I was thinking less from a flow point of view (and restrictions) but more for temperatures and increasing radiator performance. I would need to punch up some numbers but two rads in parallel should have a large increase in heat dissipative capacity as they have a higher dt but no loss in performance due to lower flow.
I was thinking of doing something similar to your java app in flash (to learn the program /programming language it uses properly) but the maths got hard. I tried a more general approach to yours using the algebraic riccati equations (solution to a symmetric quadric matrix Ax^2+ Bx+C=0) which assumed that everything could be modeled as a quadratic head loss (or head creator in a pumps case). After thinking about it im not sure about limiting myself to only quadratic models of head losses though. Also my (crappy) programming ran into a brick wall with all the look ups need for wattage and stuff. I was going to fall back and use the approach you were using (which is i assume to use a 3 way splitter in which Q is conserved and then use dp = f(v) where you look up f(v) and use and iterative loop to solve).
In answer to your questions and problems on your page.
Pumps in “manifolds” is an intrinsic problem with your approach. A test to make sure that a pump cannot pump water backwards would help. I need to think and punch numbers but im not sure if using the extended Bernoulli (which is an approximation after all) can model the way you want. Water may flow backwards in the manifold simply recalculating around the parallel loop from the pump entrance to exit without flowing in the overall loop. Either way there are major problems with having pumps in parallel paths.
For some loops you may not be able calculate an answer.
Correction of source data for fittings is easy as pie. Head loss because of fitting is about as easy to calculate as your going to get. All you need is the actual pump fittings that go in an out.
Derivation of losses for pipe diameter changes is easy. I cant remember it off the top of my head but the analytical solution (doesn’t include stuff like recirculation losses) uses conservation of mass flow then energy loss being from momentum being conserved. I have the derivation somewhere. The loss is of the order v^2.
Extrapolation good. The problem is extrapolate to what. I think for the purposes of the program a simple dp=k*v^2 is good enough but a lot of work needs to be done to establish this fact. Some turbulent losses work on v^4 scales for example and some due to the differential nature of the navier stokes equations are going to be logarithmic. The flow in channels of a waterblock is going to be all turbulence and probably all boundary layer this makes things tricky. It may also be temperature dependent. I would like at sometime to run a DIY blocks for whom I have dxf files through CFD to see what happens.
For pipe friction factor I had always planned on using for my proggie the darcy friction factor for the pipe friction instead of hazel williams which posed problems in getting a stable solution as its has to be iterative (checking lamina or turbulent flow etc). I think darcy is better as it can easily model water cooling friction factors (can calculate data instead of getting hold of empirical results) and is more accurate especially if some viscosity numbers for actual water cooling fluids. Plus I was planning on including some corrections for bends in pipes (you know the vector of where the pipes are coming out so you can work out a “good route” between them) and it would be more accurate to use darcy for this, though using the shallow bend hazel Williams factor might be good also.
If you would like pressure drop calcs for a pipe I could send you a subroutine with ease.
Head loss for various stuff should be easily available. I can get your weight in empirical data if you want. Doing stuff from first principals is a little hard but its gold standard empirical data so cant complain.
The heat inputs stuff should be easy with look ups (if your not a crap programmer like me). The pump stuff I was just going to model as a singular heat input of X watts. Which I think is okay heat is mostly transferred from the pump to the water instead of the air. Could use an insulated pump to test this.
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