# Fluid and celestial mechanics

?
• 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
• 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