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In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. [1] The Euler equations can be applied to incompressible and ...
Leonhard Euler is credited of 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]
Euler’s pump and turbine equations can be used to predict the effect that changing the impeller geometry has on the head. Qualitative estimations can be made from the impeller geometry about the performance of the turbine/pump. This equation can be written as rothalpy invariance: =
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. [2] The column will remain straight for loads less than the critical load. The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally.
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.
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments ) acting on the rigid body.
Euler's continued fraction formula connecting a finite sum of products with a finite continued fraction; Euler product formula for the Riemann zeta function. Euler–Maclaurin formula (Euler's summation formula) relating integrals to sums; Euler–Rodrigues formula describing the rotation of a vector in three dimensions