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An example of a velocity triangle drawn for the inlet of a turbomachine. The "1" subscript denotes the high pressure side (inlet in case of turbines and outlet in case of pumps/compressors). A general velocity triangle consists of the following vectors: [1] [2] V = absolute velocity of the fluid. U = blade linear velocity.
With the help of these equations the head developed by a pump and the head utilised by a turbine can be easily determined. As the name suggests these equations were formulated by Leonhard Euler in the eighteenth century. [1] These equations can be derived from the moment of momentum equation when applied for a pump or a turbine.
The velocity triangle [2] (Figure 2.) for the flow process within the stage represents the change in fluid velocity as it flows first in the stator or the fixed blades and then through the rotor or the moving blades. Due to the change in velocities there is a corresponding pressure change. Figure 2. Velocity Triangle for fluid flow in turbine
Usually the flow velocity (velocity perpendicular to the tangential direction) remains constant throughout, i.e. V f1 =V f2 and is equal to that at the inlet to the draft tube. Using the Euler turbine equation, E/m=e=V w1 U 1, where e is the energy transfer to the rotor per unit mass of the fluid. From the inlet velocity triangle,
The color triangle formed by velocity vectors ,, is called the velocity triangle. This rule was helpful to detail Eq.(1) become Eq.(2) and wide explained how the pump works. Fig 2.3 (a) shows the velocity triangle of a forward-curved vane impeller; Fig 2.3 (b) shows the velocity triangle of a radial straight-vane impeller.
The radial component of the fluid velocity is negligible. Since there is no change in the direction of the fluid, several axial stages can be used to increase power output. A Kaplan turbine is an example of an axial flow turbine. In the figure: U = Blade velocity, V f = Flow velocity, V = Absolute velocity, V r = Relative velocity,
Velocity triangles for an inward-flow radial (IFR) turbine stage with cantilever blades The radial and tangential components of the absolute velocity c 2 are c r2 and c q2 , respectively. The relative velocity of the flow and the peripheral speed of the rotor are w 2 and u 2 respectively.
The image describes the changes in velocity triangles on decreasing the specific speed or decreasing the pressure head, and finally shows the evolution from the Francis hydraulic turbine to the Kaplan hydraulic turbine. Nomenclature of a velocity triangle: A general velocity triangle consists of the following vectors: [1] [2]