The Reynolds-averaged Navier-Stokes equations (RANS) are a set of equations used in fluid dynamics to describe the motion of fluid substances. They are derived from the Navier-Stokes equations, which govern fluid flow, but incorporate averaging techniques to account for turbulence. This averaging helps simplify complex flow patterns, making it easier to analyze and predict fluid behavior in various applications. RANS equations are widely used in engineering fields, such as aerospace and mechanical engineering, to model airflow over aircraft wings or the flow of liquids in pipes. By using these equations, engineers can design more efficient systems and improve performance while managing turbulent flow conditions.