page_title: Steam turbine
section_title: Stage efficiency
hierarchical_section_title: Steam turbine / Principle of operation and design / Impulse turbines / Stage efficiency
caption_attribution_description: English: Convergent Divergent Nozzle
context_page_description: A steam turbine is a device that extracts thermal energy from pressurized steam and uses it to do mechanical work on a rotating output shaft. Its modern manifestation was invented by Charles Parsons in 1884.
  The steam turbine is a form of heat engine that derives much of its improvement in thermodynamic efficiency from the use of multiple stages in the expansion of the steam, which results in a closer approach to the ideal reversible expansion process. Because the turbine generates rotary motion, it is particularly suited to be used to drive an electrical generator—about 85% of all electricity generation in the United States in the year 2014 was by use of steam turbines.
context_section_description: A stage of an impulse turbine consists of a nozzle set and a moving wheel. The stage efficiency defines a relationship between enthalpy drop in the nozzle and work done in the stage.
  Where  is the specific enthalpy drop of steam in the nozzle.
  By the first law of thermodynamics:
  Assuming that  is appreciably less than , we get . Furthermore, stage efficiency is the product of blade efficiency and nozzle efficiency, or .
  Nozzle efficiency is given by , where the enthalpy (in J/Kg) of steam at the entrance of the nozzle is  and the enthalpy of steam at the exit of the nozzle is .
  The ratio of the cosines of the blade angles at the outlet and inlet can be taken and denoted . The ratio of steam velocities relative to the rotor speed at the outlet to the inlet of the blade is defined by the friction coefficient .
   and depicts the loss in the relative velocity due to friction as the steam flows around the blades ( for smooth blades).
  The ratio of the blade speed to the absolute steam velocity at the inlet is termed the blade speed ratio .
   is maximum when  or, . That implies  and therefore . Now  (for a single stage impulse turbine).
  Therefore, the maximum value of stage efficiency is obtained by putting the value of  in the expression of .
  We get: .
  For equiangular blades, , therefore , and we get . If the friction due to the blade surface is neglected then .
caption: Convergent-divergent nozzle
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