Foundation of Navier-Stokes Equations in Spherical Coordinates System Based on Coordinate Transformation

Based on the mathematic expression of Navier-Stokes equations in Cartesian coordinate system,this paper presents a simple method for deriving Navier-Stokes equations in spherical coordinate system.Navier-Stokes equations in spherical coordinate system are derived by utilizing a new method by which the coordinate transformation and the simplification of Laplaceian operator, the divergence of particles and the acceleration of particles from Cartesian coordinate system to spherical coordinate system are made. The consistence of Navier-Stokes equations both in Cartesian coordinate system and in spherical coordinate system is proved,and the references for research about the coordinate transformation of Navier-Stokes equations in other coordinate systems are provided.