Steam nozzles – factors governing maximum (choked) discharge For a convergent–divergent steam nozzle operating under choked conditions, the maximum mass discharge rate depends primarily on which parameters?

Introduction / Context:
In steam turbines and ejectors, convergent–divergent nozzles accelerate steam to high velocities. Once the flow is choked at the throat, understanding what controls the maximum discharge is vital for sizing and performance predictions.

Given Data / Assumptions:

• Dry or superheated steam modeled with standard nozzle relations.
• Choked flow at the throat when the pressure ratio exceeds the critical value.
• Steady, one-dimensional flow with negligible inlet velocity.

Concept / Approach:
Under choked flow, the mass flow rate becomes independent of further reductions in back pressure. The maximum discharge is set by the sonic condition at the throat, which depends on the throat area and the inlet thermodynamic state (pressure and specific volume/temperature). Exit (back) pressure matters only until choking occurs.

Step-by-Step Solution:
Recognize choking: when p_exit ≤ p_critical, Mach number at throat = 1.Write mass flow per unit area in plain form: m_dot/A_throat = function(p0, v0, k) that is independent of p_exit once choked.Therefore, total m_dot ∝ A_throat and is set by inlet total state (p0, T0 or p0, v0).Hence, the governing parameters are throat area and initial pressure/volume, not the final (back) pressure after choking.

Verification / Alternative check:
Performance charts show a plateau of m_dot versus back pressure beyond the critical ratio; increasing A_throat or raising inlet pressure increases m_dot_max.

Why Other Options Are Wrong:

• (c) Back pressure affects discharge only until choking; beyond, it does not raise m_dot.
• (e) Surface roughness influences losses and velocity slightly but does not set the maximum choked m_dot.

Common Pitfalls:
Assuming exit pressure always controls flow rate; once choked, it does not. Confusing throat and exit areas.

Final Answer:
both (a) and (b)