Laminar flow criterion in open channels For open-channel flow, the motion is considered laminar when the Reynolds number (based on hydraulic radius) is below what threshold?

Introduction / Context:
Classifying open-channel flow as laminar or turbulent guides the choice of resistance equations and roughness parameters. While pipes commonly use a 2300 threshold, open channels use a different criterion due to the free surface and characteristic length choice (hydraulic radius).

Given Data / Assumptions:

• Reynolds number for channels: Re = V R_h / ν, where R_h = A/P.
• Newtonian fluid (water), steady uniform flow conceptually.
• Free surface effects present.

Concept / Approach:

Empirical evidence places laminar-channel behavior at Re below approximately 500. For 500 < Re < 2000, transitional effects may occur, and above roughly 2000, fully turbulent regimes dominate for most practical channels.

Step-by-Step Solution:

Verification / Alternative check:

Compare observed velocity profiles: laminar exhibits parabolic profile; turbulent shows fuller profile and eddy viscosity behavior.

Why Other Options Are Wrong:

(b) and (c) do not represent the typical laminar threshold in channels. (d) is incorrect as a practical criterion exists. (e) is overly conservative for channels.

Common Pitfalls:

Using the pipe threshold (2300) directly for open channels; choosing wrong characteristic length (use hydraulic radius, not depth alone).

Final Answer:

less than 500