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Maximum efficiency condition for a reaction turbine Let V be the absolute velocity of water at inlet making angle α with the tangent, so its whirl component is V cos α. Find the blade speed Vb for maximum hydraulic efficiency (ideal analysis). Choose the correct relation.

Mechanical Engineering Steam Nozzles and Turbines Difficulty: Medium
Choose an option
  • A
    Vb = 0.5 × V cos α
  • B
    Vb = V cos α
  • C
    Vb = 0.5 × V<sub>2</sub> cos α
  • D
    Vb = V<sub>2</sub> cos α

Answer

Correct Answer: Vb = 0.5 × V cos α

Explanation

Given/Definitions

  • Guide vane angle α gives the whirl component at inlet: Vw1 = V cos α.

Concept/Approach

  • From Euler's turbine equation and ideal velocity triangles (no losses, outlet whirl minimized), hydraulic efficiency is maximized when blade speed equals Vb = Vw1/2.

StepTherefore, Vb = (V cos α)/2.

Final AnswerVb = 0.5 × V cos α

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