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

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Question 1 in \"Chemical Production Knowledge (59)\\" reads as follows: Water with a constant flow rate flows laminarly inside 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. There is no doubt that this question is incorrect; both the person who set it and many respondents 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 correct answer is indeed 1/32. 1. In laminar flow, the pressure 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 pressure 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