Potential Equation for Navier-Stokes
The Navier-Stokes equation is a fundamental equation in fluid mechanics, used to describe the motion of fluids in space and time. It consists of two main parts, the continuity equation and the momentum equation. The continuity equation states that the rate of change of density with respect to time, plus the divergence of the mass flux (the product of the density and the velocity), is zero. The momentum equation is more complex, as it takes into account the various forces acting on the fluid. It includes terms for viscosity (ν), pressure (p), and external forces (f). The equation is written as: ∂(ρu)/∂t + ∇ ·(ρu ⃗ u) = − ∇ p + ∇ ·τ ⃗ + ρf ⃗ where τ is the stress tensor, which takes into account the viscosity of the fluid. One may wonder why the equation ∂ρ/∂t + ∇ ·(ρu) = 0 is insufficient. While this equation does satisfy the continuity condition, it does not account for the momentum of the fluid. It describes how the density changes over time...