Tubing Pressure drops with Compressible Fluids

AI Thread Summary
The discussion revolves around calculating tubing sizes for compressible fluids, specifically oxygen, while managing pressure drops. The original poster typically uses Darcy-Weisbach for calculations but seeks to refine their approach after a recent installation error. They developed an Excel workbook to analyze pressure drops across segmented tubing runs, finding that the calculated pressure drop increases with the number of segments. Other participants suggest alternative methods and formulas, emphasizing the importance of accounting for fluid compressibility and flow resistance. The conversation highlights the balance between ensuring adequate tubing size without oversizing, particularly in applications like air conditioning.
Dullard
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Is this a valid technique?
I am a poor, dumb EE often stuck with the odd plumbing calculation. I am often asked questions like: "what size tubing do I need to convey 10 SLPM of 20 PSIG oxygen 200' with no more than 2 PSI pressure drop?"

I generally treat the fluid as in-compressible and use Darcy-Weisbach (I like Bellos for friction factor). So long as the pressure drop is < 10% of the inlet absolute pressure, my calcs correspond pretty well with reality. I try to stay conservative (It's not usually obvious when a tube is a little bit too big).

I had a situation this week where my installers were certain that they knew what they needed (they didn't ask me anything). They screwed up - the tubing will have to be replaced. When I did my normal calculation on what they actually installed it was too small by my standards, but should have worked (just - if I ignored the 10% rule). This got me thinking that I'd like to be able to (semi-accurately) go a bit beyond my previous comfort zone. I created an excel workbook (with some automation) to break a tubing run into 'n' segments. The outlet conditions for one segment are the inlet conditions for the next. This (mathematically) appears to work pretty well: The calculated pressure drop increases with 'n' and converges (increases at a decreasing rate). I'd appreciate any comments on the accuracy/validity/limits of this approach. If I'm missing an alternative approach, I'd love to hear about that, too. Thanks.
 
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That sounds exactly like the approach that I vaguely remember from undergrad fluids class. Typical design problems require only enough design calculations to make sure that a tube is big enough, but not grossly oversized, so high accuracy is rarely needed. Capillary tubes in air conditioning systems may have a tight flow resistance tolerance.
 
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I would approach this differently. From Darcy-Weisbach, we have $$-\frac{dp}{dx}=\frac{\rho v^2 }{2D}f(Re,\epsilon)$$where f is the friction factor. The velocity is related to the mass flow rate m by
$$v=\frac{4m}{\rho \pi D^2}$$So, combining these two equations, we have: $$-\frac{dp}{dx}=\frac{8m^2 }{\rho \pi^2 D^5}f(Re,\epsilon)$$and $$Re=\frac{4m}{\pi D\mu}$$where ##\mu## is the viscosity. Everything on the right hand side is constant, except the density. But, from the ideal gas law, we have: $$\rho=\frac{pM}{RT}$$where M is the molecular weight. Substituting this yields:$$-\frac{dp^2}{dx}=\frac{16RTm^2 }{M \pi^2 D^5}f(Re,\epsilon)$$Integrating this yields: $$p^2=p_0^2-\frac{16RTm^2L }{M \pi^2 D^5}f(Re,\epsilon)$$
 
I was sure that an elegant solution was possible - I posted the question because I thought "Chestermiller will know how to do this." I follow what you did - but I never would have gotten there by myself. Thank you very much!

Jim
 
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