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I have a project where I am running water through very small diameter tubes and I am trying to show for this plot that if you double the pressure that you double the flow rate out of these capillaries. The thing is though that I have different diameter tubes that I have tested this relationship for, so I am trying to compare three variables. I have to show that if you double the pressure and keep the diameter constant your flow rate doubles, and I have different diameters to show that this is true. How do I make an elegant graph that compares these three variables?

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  • $\begingroup$ Can you post your data (or a small sample of them) for people to work with? $\endgroup$ – gung - Reinstate Monica Oct 14 '16 at 19:34
  • $\begingroup$ Sure, give me a sec $\endgroup$ – Shrodinger 2016 Oct 14 '16 at 19:53
  • $\begingroup$ That's a long second. Can you post any data? $\endgroup$ – gung - Reinstate Monica Oct 16 '16 at 16:12
  • $\begingroup$ Haha sorry for the delay, I decided to plot the Data as ratio of flow rates vs. Diameter. A correlation of 2 shows that it is linear, and I am happy with the results so I don't need any more help :) $\endgroup$ – Shrodinger 2016 Oct 16 '16 at 19:46
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This depends on what you want to show with your plots. In engineering generally, and fluid mechanics in particular, it is quite common to collapse different parameters using dimensional analysis.

For example in your case (Poiseuille flow, similar to Darcy flow) you could show that, "other things being equal"* the relation $$\frac{Q}{Pd^4}=\text{constant}$$ holds, where $Q$ is flow rate, $P$ is applied (differential) pressure, and $d$ is diameter.

(*where "other things" = outflow pressure, flow length, and viscosity.)


If you expand on the details of your data and on what you want to show, I can give more specific suggestions.

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  1. I'd suggest plotting on the log scale for all variables -- specifically, I'd plot log(flow rate) on the y-axis vs log(pressure) on the x-axis

  2. I'd use colours for the different diameters (or some other way to distinguish them)

  3. I'd plot background lines (in grey, say) of slope 1 so that it would be easy to see if the points of a given colour tended to lie close to the expected slope for the stated relationship.

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