# Taylor Number

on . Posted in Dimensionless Numbers

Taylor number, abbreviated as Ta, a dimensionless number, also called Taylor-Reynolds number, is used in fluid dynamics to characterize the relative importance of inertial forces to viscous forces in a fluid flow.  It is the quantity that characterizes the importance of centrifugal forces due to the rotation of a fluid about an axis, relative to viscous forces.

The Taylor number is commonly used in studies of rotating flows, such as those found in geophysical and astrophysical contexts, as well as in engineering applications involving rotating machinery, like turbines and impellers.

The Taylor number provides insight into the stability of a flow regime.  A low Taylor number indicates that viscous forces dominate, resulting in smooth, laminar flow.  In contrast, a high Taylor number suggests that inertial forces are more significant, potentially leading to turbulent flow patterns.  Understanding the Taylor number helps researchers and engineers predict and analyze the behavior of fluid flows under different conditions, aiding in the design and optimization of various systems and processes involving fluid dynamics.

### Taylor Number formula

$$Ta \;=\; 4 \; \Omega^2 \; r^4 \;/\; \nu^2$$
Symbol English Metric
$$Ta$$ = Taylor number $$dimensionless$$ $$dimensionless$$
$$\Omega$$  (Greek symbol Omega) = characteristic angular velocity $$deg\;/\;sec$$ $$rad\;/\;s$$
$$r$$ = characteristic linear dimension perpendicular to the rotation axis $$in$$ $$mm$$
$$\nu$$  (Greek symbol nu) = kinematic viscosity $$ft^2\;/\;sec$$ $$m^2\;/\;s$$

Tags: Fluid