Euler Number in Fluid Mechanics

Introduction to Euler Number in Fluid Mechanics

The Euler number, denoted as Eu, is a dimensionless number used in fluid mechanics to characterize the flow regime. It is named after the Swiss mathematician Leonhard Euler. The Euler number is defined as the ratio of inertial forces to viscous forces in a fluid flow.

Mathematical Background:

The formula for the Euler number is given by:

Eu = V * L / v

Where:
V = velocity of the flow
L = characteristic length
v = kinematic viscosity of the fluid

Parameter Usage:

• velocity = velocity of the flow (in m/s, ft/s, etc.)
• characteristicLength = characteristic length of the flow system (e.g., diameter of a pipe, chord length of an airfoil)
• kinematicViscosity = kinematic viscosity of the fluid (in m²/s, ft²/s, etc.)

Output:

• EulerNumber = value representing the flow regime based on the Euler number

Data Validation:

The numbers should be greater than zero. The formula requires that the kinematic viscosity should not be zero.

Practical Applications:

The Euler number is particularly useful in fluid mechanics for determining the flow regime, which in turn affects various aspects of fluid behavior, such as pressure drop, heat transfer, and drag force.