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I would like to determine the pressure drop of fluid in cross flow over a bank of tubes. (see figure 1).

Horizontal cylinders represent tubes. Arrows parallel to the cylinders are labeled "internal flow of fluid through tube." Arrows perpendicular to tubes are labeled "fluid in cross flow over tube bank."

Previously, I've used the correlation listed in "Fundamentals of Heat and Mass Transfer" by Incopera and DeWitt. However, this correlation requires looking up coefficients on a graph (see figure 2 - f is used to mean Eu/k by Incopera).

A graph showing a variety of lines correlating f to Re at a variety of values of Pt, and another graph correlating chi to Pt/Pl at a variety of values of Re

Now, I'd like calculate a pressure drops across a large number of tube banks in a computer program I'm running, so I need a correlation that's either just one equation or based on a lookup table. I tried using tables 1 and 2 from the Thermopedia article on tube banks in crossflow. While this gives reasonable answers at some points, it also produces clearly incorrect answers at others. For example, for a square in-line bank, this correlation shows that Euler's number for b=2.0 exceeds Euler's number for b=1.5 as Re approaches 1e6, which doesn't line up with the graphs and also is obviously an incorrect answer (See figure 3, b=1.5 is in orange and b=2.0 is in green).

Log/log graph showing a blue (b=1.25), orange (b=1.5), and green (b=2.0) line.

Is there a correlation which I could use in my program which is more accurate than the one on Thermopedia?

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    $\begingroup$ So make a data table of x & y values then use vlookup() or interpolation to get the value of y for a given x based on the curve you want. Did this for many characteristics when i first got into excel. There is a program called DataThief which will take an image of a graph and give you x & y values... $\endgroup$
    – Solar Mike
    Mar 10, 2022 at 16:48
  • $\begingroup$ Thank you for recommending DataThief - I think that is the right solution! $\endgroup$
    – Emily Conn
    Mar 10, 2022 at 18:03
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    $\begingroup$ My favourite plot digitizer is the online WebPlotDigitizer. $\endgroup$ Jul 27, 2022 at 20:32

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I developed a solution to this problem and published it as a Python library called tubebank. You can install it using pip. I used the method proposed here by Solar Mike.


Edit The comment made by Solar Mike, regarding the methodology to solve the problem.

So make a data table of x & y values then use vlookup() or interpolation to get the value of y for a given x based on the curve you want. Did this for many characteristics when i first got into excel. There is a program called DataThief which will take an image of a graph and give you x & y values...

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