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(Fluid Mechanics: Fundamentals and Applications 4th Edition, Yunus Cengel and John Cimbala, problem 2-88)

Fluid Mechanics Problem

I am having some trouble with the order of operations. In the case of the below equation:

$4\frac{\sqrt{\frac{1}{4}}}{1-\sqrt{\frac{1}{4}}{}}=1$

I do not see how it is true, but in reference to the problem it results from, it just has to be. No matter what I try, I get $4 = 1$. The problem that this originates from is attached as an image. Can someone please let me know whether the problem is with the textbook or with my calculations. This is a simple problem, and yet it is driving me crazy, so I would greatly appreciate some help.

Parcly Taxel
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Kilian Olen
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  • You are right and there must be a mistake somewhere. – Sassatelli Giulio Sep 22 '22 at 22:07
  • I would make sure that you have read understood the result because weather the suggested value is meant to be read as a mixed number or as a 4 times the fraction the result is wrong. So there is either a typo or you misread. – Cow Sep 22 '22 at 22:08
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    You should provide the textbook (title and author) from which this image was taken. – hardmath Sep 22 '22 at 22:11
  • The second sentence at the top of the problem sheet ends abruptly... something is missing, or garbled, maybe. – 311411 Sep 22 '22 at 22:11
  • The textbook is Fluid Mechanics: Fundamentals and Applications 4th Edition, written by Yunus Cengel and John Cimbala. The problem is 2-88. – Kilian Olen Sep 22 '22 at 22:16

1 Answers1

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After careful consideration, I believe that the author made an algebraic error. The author went from

$$\frac{y}{h-y}=\sqrt{\frac{\mu_{\text{lower}}}{\mu_{\text{upper}}}}$$

to

$$y = \frac{\sqrt{\frac{\mu_{\text{lower}}}{\mu_{\text{upper}}}}}{1-\sqrt{\frac{\mu_{\text{lower}}}{\mu_{\text{upper}}}}}h$$

I believe that the denominator should be a plus not a negative. Following this logic the answer would be $y=4/3$.

lonza leggiera
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Kilian Olen
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  • I understand that typos can be common in textbooks, but I'm quite curious at how common mathematical errors are in textbooks. Is the about the same frequency? – Kilian Olen Sep 22 '22 at 22:47
  • Errors happen. That's why textbooks sometimes have "errata" sheets. – David K Sep 22 '22 at 23:08
  • And I agree with your conclusions about the algebra. As additional confirmation, your answer is consistent with the earlier equations, while the book's answer is not. – David K Sep 22 '22 at 23:10