[Test Your Knowledge] Questions regarding Question 1 of Chemical Production Knowledge (59)

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No one replied over there, so I’m posting this here. Please forgive me if there’s anything incorrect. The question number 1 in “Chemical Production Knowledge (59)” is as follows: Water with a constant flow rate flows in laminar flow within a circular straight pipe. If the inner diameter of the pipe is doubled, the flow resistance will be 1/8 of the original value. The original post can be found at: http://bbs.hcbbs.com/viewthread.php?tid=611340&highlight=%BB%AF%B9%A4%C9%FA%B2%FA%D6%AA%CA%B6. It’s obvious that this question is incorrect; both the person who created it and many of those who answered it gave the answer that the flow resistance would be 1/32 of the original value. However, my calculations show that it should be 1/16. Please let me know if I’m wrong or if the answer itself is incorrect. 1. In laminar flow, the friction loss in a straight pipe can be calculated using Poiseuille’s equation: hf = 32μl u/(ρd²). If the inner diameter of the pipe is doubled, the flow velocity becomes 1/4 of its original value; using the above formula, the resulting value is 1/16.

2. Using the general formula for friction loss in a straight pipe: hf = λl u²/(2d). Since the square of the flow velocity is 1/16, and dividing by twice the diameter gives 1/32. Don’t forget that there is also a friction coefficient involved. In laminar flow, the friction coefficient is inversely proportional to the Reynolds number, and it can be expressed as λ = 64/Re. If the diameter is doubled, the flow velocity becomes 1/4 of its original value, and the Reynolds number becomes 1/2 of its original value. As a result, the friction coefficient becomes twice its original value. Overall, the flow resistance remains 1/16 of its original value. I’m not sure where my calculation went wrong; please share your thoughts