Editing Lift (force) (section)

===Navier–Stokes (NS) equations===

These equations represent conservation of mass, Newton's second law (conservation of momentum), conservation of energy, the [[Viscosity#Newtonian and non-Newtonian fluids|Newtonian law for the action of viscosity]], the [[Fourier heat conduction equation#Fourier.27s law|Fourier heat conduction law]], an [[equation of state]] relating density, temperature, and pressure, and formulas for the viscosity and thermal conductivity of the fluid.<ref>Batchelor (1967), Chapter 3</ref><ref>Aris (1989)</ref>

In principle, the NS equations, combined with boundary conditions of no through-flow and no slip at the airfoil surface, could be used to predict lift with high accuracy in any situation in ordinary atmospheric flight. However, airflows in practical situations always involve turbulence in the boundary layer next to the airfoil surface, at least over the aft portion of the airfoil. Predicting lift by solving the NS equations in their raw form would require the calculations to resolve the details of the turbulence, down to the smallest eddy. This is not yet possible, even on the most powerful computer.<ref name=Spalart>Spalart, Philippe R. (2000) Amsterdam, the Netherlands. Elsevier Science Publishers.</ref> So in principle the NS equations provide a complete and very accurate theory of lift, but practical prediction of lift requires that the effects of turbulence be modeled in the RANS equations rather than computed directly.