Question

In turbulent flow through a pipe, the Reynolds number is typically:

• A. Less than 2000
• B. Between 2000 and 4000
• C. Greater than 4000
• D. Exactly 2300

Hint:

The critical limits of Reynolds number differ between pipe flow ($\text{Re} > 4000$ for turbulence) and flow over a flat plate ($\text{Re} > 5 \times 10^5$ for turbulence).
Be sure to check whether the flow is internal or external.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the typical threshold value of the Reynolds number that defines a turbulent flow regime inside a pipe.

Step 2: Key Formula or Approach: The Reynolds number (\(\text{Re}\)) determines the transition of fluid flow regimes. For internal flows through circular conduits, the flow regimes are defined by experimental limits:
Laminar flow: \(\text{Re} < 2000\).
Transition flow: \(2000 \leq \text{Re} \leq 4000\).
Turbulent flow: \(\text{Re} > 4000\).

Step 3: Detailed Explanation:

• The Reynolds number is a ratio of inertial forces to viscous forces in a fluid.

• At low values (\(\text{Re} < 2000\)), viscous forces dominate, and fluid particles travel in smooth, parallel layers (laminar flow).

• As \(\text{Re}\) increases, inertial forces begin to destabilize the laminar layers.

• Once \(\text{Re}\) exceeds 4000, inertial forces dominate, causing flow instabilities, random eddies, and rapid mixing, which are characteristic of turbulent flow.

• The value of 2300 (Option D) is often cited as the lower critical limit where transition begins, but true turbulent flow is established above 4000.

Step 4: Final Answer:
For turbulent flow through a pipe, the Reynolds number is typically greater than 4000.