In Pipe Flow the Reynolds number can be written in simplified form:

{\rm Re} =  \frac{j_m \cdot d}{\mu(T,p)} = \frac{4 \, \dot m}{\pi \, d} \cdot \frac{1}{\mu(T,p)}

where

	mass flux
	mass flowrate
	characteristic linear dimension of the pipe (or exactly a pipe diameter in case of a circular pipe)
	dynamic viscosity as function of fluid temperature and pressure

{\rm Re} =  \frac{u \cdot d}{\nu} =  \frac{\rho \cdot u \cdot d}{\mu} = \frac{j_m \cdot d}{\mu(T,p)}

where

	average cross-sectional flow velocity
	fluid density
	kinematic viscosity

The mass flowrate is constant along the pipe: .

In many engineering application the pipeline is built from inter-connected pipes or ducts with constant cross-sectional area which means that mass flux is also constant along pipes: .

Equation shows that in this case a variation of Reynolds number along the pipe will be a function of fluid viscosity only: which in turn is a function of fluid temperature and pressure along the pipe.

See also