Solution of the Navier-Stokes Equation (NSE) for the incompressible laminar flow along a cylindrical pipe using finite difference method

Abstract

Within this paper, three fluid flow configurations along a cylindrical pipe have been used namely the Poiseuille, rotating Couette flow and the cylindrical flow with a rotating disc where the Navier-Stokes Equation (NSE) was used to solve for the velocities within a specified region of interest. Finite difference method was used in the numerical/computational method and the FORTRAN programming language was utilized in coding. Velocity values taken from the numerical/finite difference method that were compared to the analytical/closed form equation showed fairly accurate velocity profiles The rotating disc problem showed high values for maximum velocities especially when nearing the center of the cylinder but due to the presence of the lid at the top of the cylinder, velocities reach a peak somewhere in between.