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I am trying to model a prototype resembling a section of vein channels. I am wondering if there are some basic rules for such fluid channels, for instance when a vein splits in two capillaries, is there some quantity conserved (area of the section or else)? I observed that with my current design (which is done by hand just imitating pictures I saw) the fluid I pump in tends to flow very fast in some channels and very slow in others. I'd want some sort of common front to advance. I am a mathematician and have ZERO education on fluid dynamics or else :) any help is much appreciated!

EDIT: I saw the comment answer and I apologise because I am not sure I will be able to formulate my question in a decent way for engineers :). I am printing my model in rigid plastic and the application is scanning its section in the X-ray CT lab. Here's a couple of pics that I hope will clarify my position: My current prototype

I need to scan the section

The idea is to have a viscous fluid (honey+iodine) put in the top "funnel" and start measuring in the CT lab, observing it flowing into the bottom channels. Observe that the channels have a rectangular section.

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  • $\begingroup$ You question has has been nominated for closure as some members are unclear of what you're asking. Some context would help your question. Is your main concern the network of channels or the fluid flow parameters in the channels, or both? Also, is your network of vein type channels composed of rigid walled channels (like pipes) or flexible (like veins in an animal/plant)? Also, are your channels closed (like tubes) or open (like canals/rivers)? Are your channels of uniform or varying x-section between bifurcations/joins? $\endgroup$
    – Fred
    Feb 11 '16 at 13:53
  • $\begingroup$ On the lower right picture, the fluid is enteringthe network from the left. Can you mark where the fluid leaves the network, and the flow conditions you want to achieve? $\endgroup$
    – mart
    Feb 14 '16 at 20:32
  • $\begingroup$ There is no planned exit. As you can see from the top picture, the fluid may overflow from the top at most. This was done because it may be useful also to take scans when the liquid has settled and filled the channels. $\endgroup$ Feb 15 '16 at 12:42
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If I understand your question correctly, you are designing and building a small network of pipes or the like that involves different diameters. You have little experience with this kind of design work. You are looking for rough heuristics to help you get started. I assume pipe flow, not open channels.

... when a vein splits in two capillaries, is there some quantity conserved (area of the section or else)?

This is actually a good idea. In a first approximation, if you conserve area flow velocity will be equal in all branches.

I'd advise you however to look at and understand the Darcy-Weisbach equation. Looks daunting, but its probably less work to understand than to build endless prototypes. The upshot is that specific pressure loss (pressure / length) depends strongly on flow velocity, but not only - so our first approximation is wrong but maybe useful.

The next thing you need to understand is pipe network analysis. Then you can build a simulated model of your system.

Give that you say "ZERO education on fluid dynamics" I'll throw in a link on how to read pump and system curves.

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