Critical pressure ratio for initially dry saturated steam in a nozzle Choose the approximate critical pressure ratio (p2/p1 at choking) for initially dry saturated steam expanding through a nozzle to maximum mass flow.

Introduction / Context:
The critical pressure ratio determines when flow through a nozzle becomes choked, i.e., mass flow reaches a maximum and further downstream pressure reduction does not increase flow. For steam, the critical ratio depends on its thermodynamic state and effective isentropic exponent during expansion.

Given Data / Assumptions:

• Initially dry saturated steam at the nozzle inlet.
• Isentropic (ideal) nozzle expansion to sonic conditions at the throat at critical ratio.
• Negligible inlet velocity and heat transfer.

Concept / Approach:

Using steam tables or empirical relations for saturated steam, the critical pressure ratio for dry saturated conditions is commonly taken as approximately 0.577. For superheated steam, a slightly lower value near 0.546 is widely cited due to a different effective isentropic exponent. The distinction matters in nozzle design, staging, and flow measurement applications.

Step-by-Step Solution:

Verification / Alternative check:

Textbook examples and nozzle discharge tables list p_critical/p0 ≈ 0.577 for saturated inlet steam. Design charts for De Laval nozzles corroborate this selection.

Why Other Options Are Wrong:

0.546 corresponds more closely to superheated steam; 0.582 and 0.601 are outside the typical accepted range.0.500 is a round figure not supported by steam expansion data.

Common Pitfalls:

Applying the ideal-gas formula blindly; steam deviates from ideal-gas behavior, and saturated versus superheated states yield different practical ratios.

Final Answer:

0.577