## Dimensionless Numbers

**Introduction: **The non dimensionalization of the governing equations of fluid flow is important for both theoretical and computational reasons. Non dimensional scaling provides a method for developing dimensionless groups that can provide physical insight into the importance of various terms in the system of governing equations. Computationally, dimensionless forms have the added benefit of providing numerical scaling of the system discrete equations, thus providing a physically linked technique for improving the ill-conditioning of the system of equations. Moreover, dimensionless forms also allow us to present the solution in a compact way. Some of the important dimensionless numbers used in fluid mechanics and heat transfer are given below.

Introduction: The non dimensionalization of the governing equations of fluid flow is important for both theoretical and computational reasons. Non dimensional scaling provides a method for developing dimensionless groups that can provide physical insight into the importance of various terms in the system of governing equations. Computationally, dimensionless forms have the added benefit of providing numerical scaling of the system discrete equations, thus providing a physically linked technique for improving the ill-conditioning of the system of equations. Moreover, dimensionless forms also allow us to present the solution in a compact way. Some of the important dimensionless numbers used in fluid mechanics and heat transfer are given below.

Nomenclature:

Archimedes Number:

Atwood Number:

Note: Used in study of density stratified flows.

Biot Number:

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** Weber Number:

Taylor Number:

Stokes Number:

Rotating Froude Number:

Reynolds Number:

Mach number:

Lewis Number:

Laplace Number:

Galileo Number:

Froude Number:

Euler Number:

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