Critical pressure ratio comparison For flow of initially superheated steam through a nozzle, the critical pressure ratio (p2/p1 at choking) is how compared with the value for initially dry saturated steam?

Introduction / Context:
The critical pressure ratio indicates the pressure ratio at which mass flow through a nozzle becomes choked. For steam, this ratio depends on the inlet state. Designers must know how it changes between saturated and superheated inlet conditions to size throats correctly and predict mass flow.

Given Data / Assumptions:

• Isentropic (ideal) expansion to sonic velocity at the throat.
• Initially superheated versus initially dry saturated inlet states.
• Steam's effective isentropic exponent varies with state.

Concept / Approach:

Empirical/thermodynamic data show that the critical pressure ratio for initially dry saturated steam is about 0.577, whereas for initially superheated steam it is lower, commonly near 0.546 under typical conditions. Hence, for superheated inlet, choking occurs at a smaller downstream-to-upstream pressure ratio; equivalently, a larger pressure drop is needed to reach sonic conditions compared with the saturated case.

Step-by-Step Solution:

Verification / Alternative check:

Design charts and nozzle discharge tables corroborate the lower critical ratio for superheated conditions, reflecting different thermodynamic response (effective k) during expansion.

Why Other Options Are Wrong:

More/approximately equal: conflict with standard reference values.Twice or undefined: physically and dimensionally incorrect.

Common Pitfalls:

Applying the ideal-gas formula without adjusting for real-steam behavior and state dependence, which leads to inaccurate nozzle sizing.

Final Answer:

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