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14 Nov 2008

Fluid dynamics modelling question

I'm trying to model the pressures and motions in this system I'm working with. Imagine two cylindrical pistons connected to each other with some tube that allows fluid flow. Now imagine the heads of the pistons are connected to each other with a bar that rests at its midpoint on a vertical support that allows levering side to side, such that when piston head 1 moves down, piston head 2 moves up and equal distance. Now, I'm working with a (theoretically) incompressible, dilatant fluid, although it being dilatant I don't think is pertinent to my question, just FYI I guess. My question is, assuming that the fluid levels in each piston reach the heads (such that no compressible air is present), when piston head 1 moves down, how do I model the response in piston head 2? I'm sure there are a few differential equations in here, but it's been a while since that class 😀

The way I'm seeing it, is that as piston head 1 moves down, piston head 2 receives force in the upward direction due to fluid flow into piston 2, and piston 2 contributes to piston head 1 moving downward due piston head 2's upward motion. Shouldn't those two force contributions essentially cancel each other out, and wouldn't I be left with just piston head 1 moving downward, with rate limited by the shear stress of the fluid through the tube? Would I just need to model the resulting motion from the delta(F) (and subsequently delta(P)) on the two piston heads, and that one piston would just mimic the other? I'm getting caught up in the coupling here...

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