Fluid Flow - Euler Equations
The behavior of ideal compressible gas can be described with Euler equations. The Euler Equations govern the motion of compressible, inviscid fluids.
Euler Equations for Compressible Fluid Flow
The Euler equations describe the motion of ideal compressible fluids without viscosity. These conservation equations form the foundation for understanding gas dynamics and fluid behavior.
Key Equations:
Conservation of Mass (Continuity Equation): $$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0$$
Conservation of Momentum: $$\frac{\partial (\rho \mathbf{v})}{\partial t} + \nabla \cdot (\rho \mathbf{v} \otimes \mathbf{v}) + \nabla p = 0$$
Conservation of Energy: $$\frac{\partial E}{\partial t} + \nabla \cdot ((E + p)\mathbf{v}) = 0$$
Where:
- ρ = Density
- v = Velocity vector
- p = Pressure
- E = Total energy per unit volume