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Derivation of Euler’s pump and turbine equation Velocity triangles for a radial turbine Velocity triangles for an axial

Derivation of Euler’s pump and turbine equation Velocity triangles for a radial turbine Velocity triangles for an axial turbine Velocity triangles for a radial pump. Absolute specific stagnation energy.

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Derivation of Euler’s pump and turbine equation Velocity triangles for a radial turbine Velocity triangles for an axial

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  1. Derivation of Euler’s pump and turbine equation • Velocity triangles for a radial turbine • Velocity triangles for an axial turbine • Velocity triangles for a radial pump

  2. Absolute specific stagnation energy Starting with Newton 2. law, the absolute acceleration for stationary flow can be derived as: Where: E = Specific stagnation Energy [J/kg] c = Velocity [m/s] f = Friction [N/kg] The absolute specific stagnation energy is constant along a streamline in a frictionless system. Ref. Grunnkurs i Hydrauliske Strømningsmaskiner

  3. The Rotalpy is constant along a streamline Relative specific stagnation energyRotalpy Relative acceleration in a rotating channel can be derived as: Where I = Rotalpy [J/kg] c = Velocity [m/s] f = Friction force [N/kg]

  4. Energy conversion w c

  5. cu cm w c

  6. Euler’s pump and turbine equation

  7. u1 c1 w1 u2 w2 c2 Velocity Triangles for a Radial Turbine

  8. Velocity triangles for an axial turbine Guidevanes Runnerblades

  9. u2 c2 w2 w1 c1 u1 c w

  10. w1 c1 u1 w2 c1 u2 Velocity Triangles for a Radial Pump w

  11. SVARTISEN u1=75 m/s P = 350 MW H = ? m Q* = 71,5 m3/S D0 = 4,86 m D1 = 4,31m D2 = 2,35 m B0 = 0,28 m n = 333 rpm c1 w1 b1 = 63o hh = 96 % cm1 = 13,9 m/s cu1 = 68 m/s

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