Identifying a convergent–divergent (Laval) nozzle by geometry A nozzle whose cross-section first decreases from its entrance to a minimum (throat) and then increases from the throat to the exit is:

Introduction / Context:
Supersonic expansion of compressible fluids demands a geometry that accommodates the transition from subsonic acceleration to sonic conditions and then to supersonic speeds. The convergent–divergent (CD or Laval) nozzle provides exactly this shape.

Given Data / Assumptions:

• Single-stream nozzle with smooth area variation.
• Choking occurs at the minimum area (throat).
• Back pressure is appropriately set to allow fully expanded or correctly expanded flow.

Concept / Approach:
In subsonic flow, converging passages accelerate the fluid; at the throat Mach = 1; beyond the throat, a diverging passage accelerates supersonic flow further. Thus, a geometry that first converges to a throat and then diverges is the textbook definition of a CD nozzle.

Step-by-Step Solution:
Identify geometric sequence: converge → throat → diverge.Map to compressible behavior: subsonic acceleration to sonic at throat, then supersonic acceleration downstream.Therefore, the device is a convergent–divergent (Laval) nozzle.

Verification / Alternative check:
Mach number distributions measured in Laval nozzles confirm the accelerate–choke–accelerate pattern consistent with the stated geometry.

Why Other Options Are Wrong:

• (a) Directly contradicts the definition.
• (c) and (d) describe single-section devices lacking a throat followed by the opposite section.
• (e) A throttling valve is a constant-area orifice introducing an isenthalpic pressure drop, not a shaped nozzle.

Common Pitfalls:
Confusing diffusers (pressure-recovery devices) with nozzles (velocity-increase devices).

Final Answer:
a convergent–divergent nozzle (Laval nozzle)