Authored by : Dr. Harold Alden Williams Montgomery College at the Takoma Park/Silver Spring Campus, Planetarium Director and Physics and Geology Laboratory CoordinatorPlanetarium The Physics of Star Formation

A few important equations in Newtonian hydrodynamics Continuity equation, conservation of mass Equation of Motion, force/volume, in the fluid continuum Energy Equation Equation of State Newtonian Gravity, Poisson’s Equation

Equation of Continuity, conservation of mass where is the mass density, is the time, is the fluid velocity.

Newton’s Second Law, conservation of momentum written here in per unit volume. Where is the mass density, is the fluid velocity, is the time, is the force per unit volume, is the pressure, is the gravitational potential.

Relationship between total derivative with respect to time and partial derivatives with respect to time for any function g(x;t)

Newton’s Second Law, conservation of momentum in conservative form using previous equation Where is the mass density, is the fluid velocity, is the time, is the momentum density is the pressure, is the gravitational potential. Text

Energy Equation The Energy Equation is the internal energy density is the velocity is the pressure is the local heating functions is the local cooling function is the thermal conductivity is the temperature

Three ways to do science 1. Observation or Experiments, requires large expensive telescopes and/or research grants, doable with graduate student helpers. 2. Theory, largely algebra and calculus, cheap, doable in an undergraduate institution even a community college. 3. Simulation, solving equations on a computer at a super computers center, doable with graduate student helpers in a few institutions with super computer centers.