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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
Turbomachinery, in mechanical engineering, describes machines that transfer energy between a rotor and a fluid, including both turbines and compressors. While a turbine transfers energy from a fluid to a rotor, a compressor transfers energy from a rotor to a fluid. [1] [2] It is an important application of fluid mechanics. [3]
The Euler equations first appeared in published form in Euler's article "Principes généraux du mouvement des fluides", published in Mémoires de l'Académie des Sciences de Berlin in 1757 [3] (although Euler had previously presented his work to the Berlin Academy in 1752). [4]
so Euler equation of turbomachinery can be written in terms of rothalpy. This form of the Euler work equation shows that, for rotating blade rows, the relative stagnation enthalpy is constant through the blades provided the blade speed is constant.
The rotational energy typically comes from an engine or electric motor. They are a sub-class of dynamic axisymmetric work-absorbing turbomachinery. [1] The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward into a diffuser or volute chamber (casing), from which it exits.
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.
In turbomachinery, a velocity triangle or a velocity diagram is a triangle representing the various components of velocities of the working fluid in a turbomachine.Velocity triangles may be drawn for both the inlet and outlet sections of any turbomachine.
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. Their general vector form is