Nozzle efficiency — correct definition Select the correct definition of nozzle efficiency for a steam or gas nozzle operating between a given inlet state and a specified outlet pressure.
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ANozzle efficiency = (work done on the blades) / (energy supplied to the blades)
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BNozzle efficiency = (work done on the blades per kg of steam) / (total energy supplied per stage per kg of steam)
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CNozzle efficiency = (actual kinetic energy at nozzle exit per kg) / (ideal isentropic heat drop across the nozzle per kg)
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DNone of the above
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E—
Answer
Correct Answer: Nozzle efficiency = (actual kinetic energy at nozzle exit per kg) / (ideal isentropic heat drop across the nozzle per kg)
Explanation
Introduction / Context:Nozzles convert enthalpy into directed kinetic energy. The nozzle efficiency indicates how effectively the available isentropic enthalpy drop is transformed into jet kinetic energy, a crucial metric for turbine stage matching and thrust devices.
Given Data / Assumptions:
- Specified nozzle inlet state and outlet pressure.
- Adiabatic device with no shaft work.
- Negligible changes in potential energy.
Concept / Approach:The ideal kinetic energy per kilogram obtainable from a given pressure drop equals the isentropic enthalpy drop h_in − h_out,s. The actual kinetic energy equals V_actual^2 / 2. Their ratio defines nozzle efficiency: η_nozzle = (V_actual^2 / 2) / (h_in − h_out,s). This measure excludes blade work and stage aggregation; those are covered by diagram and stage efficiencies.
Step-by-Step Solution:Establish ideal reference using isentropic outlet: Δh_s = h_in − h_out,s.Measure actual outlet velocity V_actual; compute KE_actual = V_actual^2 / 2.Form η_nozzle = KE_actual / Δh_s.Interpret: η_nozzle < 1 due to friction, shock, and boundary-layer losses.
Verification / Alternative check:The velocity coefficient φ_v = V_actual / V_ideal relates as η_nozzle = φ_v^2, providing an alternative way to determine nozzle efficiency from measured velocities.
Why Other Options Are Wrong:Option A is the diagram (blading) efficiency. Option B is the stage efficiency. Option D is false because option C states the standard definition correctly.
Common Pitfalls:Confusing nozzle efficiency with discharge coefficient (area flow losses) or with stage/overall efficiencies that include rotor effects.
Final Answer:Nozzle efficiency = (actual kinetic energy at nozzle exit per kg) / (ideal isentropic heat drop across the nozzle per kg)