Fluid and celestial mechanics

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  • Physics 110 - fluid and celestial mechanics
    • Celestial mechanics
      • Kepler's Laws
        • 1. All planets move in elliptical orbits with the sun at one focus
          • Speed changes, both tangential and radial velocity change
        • 2.  A planet sweeps out equal areas in equal amounts of time
          • Planets move faster close to the sun
        • 3.  The square of the orbital period is proportional to the cube of the semi major axis
          • The smaller the velocity, the larger the orbit
      • Newtons AHA moment: Everything in the universe follows a set of rules.
        • F =?Gm1m2                  /r^2
        • Simplifies when on earth to F=-mg
      • Universal gravitation
        • Pulls any two masses together
          • F =?Gm1m                   /r^2
            • Only works for objects that can be treated as point masses
      • Gravitational Potential energy
        • U = ? Gm1m2 /r
          • ugh near earth
        • Conservation of energy- escape speed.
          • NOT mass dependent
          • To get a higher orbit a spec craft must lose energy
          • Gravitational slingshots!
    • Fluids
      • Fluid- something that flows
        • Viscosity
        • Density
        • Pressure
          • Force per unit area
          • Non uniform, greater at the bottom than the top due to extra weight
            • Can use gravity to drive fluid flow
        • Hydrostatics
          • Hydrostatic equilibrium
            • Pressure is constant throughout a system
          • Pascal: An increase in pressure is felt throughout the system
          • Hydraulic press- fluid equivalent to lever
            • Mechanical advantage
      • Can be Newtonian or non- Newtonian. Non Newtonian is 'rheology, study of flow of matter.
      • Two regimes due to drag:
        • Ideal fluids, viscosity not importan
          • High Re, inertia dominates, NS eq not time reversible, turbulent flow
        • Viscous fluids
          • Low Re,  thick, small speed, small length scale, NS eq time reversible, laminar flow regime.
        • Archimedes principle- buoyant force
      • Flow
        • Conservation mass- continuity equation.
        • Bernoulli (high Re)
          • Low speed- high pressure
          • High speed- low pressure
        • Poiseuille flow- low Re
  • F =?Gm1m2                  /r^2

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