Fluid mechanics problem about selecting pump

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HOMEWORK NO. 13 SOLUTION

Problem Statement

Compare results from the implicit Colebrook equation to the following explicit equation

sometimes used in spreadsheet models as a good approximation:

It is valid for 10 –6

< ε/D < 10 –2

and 5000 < Re <10 +8

. An advantage of the equation is that given

Re and ε/D it does not require an iteration procedure to obtain f, i.e., it is explicit in f. Plot a graph of the percent difference in f as given by this equation and the original Colebrook equation

for Re values in the range of validity of the approximate equation, specifically for ε/D = 10 –4

.

Spreadsheet software is mandatory for completing the required repetitive calculations and

plotting the required graph of percent difference in friction factor f between the two formulas,

     29.0Re74.57.3ln 325.1

 

D f



100e Differenc%  

  

  

f

ff app

100e Differenc%  

  

  

f

ff app

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  (%) fff app

 app

ff