The Reynolds-Averaged Navier-Stokes (RANS) equations are a set of mathematical equations used to describe the motion of fluid substances, such as liquids and gases. They are derived from the Navier-Stokes equations, which govern fluid dynamics, but RANS incorporates averaging techniques to account for turbulent flow. This averaging helps simplify complex fluid behavior, making it easier to analyze and predict. RANS is widely used in engineering and physics to model various applications, including aerodynamics, hydrodynamics, and climate modeling. By averaging the effects of turbulence, RANS provides valuable insights into how fluids interact with surfaces and other fluids, aiding in the design of vehicles, buildings, and other structures.