If Reynolds number is less than 500, the flow is said to be laminar for the:
- Afree surface flowCorrect
- Bflow through soil
- Cflow between parallel plates
- Dpipe flow
Solution
Concept
In open channel (free surface) flow, Reynolds number is based on hydraulic radius R, and the flow is laminar when Re < 500.
Formula
Re = V R / ν, where R = A / P
Step-by-step solution
1. Recall the laminar limits of Reynolds number for each flow type. 2. Free surface (open channel) flow, using hydraulic radius: laminar if Re < 500. 3. Flow through soil (Darcy law valid): Re < 1. 4. Flow between parallel plates: laminar up to about Re = 1000. 5. Pipe flow, using diameter: laminar if Re < 2000. 6. So Re < 500 matches free surface flow.
Explanation
For open channel flow, Reynolds number uses hydraulic radius as the length. With this length, flow stays laminar only when Re is below about 500. This is why option A is correct.
Why the other options are wrong
B: For flow through soil, the laminar limit is Re < 1, not 500. C: For flow between parallel plates, the laminar limit is about Re < 1000. D: For pipe flow, the laminar limit is Re < 2000.
Shortcut
Remember the laminar limits: soil 1, open channel 500, parallel plates 1000, pipe 2000.
Common mistake
Students often use the pipe limit of 2000 for all flows. They forget that open channel flow uses hydraulic radius, which gives a lower limit of 500.
Correct answer: A) free surface flow