Compressible flow regimes – definition of supersonic A flow is called “supersonic” if which of the following conditions holds?

Introduction:
Compressible-flow classification uses the Mach number M = V / a, where a is the local speed of sound. This question asks you to identify the condition for supersonic flow.

Given Data / Assumptions:

• Local thermodynamic state defines a (e.g., a = sqrt(gamma * R * T) for an ideal gas).
• Flow speed V may vary spatially.
• Standard regime naming: subsonic, sonic, supersonic, hypersonic.

Concept / Approach:
By convention, subsonic: M < 1; sonic: M = 1; supersonic: M > 1 up to about 5 (some texts extend to ~6); hypersonic: typically M ≥ 5. The key distinguishing feature is M > 1 for supersonic, where compressibility shocks and expansion fans dominate behaviour.

Step-by-Step Solution:
1) Compute M from local V and a.2) If M > 1, classify as supersonic; if M ≈ 1, sonic; M < 1, subsonic.3) The option that encodes M > 1 is “between 1 and 6.”

Verification / Alternative check:
In a converging–diverging nozzle, the diverging section supports supersonic flow only after the throat reaches M = 1 (choked) and backpressure is low enough; measured Mach numbers then exceed unity.

Why Other Options Are Wrong:

• “Very high velocity” is vague and medium-dependent.
• Discharge difficulty is not a defining criterion.
• Reynolds number compares inertia to viscosity, not sound speed.
• “None” is false because M-based definition exists.

Common Pitfalls:
Using a fixed velocity threshold in m/s without considering the medium’s sound speed.

Final Answer:
the Mach number is between 1 and 6 (i.e., M > 1)