Question

The Mach Number is a critical parameter in fluid flow when ______.

• A. the fluid is highly viscous
• B. the flow is taking place in an open channel
• C. the velocity of the fluid approaches the speed of sound
• D. surface tension effects are dominant

Hint:

The Mach number ($Ma = v/c$) compares fluid velocity to the speed of sound. It is used to evaluate compressibility effects, which become significant when the fluid speed approaches or exceeds the speed of sound ($Ma \ge 0.3$).

Answer 1

The Correct Option is C

Step 1: Understanding the Problem:
The question asks for the physical condition under which the dimensionless Mach Number ($Ma$) becomes a critical parameter for describing fluid flow behavior.

Step 2: Key Formula or Approach:
The Mach Number is a dimensionless ratio defined as:
\[ Ma = \frac{v}{c} \] where:
$v$ = local velocity of the fluid flow ($\text{m/s}$),
$c$ = speed of sound in that specific fluid medium under the given physical conditions ($\text{m/s}$).

Step 3: Detailed Explanation:

• Compressibility Effects: Under low-velocity conditions ($Ma < 0.3$), fluids can be assumed to be incompressible (constant density).

• Approaching the Speed of Sound: As the fluid flow velocity ($v$) increases and approaches the speed of sound ($c$), the Mach number approaches $1.0$ ($Ma \approx 1$). Under these high-speed conditions, pressure changes in the fluid propagate as compression waves, and compressibility effects can no longer be ignored.

• Flow Regimes based on Mach Number:

• Subsonic flow: $Ma < 1.0$.

• Transonic flow: $Ma \approx 1.0$.

• Supersonic flow: $Ma > 1.0$.

• Other Options: Highly viscous fluid flows are characterized by low Reynolds numbers. Open channel flows are characterized by the Froude number. Surface-tension-dominated flows are characterized by the Weber number.

Step 4: Final Answer:
The Mach Number is a critical parameter when the fluid velocity approaches the local speed of sound, corresponding to option (C).