# 9.4.2: Relationship Between Dimensionless Numbers

- Page ID
- 769

The Dimensionless numbers since many of them have formulated in a certain field tend to be duplicated. For example, the Bond number is referred in Europe as Eotvos number. In addition to the above confusion, many dimensional numbers expressed the same things under certain conditions. For example, Mach number and Eckert Number under certain circumstances are same.

Example 9.16

Galileo Number is a dimensionless number which represents the ratio of

\[
\label{GalileoNumber:def}

Ga = \dfrac{\rho^2\,g\,\ell^3}{\mu^2}

\]

Example 9.17

Laplace Number is another dimensionless number that appears in fluid mechanics which related to Capillary number. The Laplace number definition is

\[
\label{Laplace:def}

La = \dfrac{\rho \, \sigma \, \ell }{\mu^2}

\]

Example 9.18

The Rotating Froude Number is a somewhat a similar number to the regular Froude number. This number is defined as

\[
\label{RotatingFr:def}

Fr_R = \dfrac{\omega^2\,\ell}{g}

\]

Example 9.19

Ohnesorge Number is another dimensionless parameter that deals with surface tension and is similar to Capillary number and it is defined as

\[
\label{ohnesorge:def}

Oh = \dfrac{\mu}{\sqrt{\rho\,\sigma\,\ell} }

\]

## Contributors and Attributions

Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.