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PHYS16 – Lecture 31

PHYS16 – Lecture 31. Ch. 14 Fluid Mechanics. This Week. Fluid Statics Pressure and Pascal’s Principle Buoyant Force and Archimedes’ Principle Fluid Dynamics Equation of Continuity Bernoulli’s Equation. Fluids pre-question.

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PHYS16 – Lecture 31

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  1. PHYS16 – Lecture 31 Ch. 14 Fluid Mechanics

  2. This Week • Fluid Statics • Pressure and Pascal’s Principle • Buoyant Force and Archimedes’ Principle • Fluid Dynamics • Equation of Continuity • Bernoulli’s Equation

  3. Fluids pre-question • Salt water has a greater density than freshwater. A boat floats in both freshwater and salt water. The buoyant force on the boat in salt water is _________ that in freshwater. • Equal to • Smaller than • Larger than • Not enough information

  4. Fluids pre-question • You are in a boat filled with large rocks in the middle of a small pond. You begin to drop the rocks into the water. What happens to the water level of the pond? • It rises. • It falls. • It doesn’t change. • It rises momentarily and then falls when the rocks hit bottom. • Not enough information

  5. Fluid Statics: Pressure

  6. Pressure • Pressure- quantity that relates force per area, force is perpendicular to area • Scalar • Units = Pa = N/m2 • Atmospheric pressure = 1E5 Pa = 760 torr

  7. Discussion: Bed of Nails • Why would you want to lay on a bed of nails instead of just one nail? • Why might it be easier for a 20-kg child to lay on a bed of nails than a slightly larger 60-kg adult? http://www.ill-use.com/home/images/stories/bed-of-nails/nails-kid.jpg

  8. Water Pressure – constant density • Find the pressure difference across a cube of water Would the pressure change be larger in salt water or fresh water? http://www.open2.net/open2static/source/file/root/0/30/19/124156/pressure_cube_b.jpg

  9. Example: Container Height • If I start filling the following container with water, where will the highest water level be? Manoharan Lectures, Harvard University, Fall 2010

  10. Example: Submarines • A submarine is submerged to a depth of 960 m. What air pressure is needed to blow water out of the ballast tanks? (density = 1024 kg/m3) http://www.yesmag.ca/how_work/submarine.html

  11. Air Pressure – Not constant density • As height increases pressure decreases and density decreases http://eo.ucar.edu/webweather/images/density.gif

  12. Example Question: Pistons • Given that the density of air is proportional to pressure, how does the air pressure inside a confined volume change if the volume decreases by half? http://www.tpub.com/fireman/25.htm Changes by 2…

  13. Fluid Statics: Buoyant Force

  14. Archimedes’ Principle • Buoyant force = the weight of the water displaced Density water = 1E3 kg/m^3 Density air = 1 kg/m^3 http://www.open2.net/open2static/source/file/root/0/30/19/124156/pressure_cube_b.jpg

  15. Discussion: Bathtub physics • If the object is floating, is the buoyant force greater than the force of gravity on the object? • Is there a buoyant force for a sunken object? • Can the buoyant force ever cause an object to go down instead of up?

  16. Example: Buoyant force on objects • Buoyant force on brick in water Volume= 0.2 m X 0.08 m X 0.05 m FB=8 N • Buoyant force on ball in water Volume= (4/3)pi(0.025)^2 FB=0.6 N • Buoyant force on Diet Coke vs. Coke Volume= same in both cases FB=same Coke sinks more than Diet Coke bec. Coke more dense (Fgravity is more for Coke!)

  17. Main Points • Pressure = Force/Area • Pressure varies with height • Water – density is constant • Air – density is not constant • Buoyant force is equivalent to the weight of the water displaced

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