Consider a cylindrical coordinate system ( ρ , φ , z ), with the z–axis the line around which the incompressible flow is axisymmetrical, φ the azimuthal angle and ρ the distance to the z–axis. Then the flow velocity components u and u can be expressed in terms of the Stokes stream function  by:
The azimuthal velocity component u does not depend on the stream function. Due to the axisymmetry, all three velocity components ( u , u , u ) only depend on ρ and z and not on the azimuth φ.
The volume flux, through the surface bounded by a constant value ψ of the Stokes stream function, is equal to 2π ψ.