ideal?

  10. Poiseuille's Law • When frictional forces dominate velocity decreases • Viscous fluids • Small Diameters Ideal – larger diameters With Friction – small diameters

  11. Fluid Dynamics: Equation of Continuity

  12. Equation of Continuity • For an ideal fluid flowing in a pipe, the volume flow rate through the pipe is constant Narrower section Larger speed Wider section Smaller speed

  13. Example: Water out of faucet • Why does the stream of water flowing from a faucet often get more narrow as the water falls? Gravity accelerates water so velocity increases. If velocity goes up, then area goes down… http://thegoldenspiral.org/wp-content/uploads/2008/10/faucet_waterglass.jpg

  14. Example: Arterial branching • An artery branches into two smaller arteries, each with half the diameter of the first. What is the velocity in the smaller artery compared to the larger artery? • Half • Same • Twice • Four times http://cardiovascres.oxfordjournals.org/content/65/3/619/F4.small.gif

  15. Fluid Dynamics: Bernoulli’s Equation

  16. Bernoulli’s Equation • For an ideal fluid flowing in a pipe, pressure in the pipe is related to the velocity and height of fluid

  17. Discussion: Two sheets in the wind? • What happens if I take two sheets of paper, separate them by 1” and blow between them? A) sheets will move apart B) sheets will come together C) sheets will stay at same spots http://www.practicalphysics.org/imageLibrary/jpeg273/735.jpg

  18. Main Points • Buoyant force • Ideal fluid is incompressible, laminar, nonviscous, and irrotational • Equation of continuity • Bernoulli’s Equation

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