More generally, in a non-isotropic Newtonian fluid, the coefficient  that relates internal friction stresses to the spatial derivatives of the velocity field is replaced by a nine-element viscous stress tensor .
There is general formula for friction force in a liquid: The vector differential of friction force is equal the viscosity tensor increased on vector product differential of the area vector of adjoining a liquid layers and rotor of velocity:
where  is the viscosity tensor. The diagonal components of viscosity tensor is molecular viscosity of a liquid, and not diagonal components – turbulence eddy viscosity.