In momentum transfer, the fluid is treated as a continuous distribution of matter. The study of momentum transfer, or fluid mechanics can be divided into two branches: fluid statics (fluids at rest), and fluid dynamics (fluids in motion).
When a fluid is flowing in the x-direction parallel to a solid surface, the fluid has x-directed momentum, and its concentration is υρ. By random diffusion of molecules there is an exchange of molecules in the z-direction.  Hence the x-directed momentum has been transferred in the z-direction from the faster- to the slower-moving layer.
The equation for momentum transfer is Newton's law of viscosity written as follows:
where τ is the flux of x-directed momentum in the z-direction, ν is μ/ρ, the momentum diffusivity, z is the distance of transport or diffusion, ρ is the density, and μ is the dynamic viscosity. Newtons law of viscosity is the simplest relationship between the flux of momentum and the velocity gradient. It may be useful to note that this is an unconventional use of the symbol τ'; the indices are reversed as compared with standard usage in solid mechanics, and the sign is reversed.