Buckingham Pi Theorem

Sample questions

  1. What is the pressure within a soap bubble of given radius of curvature?
  2. What is the frequency of oscillation of a small water droplet suspended in air (like the kind you see coming out of astronauts’ straws in zero-gravity environments)?
  3. Sterl’s problem on thermodynamics of a relativistic gas (for homework).
  4. A photograph of an atomic explosion in New Mexico reveals that the radius of the shock wave is 150 meters at a time of 1.5 milliseconds after detonation. Estimate the energy released in the explosion in equivalent tons of TNT.
  5. An isothermal, non-rotating molecular cloud core that is in marginal hydrostatic equilibrium begins to collapse gravitationally. At what rate does mass accrete onto the young star at its center?
  6. Derive the maximum size of a falling raindrop.