Question

For a fully-developed pipe flow, which of the following options is/are correct?

• A. For the same maximum velocity, the average velocity is higher in the turbulent regime than that of the laminar regime
• B. Compressibility effects are important if Mach number is less than 0.3
• C. For laminar flow, the friction factor is independent of surface roughness
• D. For laminar flow, friction factor decreases with decrease in Reynolds number

Hint:

In pipe flow, the nature of the flow regime (laminar vs. turbulent) significantly affects the velocity distribution and friction factor. In turbulent flow, the average velocity is typically higher for the same maximum velocity, and the friction factor in laminar flow is independent of surface roughness.

Answer 1

The Correct Option is A, C

Step 1: Understanding the velocity in different flow regimes
In laminar flow, the fluid moves smoothly in layers with a parabolic velocity profile, which leads to a lower average velocity for the same maximum velocity compared to turbulent flow.
In turbulent flow, the velocity profile is flatter and more chaotic, allowing for a higher average velocity for the same maximum velocity.
Thus, option (A) is correct: For the same maximum velocity, the average velocity is higher in the turbulent regime than in the laminar regime.

Step 2: Compressibility effects
Compressibility effects are important when the Mach number exceeds 0.3. The statement in option (B) is incorrect because compressibility effects become significant for Mach numbers greater than 0.3, not less. Thus, option (B) is incorrect.

Step 3: Friction factor for laminar flow
For laminar flow, the friction factor is a function of Reynolds number, and it is independent of surface roughness. This makes option (C) correct.

Step 4: Friction factor vs Reynolds number
In laminar flow, the friction factor decreases with decreasing Reynolds number. However, this is not the case in turbulent flow, which makes option (D) incorrect.

Thus, the correct answer is (A) and (C).