What is the derivation of Navier-Stokes equation in cylindrical coordinates?

Answer 1

The Navier-Stokes equations describe the motion of fluid substances and can be derived in cylindrical coordinates by starting from the fundamental principles of conservation of momentum, mass, and energy. In cylindrical coordinates (r, θ, z), the equations account for the radial, angular, and axial components of velocity. The derivation involves applying the continuity equation for mass conservation and the momentum equations, incorporating the effects of pressure, viscous forces, and body forces while using the appropriate transformation of the Laplacian and divergence operators to fit the cylindrical coordinate system. The resulting equations capture the dynamics of fluid flow in cylindrical geometries.