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Physics Part 1 MECHANICS Physics 1700

Physics Part 1 MECHANICS Physics 1700. Gasses (& Hydrodynamics). W. Pezzaglia Updated: 2013Jul23. 2. Gasses & Hydrodynamics. Gas Laws Atmospheric Pressure Hydrodynamics (Bernoulli’s Law). 3. A. Gasses. Boyle’s Law Kinetic Model of Pressure Temperature of a Gas. 4.

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Physics Part 1 MECHANICS Physics 1700

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  1. Physics Part 1MECHANICSPhysics 1700 Gasses (& Hydrodynamics) W. Pezzaglia Updated: 2013Jul23

  2. 2 Gasses & Hydrodynamics • Gas Laws • Atmospheric Pressure • Hydrodynamics (Bernoulli’s Law)

  3. 3 A. Gasses • Boyle’s Law • Kinetic Model of Pressure • Temperature of a Gas

  4. 4 1. Boyle’s Law • Boyle’s Law (1662) at constant temperature, pressure is inversely proportional to volume, or Robert Boyle(1627 – 1691) https://en.wikipedia.org/wiki/File:Boyles_Law_animated.gif Demo: http://phet.colorado.edu/en/simulation/gas-properties

  5. 5 2. Kinetic Theory of Pressure • 1738 Daniel Bernoulli derives Boyle’s law by assuming gasses consist of moving molecules, and the impacts with wall causes pressure. • Impulse by collision • Time between collisions for box of width “L” knowing x-velocity • Average Force on wall for 1 molecule • Average Kinetic Energy in 3D • Pressure is related to KE • Boyle’s Law for N molecules Daniel Bernoulli (1700 – 1782)

  6. 6 3. Kinetic Theory of Temperature • Equate Kinetic pressure law with ideal gas law and we find average kinetic energy of a mole of gas is • 1900(?) Planck writes that the average Kinetic Energy of a single monoatomic gas atom is given by: • Hence “temperature” is a measure of average kinetic energy of molecules. Boltzmann Constant=R/Na

  7. B. Atmospheric Pressure Barometer Pressure & Altitude Helium Balloons 7

  8. 1. Barometer 1643 Torricelli invents Mercury Barometer 8

  9. 2. Pressure and Altitude Pascal’s law of depth assumes constant density Boyle’s law shows that density of gas decreases in proportion to decrease in pressure Modified law of depth,Pressure “P” at altitude “h”:P0 is pressure at sea levelScale height H=8500 meters 9 Pressure is 0.33 atm at top of Mt. Everest

  10. 3. Helium Balloons Molecular weight of Helium is about 1/7 that of air Hence density of Helium is always about 1/7 that of air at the same pressure. Thus Helium balloons have buoyant force which theoretically could take them to the top of the atmosphere. Record is only about 16.2 km (the balloon expands and bursts) 10

  11. C. Hydrodynamics Torricelli's law (1643) Bernoulli effect Bernoulli equation (1738) 11

  12. 1. Torricelli's law (1643) In brief, the velocity of a fluid exiting at the bottom of a tank of depth “h” is independent of the fluid’s density (i.e. the fluid analogy of Galileo’s law that all bodies fall at same rate independent of mass) 12

  13. 2. Bernoulli Effect 1738, Daniel Bernoulli notes that pressure decreases when a fluid’s velocity increases. 13

  14. 2b. Bernoulli Equation 1738, at any point in the fluid, the sum of the pressure, kinetic energy density and potential energy density is a constant 14 From this can derive Pascal’s law of depth, Torricelli’s law and Bernoulli effect

  15. 3a. Continuity Equation Based upon conservation of mass, when a fluid (liquid or gas) is forced through a smaller pipe, the speed must increase. If the density is unchanged (“incompressible”) the velocity increases inversely proportional to cross section area 15

  16. 3b. Venturi Tube Can be used to measure flow rate v1 of a liquid (or gas) from the observed pressure difference (inferred from “h”) when cross section area is decreased. 16

  17. Notes Demo PHET Bernoulli: http://phet.colorado.edu/en/simulation/fluid-pressure-and-flow Demo PHET for Gas Law: http://phet.colorado.edu/en/simulation/gas-properties Video Mechanical Universe #45 Temperature & Gas Laws 17

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