Mach number (M) is defined as the ratio of the flow speed in the undisturbed stream to the speed of sound in the medium. Is this statement correct?

Introduction:Mach number is fundamental in compressible flow, indicating the importance of compressibility effects and shock phenomena. It compares the flow speed to the medium’s acoustic speed.

Given Data / Assumptions:

• Undisturbed free-stream velocity = V.
• Local speed of sound in the medium = a.
• Idealized steady flow context.

Concept / Approach:By definition, Mach number M = V / a. Classifications follow: subsonic (M < 1), transonic (around 1), supersonic (M > 1), and hypersonic (M ≫ 1). The definition does not require gas-only context, though in liquids a depends on bulk modulus and density and compressibility effects are usually weak at typical speeds.

Step-by-Step Solution:1) Write M = V / a.2) a depends on medium properties (e.g., a = sqrt(gamma * R * T) for ideal gases).3) The statement exactly matches the definition; therefore it is correct.

Verification / Alternative check:Engineering practice in aerodynamics and gas dynamics universally uses M = V/a. Compressibility corrections, shock relations, and similarity laws are built around this definition.

Why Other Options Are Wrong:

• No: Contradicts the standard definition.
• Only for gases: Liquids can also have a defined acoustic speed; the ratio is still meaningful even if less used.
• Only at STP: The definition applies at any state; a simply changes with state.

Common Pitfalls:

• Confusing Mach number with Reynolds number or Froude number.
• Using a at sea-level conditions regardless of altitude or temperature, which skews M.

Final Answer:Yes