Mach Number Behavior in Convergent-Divergent Nozzles

A convergent-divergent nozzle is a crucial component in aerospace and thermodynamics, often used to accelerate gases to supersonic speeds. The question asks in which portion of this nozzle the Mach number (M) exceeds unity (M > 1).

Understanding Nozzle Sections and Mach Number

Let's analyze the flow characteristics in each section:

• Convergent Portion: This section's area decreases in the direction of flow. If the flow entering is subsonic (Mach number < 1), it accelerates. If the flow entering is supersonic (Mach number > 1), it decelerates.
• Throat: This is the point of minimum area in the nozzle. For a convergent-divergent nozzle designed to achieve supersonic speeds, the flow reaches sonic velocity at the throat. This means the Mach number at the throat is exactly 1 (M = 1).
• Divergent Portion: Following the throat, this section's area increases. When the flow is sonic (M = 1) at the throat, the increasing area in the divergent section allows the flow to expand and accelerate further. This expansion causes the velocity to increase significantly, pushing the Mach number beyond unity (M > 1), thus achieving supersonic flow.

Identifying the Supersonic Region

Based on the principles of compressible fluid dynamics:

• Flow accelerates in the convergent section towards the throat, reaching M=1 if designed for supersonic output.
• The throat is the location where M=1.
• The flow continues to accelerate in the divergent section, becoming supersonic (M > 1).

Therefore, the Mach number is more than unity specifically in the Divergent portion of the nozzle.