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The Euler number (Eu) is a dimensionless number used in fluid flow calculations. It expresses the relationship between a local pressure drop caused by a restriction and the kinetic energy per volume of the flow, and is used to characterize energy losses in the flow, where a perfect frictionless flow corresponds to an Euler number of 0.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
In fluid dynamics, the Euler equations are a set of partial differential ... Substitution of these inversed relations in Euler equations, defining the Froude number, ...
In fluid dynamics, inviscid flow is the flow of an inviscid fluid which is a fluid with zero viscosity. [1] The Reynolds number of inviscid flow approaches infinity as the viscosity approaches zero. When viscous forces are neglected, such as the case of inviscid flow, the Navier–Stokes equation can be simplified to a form known as the Euler ...
Euler number (physics), the cavitation number in fluid dynamics. Euler number (algebraic topology) – now, Euler characteristic, classically the number of vertices minus edges plus faces of a polyhedron. Euler number (3-manifold topology) – see Seifert fiber space; Lucky numbers of Euler [4]
Leonhard Euler is credited with introducing both specifications in two publications written in 1755 [3] and 1759. [4] [5] Joseph-Louis Lagrange studied the equations of motion in connection to the principle of least action in 1760, later in a treaty of fluid mechanics in 1781, [6] and thirdly in his book Mécanique analytique. [5]
The Euler pump and turbine equations are the most fundamental equations in the field of turbomachinery. These equations govern the power, efficiencies and other factors that contribute to the design of turbomachines. With the help of these equations the head developed by a pump and the head utilised by a turbine can be easily determined.
The dispersed phase is solved by tracking a large number of disperse particles, bubbles or droplets. The dispersed phase can exchange momentum, mass and energy with the fluid phase. [1] Euler-Euler two phase flow is characterised by the volume-averaged mass conservation equation for each phase. [4]