Basic Laws

Objectives

Our main objective will be to write the laws of physics (mass conservation, momentum, and energy conservation) in a form that we can really use to say meaningful things about flow fields.

We also want to get some idea how these laws may be used to develop systems of equations that can be solved on a computer.

We also would like to know how the equations may be transformed to partial differential equations in appropriate coordinate systems that may possible be solved analytically.

Performance Criteria

• Ability to define the vocabulary
• Can write conservation laws for a given fixed region
• Can approximate conservation laws for small regions
• Can evaluate volume and surface integrals appearing in fluid mechanics
• Can simplify governing equations using symmetries
• Can evaluate stress from the stress tensor
• Can derive partial differential equations from general conservation laws
• Can evaluate and simplify the momentum equation for stationary states
• Can transform conservations laws into other forms
• Can apply the integral conservation laws

Vocabulary

• Continuity equation
• Leibnitz rule
• Divergence theorem
• Momentum
• Body force
• Stress tensor
• Inviscid
• Viscous
• Differential conservation equations
• Integral conservation equations