Tubing Pressure drops with Compressible Fluids

In summary: Chestermiller said in a response to a question about how to calculate tubing size for conveying oxygen: "The approach 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."
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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: $$p^2=p_0^2-\frac{16RTm^2L }{M \pi^2 D^5}f(Re,\epsilon)$$
 
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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
 

Related to Tubing Pressure drops with Compressible Fluids

1. What is tubing pressure drop?

Tubing pressure drop is the decrease in pressure that occurs as a fluid flows through a tube or pipe. It is caused by friction between the fluid and the walls of the tube, as well as any changes in the direction or velocity of the fluid.

2. How is tubing pressure drop affected by compressible fluids?

Compressible fluids, such as gases, have the ability to change volume in response to changes in pressure. This means that as a compressible fluid flows through a tube, its pressure and density will change, resulting in a larger pressure drop compared to an incompressible fluid.

3. What factors affect tubing pressure drop with compressible fluids?

The main factors that affect tubing pressure drop with compressible fluids include the fluid's density, viscosity, and compressibility, as well as the tube's diameter, length, and surface roughness. The flow rate and temperature of the fluid can also have an impact.

4. How is tubing pressure drop calculated for compressible fluids?

The calculation of tubing pressure drop for compressible fluids involves using equations that take into account the aforementioned factors, as well as the type of flow (e.g. laminar or turbulent) and any fittings or obstructions in the tube. These calculations can be complex and are typically performed using specialized software or tables.

5. How can tubing pressure drop be minimized for compressible fluids?

To minimize tubing pressure drop for compressible fluids, it is important to select a tube with a larger diameter, smooth surface, and minimal obstructions. Additionally, controlling the flow rate and temperature of the fluid can help reduce pressure drop. Proper maintenance and cleaning of the tube can also help prevent buildup and reduce friction. In some cases, using a compressor or pump can increase the pressure of the fluid and decrease the pressure drop.

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