# Reynolds Number

## Table of Contents

Reynolds number is a dimensionless quantity that is used to help predict flow patterns in different fluid flow situations. It is defined as the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions.

$$ Re = \frac{\rho v L}{\mu} $$

Where:

- \(\small Re\) is the Reynolds Number,
- \(\small \rho\) is the density of the fluid,
- \(\small v\) is the velocity of the fluid relative to the object,
- \(\small L\) is a characteristic linear dimension (such as diameter of a circular pipe, hydraulic diameter of a non-circular pipe, or length of a body), and
- \(\small \mu\) is the dynamic viscosity of the fluid.

It can also be written with the kinematic viscosity \(\small \nu\) instead of dynamic viscosity:

$$ Re = \frac{v L}{\nu} $$